This appeal arose out of a complex, lengthy, and bitterly contested antitrust suit. Plaintiffs-appellants, independent California rice farmers, appeal the district court’s March 1994 judgment for defendants-appel-lees, a rice exporter, its president, and its lawyer. That judgment was based in part on a jury verdict for defendants as to plaintiffs’ Section 2 Sherman Act conspiracy claims and violations of the California Unfair Practices Act, and in part on the district court’s judgment as a matter of law for defendants as to plaintiffs’ claims for conspiracy to restrain trade in violation of Section 1 of the Sherman Act and California’s Cartwright Act.
The litigants raise numerous procedural and substantive issues on appeal. Defendants insist plaintiffs lack standing to maintain this antitrust action. Plaintiffs allege several instances of trial error, challenge the district court’s rulings involving antitrust immunity under the Noerr-Pennington doctrine, and argue that it was error for the district court to enter judgment as a matter of law as to the restraint of trade claims on. which the jury was divided. Plaintiffs also appeal the district court’s post-trial award to defendants of nearly $100,000 in costs.
We have jurisdiction pursuant to 28 U.S.C. § 1291.1
*1500FACTUAL AND PROCEDURAL HISTORY
1. The Rice Industry
A.Crisis in the World Rice Market
The marketplace can be a harsh teacher and it certainly was here. These events have their beginning in 1980, when a worldwide rice shortage drove prices on the international rice market to record highs. The following year, many rice farmers reacted to these abnormally high prices by substantially increasing rice production. This, in turn, resulted in an oversupply of rice and the collapse of world rice prices in 1981.
The 1980 shortage was especially severe in the Republic of Korea (“Korea”), which had experienced a domestic rice crop failure as a consequence of bad weather. To meet domestic demand, Korea needed to import large quantities of rice. In light of the Korean shortage, the United States agreed to the export of one million tons of rice from Japan to Korea. That decision invoked an emergency exception to a U.S.-Japan bilateral agreement, executed earlier in 1980, which prohibited Japan from “dumping” rice on markets to which U.S. companies exported rice.
In exchange for this exemption, Korea committed in early 1981 to the purchase of certain rice quotas from the United States: (1) 200,000 tons of 1980 U.S. Southern short grain rice,2 (2) the remaining balance of the 1980 California rice crop,3 and (3) 500,000 tons of the 1981 California rice crop.
The current litigation was precipitated by the alleged actions of certain participants in the California rice market in responding to Korea’s commitment to purchase rice from United States producers. The response transpired against a backdrop of continuing decline in rice prices occasioned by the 1981 world rice surplus.
B. The Parties
Plaintiffs are nineteen4 independent California rice farmers who grow California rice, harvest it in “rough” or “paddy” form, and sell it to a handful of independent rice mills: Pacific International Rice Mills, Inc. (“PIR-MI”), Comet Rice of California, and Grosjean Rice Milling.5 The independent rice mills then null the rice and sell it in milled form. The independent rice growers generally sell paddy rice to the independent mills through “participation contracts,” under which they share profits from the sale of milled rice.
The original defendants in this action included two cooperatives of rice farmers, Farmers Rice Cooperative (“FRC”) and Rice Growers Association of California (“RGA”).6 These cooperatives grow, mill, and sell rice. Plaintiffs allege that these cooperatives represent a vertical integration of all phases of rice production. Three defendants are still party to the action: Connell Rice & Sugar Company (“Connell Rice”), the export marketing agent for cooperatives RGA and FRC; Grover Connell, president of Connell Rice; and Joseph L. Alioto, a partner in the San Francisco law firm of Alioto & Alioto, past president of RGA, and sometime legal counsel to RGA, FRC, and Connell Rice.
C. Rice Sales to Korea
1. 1981-82 rice sales to Korea pursuant to Korea’s commitment to purchase 200,-000 tons of 1980 U.S. Southern short grain rice
On December 12, 1980, defendant Connell Rice bid to sell Southern rice at $515 per ton to Korea. Connell Rice was subsequently underbid, however, by an independent rice mill — PIRMI—which won the contract to *1501supply Korea with 200,000 tons of 1980 Southern rice at $449.50 per ton. A formal contract was executed January 23, 1981 by PIRMI and the Office of Supply of the Republic of Korea (“OSROK”), the Korean government agency responsible for the purchase of rice.
When it came time to perform, PIRMI had insufficient supplies to deliver on the entire 200,000 tons. PIRMI officials blamed this on two things: (1) Connell Rice’s purchase of Southern rice (thereby depleting the overall supply of such rice), and (2) Connell Rice’s subsequent sale of that rice to OSROK, both occurring just a few days after PIRMI’s January 23, 1981 contract with OSROK. On February 3, 1981, OSROK confirmed that it had purchased 120,000 tons of Southern rice from Connell Rice at $449.90 per ton. PIR-MI was able to deliver only 105,000 tons of Southern rice to Korea.
To make up for the shortfall on its promised delivery of Southern rice to OSROK, PIRMI offered to substitute 1981 California rice for the Southern rice. By letter of January 22, 1982, PIRMI’s president offered to sell OSROK 70,000 tons of California rice at $349.90 per ton, a decrease in price of $100 per ton from the Southern rice PIRMI was unable to obtain.
On January 25, 1982, while PIRMI was still discussing this substitution with OS-ROK, Connell Rice, aware that OSROK was negotiating for the purchase of California rice, offered.to sell 500,000 tons of California rice at $260 per ton.7
Plaintiffs later alleged in their lawsuit that defendants had conspired to depress the price of California rice, and that this conspiracy was part of a larger, prolonged effort to drive both the independent farmers and the independent mills out of business. They claimed they were damaged by defendants’ alleged predatory pricing because this pricing reduced the return they earned on the paddy rice they sold to the independent mills for export to Korea. •
At trial, plaintiffs attempted to establish that $260 per ton was a predatorily low price. A PIRMI official and plaintiffs’ expert witness, an agricultural economist, testified that ■ $260 was “below the [average] variable cost [of production].” Defendant Grover Connell testified, however, that $260 was a competitive price, given the oversupply in the world market at the time.
Simultaneous with its $260 bid, Connell Rice made other efforts to sell California rice to Korea. First, Connell Rice’s attorney, defendant Joseph Alioto, sent several telegrams on Connell Rice’s behalf to OSROK and other Korean officials, including the Korean ambassador to the United States, “requesting] the opportunity to bid or negotiate on the competitive merits of the impending sale of American rice to Korea.” Alioto’s telegrams also mentioned “disturbing reports that other American suppliers are attempting to persuade you to exclude Connell [Rice] from the business and to deny it even the opportunity to bid or negotiate competitively on the forthcoming sale,” and warned that such conduct would be actionable under U.S. antitrust laws.
Second, Connell Rice president Grover Connell accused Korean government officials of having accepted bribes from PIRMI in exchange for rice sale contracts. Such statements sparked investigations of commercial bribery by both the U.S. State Department and the Korean National Assembly. When State Department officials asked Grover Connell why he suspected bribery, he cited the difference between the price PIRMI negotiated with OSROK in early 1981 and the dramatically lower prices Connell Rice had bid, explaining that he inferred bribery from OSROK’s alleged “overpayment” to PIRMI.8 No evidence of bribery was ever found, however.
*1502PIRMI eventually negotiated a contract with OSROK for the sale of 70,000 tons of California rice to substitute for the undelivered Southern rice. The price was $280 per ton, a sharp reduction in price from PIRMI’s original offer of $449.90 per ton. PIRMI officials testified at trial that the substitution of California rice at $280 per ton for Southern rice at $449.90 per ton caused them losses of $12 million.
2. 1981-82 rice sales to Korea in connection with Korea’s commitment to purchase 500,000 tons of 1980 California rice
Korea counted the 70,000 tons of California rice it bought from PIRMI toward its commitment to purchase 500,000 tons of the 1981 California rice crop; it also counted a 60,000-ton purchase from Agroprom, a Swiss company, toward that quota. By March 1982, therefore, Korea needed to purchase an additional 370,000 tons to meet its commitment.
In March 1982, OSROK solicited bids on its remaining 370,000 ton commitment. Con-nell Rice offered to supply all 370,000 tons at-$249 per ton; shortly thereafter, Connell Rice lowered its bid to $246 per ton. Independent rice mill Comet later matched Con-nell Rice’s $246 per ton offer. At trial, plaintiffs attempted to prove that Connell Rice’s price was below the independent farmers’ cost of production and therefore was a predatory price.
In May 1982, Comet was awarded the entire contract to supply Korea with rice at $246 per ton. However, Comet had only 120,000 tons of California rice available to sell. Between May and November of 1982, Comet negotiated with rice cooperatives RGA and FRC in an attempt to purchase the 250,000 tons it needed to meet its commitment to Korea. Comet and the cooperatives were never able to agree on a price. Plaintiffs later alleged Connell Rice and the cooperatives had boycotted and refused to deal with Comet, while defendants insisted that Comet simply rejected the cooperatives’ repeated offers. Comet eventually satisfied the contract by renegotiating with Korea to substitute 1982 California rice.
II. Origins of the Litigation
In late 1985, plaintiffs brought federal antitrust claims and related state-law claims against several defendants: Connell Rice, Grover Connell, cooperatives FRC and RGA, Joseph Alioto, and James Robert Errecarte, former CEO of RGA.9
Plaintiffs’ first cause of action was for monopoly, attempted monopoly, and conspiracy to monopolize in violation of Section 2 of the Sherman Act, 15 U.S.C. § 2. Plaintiffs alleged rice cooperatives FRC and RGA were vertically integrated operations that had conspired with the other defendants to monopolize all three markets in the California rice industry: the California paddy rice market, the market for the milling of California rice, and the California milled rice market.
First, plaintiffs alleged that FRC and RGA “acting jointly as a combination controlled over seventy-five per cent of all paddy rice grown in California” while the independent farmers controlled the remaining twenty-five per cent. They alleged that the two rice milling cooperatives operated a monopoly or, in the alternative, a combination posing a “dangerous probability” of achieving a monopoly.
Second, plaintiffs alleged that FRC and RGA “acting jointly as a combination controlled over seventy-five per cent of all milled California rice,” while the three independent rice mills—Comet, PIRMI, and Grosjean—divided the remaining twenty-five per cent of the milled rice market. Plaintiffs alleged FRC and RGA were, together, a monopoly or, in the alternative, a combination with a “dangerous probability” of achieving a monopoly. Third, plaintiffs alleged that FRC and RGA used their monopoly power in paddy rice and in milled rice to control the intervening market: the market for rice milling, the process whereby paddy rice is converted into milled rice. Finally, plaintiffs alleged that Connell Rice controlled over *1503ninety per cent of the submarket for the export of California rice to Korea during the period 1968 through 1981, and alleged that this degree of control constituted a monopoly. Connell Rice was also alleged to have a monopoly in the market for the export of California rice under the P.L. 480 export scheme.
Also contained in plaintiffs’ first cause of action was the claim that defendants had a contract, combination, or conspiracy in restraint of trade in violation of Section 1 of the Sherman Act, 15 U.S.C. § 1. Plaintiffs alleged a far-reaching, decades-long conspiracy among defendants to “eliminate independent rice purchasers and independent rice mills from the market for nulled California rice and to eliminate independent growers of California paddy rice by driving [the] growers from the market or forcing them to become members of [one of the rice cooperatives].”
In support of their claim, the independent rice farmers alleged a long history of anti-competitive behavior by the rice cooperatives. They alleged the cooperatives had acquired several independent rice mills over the years; had used their alleged monopoly power to manipulate prices for paddy rice and milled rice with the aim of eliminating the independent farmers and mills; had refused to sell competitively priced paddy rice to the independent mills; had paid independent rice farmers diseriminatorily high prices to prevent the sale of paddy rice to the independent mills; had refused to sell competitively priced milled rice to actual or potential customers of the independent mills; had charged predatorily low prices for milled rice to prevent the independent rice mills from selling their milled rice; and had excluded independent mills from California port facilities. Finally, with respect to the California rice export market to Korea, the independent rice farmers alleged the rice cooperatives had conspired to sell only the cooperatives’ rice to Korea and had bribed Korean officials to obtain a monopoly in the export market to Korea.
Defendants-appellees Connell Rice, Grover Connell, and Joseph Alioto, it was further alleged, had all acted “in concert” with FRC and RGA in their alleged efforts to eliminate the independent rice mills and independent rice farmers. Plaintiffs accused Alioto of having masterminded the alleged anticompet-itive activities.10
A. Allegations of Anticompetitive Activities in 1981-82
Plaintiffs alleged that by 1981, defendants had succeeded in eliminating every major independent rice mill in California except PIRMI and Comet, and in that year launched a final concerted effort to drive these last two independent mills out of the rice business and to eliminate all independent rice farmers by either driving them out of business or forcing them to join the rice cooperatives.
Plaintiffs alleged, first, that defendants used their monopoly power to drive down the price of California paddy rice in ■ 1981 and 1982. Second, plaintiffs alleged that defendants boycotted independent rice mill Comet during this period by refusing to sell it paddy or milled rice. Finally, plaintiffs alleged defendants used their monopoly power to drive down the price of California milled rice from over $500 in 1981 to under $250 in 1982. Plaintiffs alleged that defendants’ activities “destroy[ed] PIRMI” and paved the way for RGA’s attempted acquisition of PIRMI’s mill operations. That acquisitioh was later enjoined by a district court order.11 In addi*1504tion, plaintiffs alleged that defendants had instituted “sham litigation” during this period. They claimed Connell Rice, Grover Con-nell, and Joseph Alioto had commenced lawsuits that they “knew to be without merit and which were prosecuted solely for the purpose of injuring competition.” Plaintiffs also alleged defendants engaged in “false testimony, false submissions to government agencies and threats to government officials” as well as threats against competitors, in furtherance of their alleged conspiracy.
B. Injuries Alleged and Damages Sought
The independent rice farmers alleged that defendants’ actions caused them harm by: (1) restraining trade in the markets for California paddy rice, California milled rice, and the milling of California rice; (2) eliminating independent mills, thereby restricting the independent farmers’ ability to sell paddy rice and reducing the number of mills selling California milled rice; (3) denying purchasers of California paddy rice and California milled rice of “the benefits of open and unrestricted competition;” and (4) causing plaintiff independent farmers “monetary injury to their business and property” by causing pre-datorily low prices for California paddy rice and California milled rice. Plaintiffs sought injunctive relief and treble damages of an unspecified amount.12
III. The Trial
After several years of pre-trial skirmishes and reassignment to several district judges, the suit finally went to a jury trial before Judge Caulfield in 1992. Although defendants had filed various counterclaims,13 the district court severed plaintiffs’ claims from defendants’ counterclaims, in view of the complexity of the litigation: The liability phase of the trial lasted approximately seven weeks, running from March 23 to May 14, 1992. The jury rendered its verdict on May 29, 1992. The following are aspects of the trial that are relevant to this appeal.
A. Time Limit
Over plaintiffs’ pretrial objection, the district court imposed a time limit on the trial. For the liability phase of the trial, the court allowed each side forty hours for direct and cross-examination, and allowed each party two hours for opening statements, two hours for closing arguments, and two-and-a-half hours for additional “commentary” to the jury. During the trial, the court granted each side six hours of supplemental time, after asking the lawyers for each side how much additional time they would need to finish trying the case.
B. Evidentiary Rulings
1. Admission of Defense Expert Testimony
In April 1991, during the discovery phase of the litigation, Chief Judge Henderson issued an order prohibiting defendants from introducing any expert testimony at trial. Judge Henderson’s order described a series of discovery abuses by defendants. Defendants failed to respond to plaintiffs’ July 1988 expert witness interrogatories. Plaintiffs moved twice to compel responses, and hearings were held before Magistrate Trumbull *1505in October and November 1988. On November 10, 1988, Magistrate Trumbull ordered defendants to “produce the information regarding their expert witness on the same day as they decide on their expert.” Defendants identified Dr. Merrill Bateman as their expert witness in Defendants’ December 2, 1988 Pretrial Conference Statement. However, it was not until two years later, in their December 3, 1990 Supplemental Responses to Plaintiffs’ First Set of Interrogatories, that defendants furnished plaintiffs’ counsel' with the information they had requested about defendants’ expert. On the basis of defendants’ two-year delay in complying with Magistrate Trumbull’s discovery order and their earlier discovery delays, Judge Henderson granted plaintiffs’ Motion to Preclude Defendants from Adducing Expert Testimony. The order was a sanction for defendants’ repeated discovery abuses. Fed. R.Civ.P. 37.
The parties’ subsequent pre-trial conduct was consistent with Judge Henderson’s order. Defendants’ March 1992 pre-trial witness list made no mention of Dr. Bateman, and plaintiffs never deposed Dr. Bateman.
At trial, however, defendants sought to call Dr. Bateman as a “rebuttal expert,” arguing that Dr. Bateman authored one of the reports plaintiffs’ expert, Dr. Ronald D. Knut-son, had analyzed during his testimony. Plaintiffs objected, arguing that Dr. Bateman was the very expert Judge Henderson had excluded in his order barring defense expert testimony, and that they had been deprived of the opportunity to conduct discovery of defendants’ expert, having learned only the night before of defendants’ plan to call Dr. Bateman as a rebuttal expert.
Despite Judge Henderson’s earlier order prohibiting defense expert testimony, Judge Caulfield allowed Dr. Bateman to testify, albeit for one purpose only: “to speak about how his report was used” by plaintiffs’ expert.
2. Admission of Defendants’ Summary Exhibits
During trial, the district court admitted two summary exhibits at issue in this appeal: Defense Exhibit 529A and 781A. Defense Exhibit 529A was a graph comparing a price-to-loan ratio with a stocks-to-use ratio. Defense Exhibit 781A summarized Thai rice prices and adjusted California rice prices, and summarized defendants’ expert’s findings based on that price information. .
C. Application of the Noerr-Penning-ton Doctrine
Among the allegations underlying plaintiffs’ antitrust claims were plaintiffs’ allegations that defendants had initiated various “sham” lawsuits and “sham” administrative proceedings as part of a conspiracy to monopolize and to restrain trade in the various rice markets alleged. During trial, the district court ruled that as a matter of law, defendants’ actions were not objectively baseless and therefore did not fall within the “sham” exception to the Noerr-Pennington doctrine of antitrust immunity for private efforts to influence government action. Because it concluded that defendants’ actions were protected by the Noerr-Pennington doctrine, the district court excluded some evidence of the allegedly “sham” lawsuits, although it did admit some evidence concerning defendants’ alleged anticompetitive conspiracy.
D. Jury Instructions on Service of Subpoenas on Foreign Government Officials
Plaintiffs alleged Joseph Alioto mailed subpoenas to the Korean ambassador to the United States and to a Korean consular official in New York as part of the alleged “sham” litigation. Both subpoenas were quashed by the State Department. At trial, plaintiffs requested that the district court instruct the jury on aspects of the law governing the service of subpoenas on foreign officials. Instead of reading plaintiffs’ proposed instructions, however, the district court read provisions of the Vienna Convention, 23 U.S.T. 3227 (April 18, 1961), the Foreign Sovereign Immunities Act, 28 U.S.C. §§ 1602-11, and certain Federal Rules of Civil Procedure.
*1506E. Verdict
On May 29, 1992, following an eight-week trial before Judge Caulfield, the jury returned a special verdict for defendants on plaintiffs’ claims of conspiracy to monopolize under Section 2 of the Sherman Act and the California Unfair Practices Act. The jury was unable to reach a unanimous verdict, however, as to plaintiffs’ claims for conspiracy in restraint of trade under Section 1 of the Sherman Act and California’s Cartwright Act.
IV. Post-Trial Proceedings
A. Directed Verdict for Defendants on Plaintiffs’ Restraint of Trade Claims
Eighteen months after the jury verdict, Judge Caulfield entered judgment as a matter of law as to plaintiffs’ claims that defendants had conspired to restrain trade in violation of Section 1 of the Sherman Act and the California Cartwright Act. Amarel v. Connel, 1994-1 Trade Cases ¶ 70,632, 1993 WL 515885 (N.D.Cal. Nov.30, 1993). In entering judgment for defendants on plaintiffs’ remaining claims, the district court held that the jury verdict for defendants as to plaintiffs’ monopolization claims precluded plaintiffs’ restraint of trade claims, since “[pjlain-tiffs maintained in their amended complaint and in their presentation to the jury that it was defendants’ attempt to conspire to monopolize that allegedly restrained trade in the relevant market.” Amarel, 1993 WL 515885, * 2.
B. Directed Verdict for Defendant Joseph Alioto
After trial, defendant Joseph Alioto moved for judgment as a matter of law on grounds of attorney immunity from antitrust liability. Judge Caulfield granted the motion, finding in the record “no legally sufficient evidentia-ry basis” to support plaintiffs’ antitrust claims against Alioto. Amarel v. Connel, 1994-1 Trade Cases ¶ 70,632, 1993 WL 515885 (N.D.Cal. Nov. 30,1993).
V. The District Court’s Post-Judgment Award of Copying Costs
Following Judge Caulfield’s entry of judgment for defendants on all plaintiffs’ claims, defendants applied for an award of costs. In December 1993, they filed two bills of costs totalling $227,001.08: a bill of $170,446.66 for Connell Rice and a bill of $56,554.42 for Joseph Alioto.
Pending plaintiffs’ appeal, Judge Caulfield stayed all proceedings, including the taxation of costs: After Judge Caulfield resigned, the ease was reassigned to Judge Walker. Although plaintiffs contended the taxation of costs would be premature in view of the pending counterclaims that remained to be tried, Judge Walker directed the clerk to tax costs. The clerk taxed plaintiffs a total of $129,695.01 in costs: $108,853.01 of the costs sought by Connell Rice and $20,842 of the costs sought by Alioto.
Both sides moved for reconsideration of the award. The day before the reconsideration hearing, Judge Walker entered an order directing defendants to present further documentation to support their claimed costs. At the May 5, 1995 hearing, counsel for defendants presented two affidavits and exhibits as further evidence of defendants’ costs. Judge Walker ruled at the close of the three-hour hearing, awarding defendants $96,-441.65 in costs: $75,599.65 for Connell Rice and $20,842 for Joseph Alioto. Plaintiffs timely appealed the district court’s award of costs, and that appeal was consolidated with, plaintiffs’ appeal on the merits.
ANALYSIS
I. Standing
On appeal, defendants renew14 their contention that plaintiffs lack standing to main-*1507thin this antitrust action. They claim, first, that plaintiffs' alleged injury is "not the type of injury the antitrust laws were intended to prevent" and, second, that plaintiffs' alleged injury "is derivative and indirect" and therefore not cognizable under the antitrust statutes.
Because antitrust standing is a question of law, we review the issue de novo. Exhibitors' Service, Inc. v. American Mnlti-Cinema, Inc., 788 F.2d 574, 578 n. 4 (9th Cir.1986). The issue of antitrust standing may be raised at any stage of litigation. R.C. Dick Geothermal Corp. v. Thermogenics, Inc., 890 F.2d 139, 145 (9th Cir.1989) (en banc). In R.C Dick Geothermal, we explained that "[w]henever it appears that [standing] has not been established and has not been conceded, an element necessary for the plaintiff to prevail is lacking." Id. (citing P. Areeda & H. Hovenkamp, Antitrust Law ¶ 335.1b (Supp.1987)).
Section 4 of the Clayton Act allows recovery of treble damages by "any person who shall be injured in his business or property by reason of anything forbidden in the antitrust laws." 15 U.S.C. § 15(a). The language of this provision is very broad and, "[dead literally, `could afford relief to all persons whose injuries are causally related to an antitrust violation.'" Lucas v. Bechtel Corp., 800 F.2d 839, 843 (9th Cir.1986) (citation omitted). It is well-settled, however, that despite the sweeping language of Section 4, "`Congress did not intend to provide a private remedy for all injuries that might conceivably be traced to an antitrust violation.'" Bubar v. Ampco Foods, Inc., 752 F.2d 445, 448 (9th Cir.) (citing Blue Shield of Virginia v. McCready, 457 U.S. 465, 472-80, 102 S.Ct. 2540, 2544-49, 73 L.Ed.2d 149 (1982)), cert. denied, 472 U.S. 1018, 105 S.Ct. 3481, 87 L.Ed.2d 616 (1985). As the Supreme Court has explained, "[h]arm to the antitrust plaintiff is sufficient to satisfy the constitutional standing requirement of injury in fact, but the court must make a further determination whether the plaintiff is a proper party to bring a private antitrust action." Associated Gen. Contractors of California, Inc. v. California State Council of Carpenters, 459 U.S. 519, 535, 103 S.Ct. 897, 907, 74 L.Ed.2d 723 (1983). Courts have developed the doctrine of antitrust standing to determine the "class of persons entitled to obtain [Section 4] damages." Los Angeles Memorial Coliseum Comm'n v. National Football League, 791 F.2d 1356, 1363 (9th Cir.1986).
The Supreme Court has identified several factors courts are to consider in determining whether a plaintiff, who has suffered an injury which bears a causal connection to the alleged antitrust violation, also satisfies the more demanding standard for antitrust standing. These factors are:
(1) the nature of the plaintiffs alleged injury; that is, whether it was the type the antitrust laws were intended to forestall;
(2) the directness of the injury;
(3) the speculative measure of the harm;
(4) the risk of duplicative recovery; and
(5) the complexity in apportioning damages.
Associated Gen. Contractors, 459 U.S. at 535, 103 S.Ct. at 907.
Ai~titrust standing involves a case-by-case analysis of "the plaintiffs harm, the alleged wrongdoing by the defendants, and the relationship between them." Id. We have held that in examining the factors set forth in Associated Gen. Contractors, "[n]o single factor is decisive. The court must balance the factors." R.C. Dick Geothermal, 890 F.2d at 146 (citing Los Angeles Coliseum Comm'n, 791 F.2d at 1363). We have also "reject[ed] any [] implication [thatb a favorable finding in each and every one of the [Associated Gem. Contractors I factors is a necessary precondition to a finding of antitrust standing." Los Angeles Memorial Coliseum Comm'n, 791 F.2d at 1363. We have said, however, that the nature of the plaintiffs alleged injury is of "tremendous significance" in determining whether a plaintiff has antitrust standing. Bhan v. NME Hospitals, Inc., 772 F.2d 1467, 1470 n. 3 (9th Cir.1985). With these factors in mind, we address defendants' challenges to plaintiffs' standing.
*1508A. The Nature of Plaintiffs' Alleged Injury
Defendants' first argument is that plaintiffs' "claimed injury is not of the type the antitrust laws were intended to prevent." Undergirding this argument is defendants' characterization of plaintiffs' alleged injury as the failure of PIRMI and Comet "to get higher prices due to the cooperative's competitive, nonpredatory quotes."
It is well-settled that a plaintiff "must prove the existence of `antitrust injury, which is to say injury of the type the antitrust laws were intended to prevent and that flows from that which makes defendants' acts unlawful." Atlantic Richfield Co. v. USA Petroleum Co., 495 U.S. 328, 334, 110 S.Ct. 1884, 1889, 109 L.Ed.2d 333 (1990) (quoting Brunswick Corp. v. Pueblo Bowt-O-Mat, Inc., 429 U.S. 477, 489, 97 S.Ct. 690, 697, 50 L.Ed.2d 701 (1977)). An injury "will not qualify as `antitrust injury' unless it is attributable to an anti-competitive aspect of the practice under scrutiny, since it is inimical to [the antitrust laws] to award damages for losses stemming from continued competition." Atlantic Richfield, 495 U.S. at 334, 110 S.Ct. at 1889 (internal quotations and citations omitted). As a corollary to the requirement that "the alleged injury be related to anti-competitive behavior," we require that "the injured party be a participant in the same market as the alleged malefactors." Bhan, 772 F.2d at 1470 (citing Associated Gen. Contractors, 459 U.S. at 538-39, 103 S.Ct. at 908-09).
In considering whether plaintiffs' alleged injuries are "of the type the antitrust laws were intended to prevent" and "flow[] from that which makes defendants' acts unlawful," Atlantic Richfield, 495 U.S. at 334, 110 S.Ct. at 1889 (1990) (citation omitted), we begin by noting that plaintiffs' allegations of injury are far broader than defendants describe. Plaintiffs' complaint contained broad, albeit sometimes vague, allegations of a decades-long conspiracy to eliminate both plaintiffs, the independent farmers, and the independent rice mills, and to monopolize all phases of rice production. Alleged participants in the conspiracy were the rice cooperatives-which plaintiffs alleged are vertically integrated operations engaged in every stage of rice production-and various other parties, including defendants Coimell Rice, Grover Connell, and Joseph Alioto. The complaint alleges that the plaintiff rice farmers are, in effect, competitors of the vertically integrated rice cooperatives, since the cooperatives compete at multiple levels of rice production.
Additionally, plaintiffs' complaint contains specific allegations as to defendants' conduct between 1980 and 1982. First, plaintiffs alleged that defendants engaged in predatory pricing during 1981 and 1982, and plaintiffs introduced evidence at trial that defendants' prices were below defendants' cost of production and therefore predatory. Such predatory pricing, alleged plaintiffs, harmed them directly because it depressed the market in which they sold their rice. Second, plaintiffs alleged that defendants engaged in a lengthy boycott by refusing to sell rice to Comet. This behavior allegedly harmed plaintiffs because it threatened to eliminate one of two remaining independent mills through which plaintiffs sold their paddy rice.
We consider the nature of plaintiffs' alleged injury in the context of the antitrust standing doctrine.
Losses a competitor suffers as a result of predatory pricing is a form of antitrust injury because "predatory pricing has the requisite anticompetitive effect" against competitors. Atlantic Richfield, 495 U.S. at 339, 110 S.Ct. at 1892 (1990) (holding plaintiff suffered no injury where it lost sales to a competitor charging nonpredatory prices pursuant to a vertical, maximum-price-fixing scheme); accord Matsushita Electrical Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 582-83, 106 S.Ct. 1348, 1353-54, 89 L.Ed.2d 538 (1986). "[Wihen defendants engage in predatory pricing or other anticompetitive acts in an attempt to gain a monopoly, the competitor who is being driven out of the market is the party with standing." In re Air Passenger Computer Reservation Systems, 727 F.Supp. 564, 568-69 (C.D.Cal.1989); see also Philip E. Areeda and Herbert Hovenkamp, 2 Antitrust Law ¶ 373d (revised ed. 1995) ("Standing is clear when the plaintiff alleges that its rival en*1509gaged in an exclusionary practice designed to rid the market of the plaintiff... so that the defendant could maintain or create a monopoly.”) An important rationale for condemning predatory pricing “is to protect competition from improper destruction. The injured competitor fits within that rationale and therefore suffers antitrust injury.” Id.
Here, plaintiffs allege that they participated in the market for milled rice by virtue of their “participation contracts” with the independent mills, and that defendants’ alleged predatory pricing harmed them because it depressed prices below their costs. Plaintiffs introduced expert testimony at trial that Connell Rice’s prices were below plaintiffs’ average variable costs. This type of predatory pricing against a de facto competitor falls squarely within the category of antitrust injury-
Our conclusion is reinforced by previous decisions in which we have held that a competitor of an alleged attempted monopolist had standing where it was either driven out of business or suffered reduced profits because of the alleged anticompetitive acts of the attempted monopolist. See LaSalvia v. United Dairymen of Arizona, 804 F.2d 1113, 1116 (9th Cir.1986) (plaintiffs, independent dairy farmers, were competitors of dairy cooperative and therefore had standing to challenge cooperative’s alleged anticompetitive conduct in suit for attempted monopolization), cert. denied, 482 U.S. 928, 107 S.Ct. 3212, 96 L.Ed.2d 699 (1987), and William Inglis & Sons Baking Co. v. ITT Continental Baking Co., 668 F.2d 1014, 1024 (9th Cir. 1981) (antitrust suit premised on allegations that defendant used discriminatory and below-cost pricing to drive out competition from independent bakers in market for wholesale bread), cert. denied, 459 U.S. 825, 103 S.Ct. 57, 58, 74 L.Ed.2d 61 (1982).
Another form of antitrust injury is “[c]oercive activity that prevents its victims from making free choices between market alternatives.” Associated Gen. Contractors, 459 U.S. at 528, 103 S.Ct. at 903 (citation omitted). Such conduct “is inherently destructive of competitive conditions and may be condemned even without proof of its actual market effect.” Id. This category of antitrust injury includes agreements to restrain trade. Id. In this ease, plaintiffs alleged that defendants, acting in concert with the rice cooperatives, conspired to eliminate both the independent mills and the independent growers. Among the specific tactics alleged are that defendants boycotted Comet, refusing to sell it rice, in an effort to undermine Comet’s ability to sell rice to Korea.
The Supreme Court has identified the anti-competitive effects that may flow from group boycotts and concerted refusals to deal. In Northwest Wholesale Stationers, Inc. v. Pacific Stationery and Printing Co., 472 U.S. 284, 105 S.Ct. 2613, 86 L.Ed.2d 202 (1985), the Court explained that such actions may “disadvantage competitors by either directly denying or persuading or coercing suppliers or customers to deny relationships the competitors need in the competitive struggle.” In particular, such actions may “cut off access to a supply, facility, or market necessary to enable the boycotted firm to compete.” Northwest Wholesale Stationers, 472 U.S. at 294, 105 S.Ct. at 2619 (citations omitted). In this case, Connell Rice was the marketing agent for the major rice cooperatives, and allegedly refused to supply one of the sole remaining independent mills with rice. That alleged refusal to deal by defendants directly harmed the farmers by harming competition in the market for milled rice.
Defendants also oppose plaintiffs’ standing because, they assert, plaintiffs “are neither consumers nor competitors in the market claimed to have been affected by the allegedly depressed prices.” We disagree with defendants’ characterization of plaintiffs’ role in the rice industry. Plaintiffs introduced evidence that they are “competitors” in the market for milled rice because they tender paddy rice to the independent mills under “participation contracts” which entitle them to a share of profits from the sale of milled rice. Because plaintiffs thus participate in the market for milled rice, defendants’ alleged predatory pricing, if true, caused them a direct monetary loss.
Moreover, standing is appropriate in certain cases where the plaintiff is “a supplier of goods or services who can prove *1510that he suffered lower selling prices or diminished volume or other profit reduction as a result of illegal conduct by the defendants).” Areeda and Hovenkamp, Antitrust Law at ¶ 375a. Although a plaintiff normally lacks standing where that plaintiffs customer is the immediate victim of the defendant’s conduct, standing is appropriate where that plaintiff also competes with the defendant. Id.; see also Associated Gen. Contractors, 459 U.S. at 542-44, 103 S.Ct. at 910-12. The plaintiff supplier’s injury is sufficiently direct where that supplier “both competes with defendants and is their target.” Areeda and Hovenkamp, Antitrust Law at ¶ 375d.
Such was the case in Yellow Pages Cost Consultants, Inc. v. GTE Directories Corp., 951 F.2d 1158 (9th Cir.1991), cert. denied, 504 U.S. 913, 112 S.Ct. 1947, 118 L.Ed.2d 552 (1992). Plaintiffs in that case were consulting firms that advised businesses on the form and content of yellow page advertisements. They also ordered, placed and processed advertisements for those businesses. Defendants were publishers of yellow page directories, but they also advised businesses on how to use yellow page advertising. Defendants included the cost of that advice in the fees they charged for yellow page advertisements. When defendants ended their practice of allowing the consultants to order, place, and process yellow page advertisements on behalf of advertisers, that policy change induced some of plaintiffs’ customers to cancel their contracts with plaintiffs because it was less convenient to deal with both the consultants and the publishers. Plaintiffs brought suit under Section 2 of the Sherman Act, claiming that the yellow page publishers were attempting to use their alleged monopoly power in the yellow page publishing market to achieve a monopoly in the market for consultation about that market. Plaintiffs also brought a Section 1 claim, alleging that the publishers’ refusal to deal with the consultants restrained trade in the market for consultation services.
The defendant publishers claimed plaintiffs lacked standing because defendants and plaintiffs did not compete in the same market. On appeal, we held that the plaintiffs and defendants did compete in the same market: the market for advising yellow page advertisers as to the form, content, and cost of yellow page advertising. Although the plaintiffs and the defendants did not offer exactly the same service, since they offered somewhat different advice and had different fee structures, we concluded that they nonetheless competed in one important respect: both offered advice to purchasers' of yellow page advertisements. Yellow Pages Cost Consultants, 951 F.2d at 1161. We explained that for purposes of antitrust standing analysis, “the field of competition [includes] ... the group or groups of sellers who have actual or potential ability to deprive each other of significant levels of business.” Id. at 1162 (citing Thurman Industries, Inc. v. Pay ’N Pak Stores, Inc., 875 F.2d 1369, 1374 (9th Cir.1989)). We also noted that the consultants, in competing with the publishers’ advice service, served a key function as competitors: “imposing ‘an essential discipline on producers and sellers of goods to provide the consumer with a better product at a lower cost....’ ” Yellow Pages Cost Consultants, 951 F.2d at 1162 (citing United States v. Syufy Enterprises, 903 F.2d 659, 662-63 (9th Cir.1990)).
This situation is similar: plaintiffs and defendants, while not identical entities, are nonetheless competitors in a particular market segment: the market for milled rice. Here, Connell Rice, the marketing agent for the rice cooperatives, was alleged to play a key role in predatory pricing and in refusing to deal with Comet. The plaintiffs supply paddy rice to the mills, and yet they also participate in the market for milled rice because their contractual arrangement with the independent mills gives them a share of the profits from the sale of milled rice. Moreover, plaintiffs insist that defendants’ alleged conspiracy to restrain trade in various segments of the rice industry had as a central aim the elimination of the independent rice farmers. Because the plaintiffs “both com-peten with defendants and [are] them target,” they have standing. Areeda and Ho-venkamp, Antitrust Law at ¶ 375d.
The Second Circuit reached a similar result in Crimpers Promotions, Inc. v. Home Box Office, Inc., 724 F.2d 290 (2nd *1511Cir.1983). The defendants in Crimpers Promotions were two companies alleged to dominate the business of buying cable television programming from producers and selling it to cable television stations. The plaintiff organized a trade show to facilitate direct contact between producers of programming and cable television stations that purchased such programming. One of the plaintiffs goals in organizing the trade show was to reduce the producers’ and the stations’ dependence on the defendants, who allegedly dominated the market for the sale of cable television programming. The plaintiff brought an antitrust suit, alleging that the defendants attempted to ruin the trade show by pressuring producers and cable system operators and threatening to boycott producers who attended the show. The .plaintiff further alleged that defendants’ tactics succeeded in keeping attendance far below plaintiffs’ projections.
The defendants in Crimpers insisted that the plaintiff lacked standing because it did not compete directly with the defendants in the market for the purchase and sale of programming, and therefore was harmed only derivatively. The Second Circuit disagreed, concluding that the plaintiff had suffered antitrust injury because it was attempting to compete against the defendants’ alleged monopoly in the market for the purchase and sale of cable television programming, and the defendants took anticompeti-tive action against the plaintiff. The Second Circuit reasoned that “Crimpers was not just a ‘supplier’ of a competitor, ...” but instead was “endeavoring to forge a link in a chain of the sale of programming ... that would compete with defendants in their role as middlemen.” Crimpers Promotions, 724 F.2d at 294. The plaintiffs injury “was the precisely intended consequence of defendants’ boycott,” and was “inextricably intertwined with the injury the defendants sought to inflict on producers and television stations in the cable programming market.” Id. at 294-95.
Similarly, plaintiffs here allege defendants attempted to destroy competition at several levels of the rice industry. They alleged that defendants’ predatory pricing and their boycott of Comet worked anticompetitive harms similar to those alleged in Crimpers Promotions: These actions allegedly thwarted plaintiffs’ attempts to compete with defendants in the market for the export of California rice to Korea.
In arguing that plaintiffs are neither their competitors nor their consumers, defendants rely heavily on Eagle v. Star-Kist Foods, Inc., 812 F.2d 538 (9th Cir.1987). In that case, plaintiffs were crewmembers on fishing vessels who caught fish that was sold by vessel owners to tuna canneries. The crew-members attempted to bring antitrust claims against the tuna canneries for allegedly conspiring to depress tuna prices, conduct the crewmembers insisted harmed them by reducing their wages and reducing their employment opportunities. We held that the crewmembers lacked standing because they were neither consumers nor competitors in the market for tuna but instead were employees of the entities that were directly injured: the owners of the fishing vessels. Id. at 541. Although the plaintiffs in Eagle insisted that they were “sellers along with the vessel owners” because their contracts with the vessel owners allowed them a share of the profits from the sale of tuna, we disagreed. We concluded that the plaintiff crewmembers were not sellers because they had no control over the vessel or the selling price of the fish, and “because the alleged anticompetitive conduct was directed at the vessel owners, not the crewmembers of the union.” Id.
Here, in contrast, defendants’ alleged anti-competitive conduct—predatory pricing and the refusal to sell rice to Comet—was allegedly directed at both the independent farmers and the independent mills. Unlike the canneries in Eagle, which allegedly directed their anticompetitive conduct at the vessel owners, defendants in this case allegedly had a broader aim: the elimination of independent entities in the California rice industry.
B. The Directness of the Injury
Defendants next assert that plaintiffs’ alleged harm is merely “derivative and indirect” because it “derived from the lower prices supposedly obtained for milled rice as *1512a result of defendants’ acts.” We disagree. Plaintiffs allege that defendants conspired to eliminate the independent farmers and independent mills. Among the particular injuries, plaintiffs allege, are depressed earnings caused by predatorily low prices and restraint of trade in the milled rice market resulting from defendants’ refusal to supply rice to mills like Comet.
The Seventh Circuit recently addressed the “directness of the injury” requirement in the context of similar facts. In Sanner v. Board of Trade of Chicago, 62 F.3d 918 (7th Cir.1995), soybean farmers sued the Chicago Board of Trade, alleging that they were injured by a Board of Trade emergency resolution ordering holders of “long” positions in soybean futures to liquidate their positions. The Board of Trade’s resolution allegedly caused- a price decline in the soybean futures market, which caused a corresponding decline in the soybean cash market. The plaintiff farmers were sellers in the soybean cash market who‘alleged that the emergency resolution harmed them because it depressed prices in the soybean cash market. The plaintiffs also claimed that the Board of Trade resolution was an illegal restraint of trade which caused them to suffer losses in the soybean cash market.
The Seventh Circuit concluded that because the farmers were sellers in the cash market who claimed injury caused by an unlawful action in the closely related futures market, the plaintiffs had antitrust standing. Id. at 927. It also found the injury alleged sufficiently direct to form a basis for antitrust standing. The court rejected the contention that the price depression in the soybean cash market was an “indirect” result and “derivative” of the price decline in the soybean futures market because it rejected the view that there was a “disjunction ... between the cash market and the futures market for soybeans.” Id. at 928. Acknowledging that there were differences between the two markets, the Seventh Circuit concluded that the two markets were not “unrelated for the purposes of antitrust standing analysis” since a significant price change in the futures market generally correlated with a similar price change in the cash market. Id. at 929. This close relationship between the two markets offered a basis for antitrust standing: “Since [the cash market] tends to move in lockstep with [the futures market], participants in the cash market can be injured by anticompetitive acts committed in the futures market.” Id. Given the “close and continuous link” between the two markets, the injury was not too indirect and derivative to support antitrust standing. Id.
We face a strikingly similar situation here. Given the close ties between the paddy rice market and the milled rice market, and given that plaintiffs’ profits were, in part, a function of profits in the milled rice market, defendants’ alleged predatory pricing in the market for milled rice “predictably would have impacted” the price of paddy rice. Id.
Defendant’s alleged boycott also caused direct injury to plaintiffs. The Supreme Court has suggested that, for purposes of standing analysis, the antitrust laws are concerned with the effect on direct victims of boycotts and secondary boycott victims. In Blue Shield of Virginia v. McCready, 457 U.S. 465, 102 S.Ct. 2540, 73 L.Ed.2d 149 (1982), the Supreme Court- stated in dicta that a plaintiff would have antitrust standing to challenge a concerted refusal to deal where that plaintiff was sufficiently affected by that refusal. It hypothesized that if a group of psychiatrists conspired to boycott a bank until that bank stopped making loans to competing psychologists, antitrust standing would exist not only for the bank, the target of the primary boycott, but also for the psychologists, “against whom the secondary boycott was directed.” Blue Shield of Virginia, 457 U.S. at 484 n. 21, 102 S.Ct. at 2551 n. 21.
Like the defendants in Blue Shield of Virginia, the defendants here allegedly intended to have an impact on both the milled rice and paddy rice markets. Given the interdependence between independent mills and independent farmers, harming one was tantamount to harming the other. Injuring the farmers was thus “an integral [] aspect of the conspiracy alleged.” Blue Shield of Virginia, 457 U.S. at 479, 102 S.Ct. at 2548; see also Sanner, 62 F.3d at 929 (intent to harm soybean futures market could suggest intent to harm soybean cash market); Yellow Pages *1513Cost Consultants, 951 F.2d at 1162-63 (close link between defendants' actions {refusal to allow plaintiff consultants to process customer advertisements] and plaintiffs' loss of customers is sufficient for antitrust standing).
In concluding that plaintiffs were sufficiently direct victims of the defendants' alleged anticompetitive activities, we distinguish cases in which we have held injuries too indirect to support the standing of putative plaintiffs where those plaintiffs were not within the "identifiable class of persons whose self-interest would normally motivate them to vindicate the public interest in antitrust enforcement." Lucas, 800 F.2d at 845. Cf. Vinci v. Waste Management Inc., 80 F.3d 1372, 1375-76 (9th Cir.1996) (shareholder and former employee of defendant lack standing to sue defendant for alleged antitrust conspiracy); R.C. Dick Geothermal, 890 F.2d at 147 (loss of royalties for lessor of property producing geothermal steam, caused by alleged conspiracy among lessees to conceal the property's steam capacity, was indirect injury); Lucas, 800 F.2d at 844-45 (union electricians working on construction project did not suffer sufficiently direct injury from alleged conspiracy between contractor and unions to monopolize the market in design and construction of such plants; electricians' alleged. injury-depressed wages-were merely indirect consequence of alleged monopoly); Legal Economic Evaluations, Inc. v. Metropolitan Life Ins. Co., 39 F.3d 951, 954 (9th Cir.1994), cert. denied, U.S. 115 S.Ct. 1420, 131 L.Ed.2d 304 (1995) (consultants to tort plaintiffs did not suffer antitrust injury where life insurance carriers allegedly blocked tort plaintiffs from gaining access to annuity price information, since blocking tort plaintiffs' access did not cause injury to consultants).
II. Time Limit
Plaintiffs contend that the district court committed reversible error by imposing a time limit on the trial. We review such challenges to trial court management for abuse of discretion. General Signal Corp. v. MCI Telecommunications Corp., 66 F.3d 1500, 1507 (9th Cir.1995).
A district court is generally free to impose reasonable time limits on a trial, Id. at 1507 (citing Dens v. Allstate Ins. Co., 15 F.3d 506, 520 (5th Cir.), cert. denied, - U.S. -, 115 S.Ct. 573, 130 L.Ed.2d 490 (1994)). Time limits may be used to "`pre• vent undue delay, waste of time, or needlese presentation of cumulative evidence.'" Monotype Corp. v. International Typeface Corp., 43 F.3d 443, 450 (9th Cir.1994) (citing Johnson v. Ashby, 808 F.2d 676, 678 (8th Cir.1987)). Rigid and inflexible hour limite on trials, however, are generally disfavored. Monotype Corp., 43 F.3d at 450-51 (citing Flaminio v. Honda Motor Co., 733 F.2d 463 473 (7th Cir.1984)).
We conclude that the time limits iin• posed by the district court were reasonable We begin by observing that the district court based the time limits, in part, on the parties estimates of trial length. Plaintiffs' ëounsel estimated that he would need four weeks tc put on the liabifity portion of the case. After the court proposed a six-week trial, with forty hours per side for witness examination, plaintiffs' counsel asked the court for ten more hours-or fifty hours total-to try the liabffity issue. Although the court initially rejected this suggestion, it subsequently reconsidered and gave each side an six additional hours for witness examination. This adjustment brought the total hours to forty-six-close to plaintiffs' counsel's original request.
In implementing the time limits, moreover, the district court was flexible. It granted each side six additional hours for witness examination, which was even more time than the parties themselves estimated. Indeed, the district court told plaintiffs' counsel that she was granting him more supplemental time than the four hours he had requested because she thought he had underestimated the time needed. Additionally, the district court allowed counsel to use some of their allotted commentary time for witness examination.
Plaintiffs advance several specific challenges to the district court's time management during the trial.
Plaintiffs argue that the times imposed were arbitrary because they did not allow for *1514delays caused by dilatory witnesses and sidebar discussions. This argument is flawed in two respects. First, it overlooks the district court’s willingness to extend the time limits for each side, which was not arbitrary but based on the parties’ own estimates of time. Second, it ignores the nature of trials, which are typically fraught with delays the parties cannot control. Especially in trials with time limits, trial counsel are responsible for case management and frequently must make strategic decisions to adjust for unforeseen delays.
Plaintiffs also contend that the district court’s decision to permit each party to use commentary time for witness examination was prejudicial because it gave defendants—who tried the case as two parties—additional time to examine witnesses, while depriving plaintiffs of the right of cross-examination.
Plaintiffs’ account of the trial mischarac-terizes the record. The district court did not, as plaintiffs allege, “arbitrarily cut” plaintiffs’ final fifteen minutes of witness examination time and give defendants additional time for cross-examination. Plaintiffs’ time was not cut; instead, the district court’s own timekeeping indicated that plaintiffs had only fifteen minutes remaining. Moreover, defendants’ time was not increased; the court’s timekeeping indicated defendants had another five minutes remaining for cross-examination.
More importantly, plaintiffs are flatly incorrect in their assertion that they “did not cross-examine [defendants’ expert] Bate-man,” since the record reflects that plaintiffs did, in fact, cross-examine Bateman at the very end of trial. They are also mistaken in their contention that they “had to forego any cross-examination of [defense witness] Erre-carte.” After defense counsel’s direct examination of Erreearte, plaintiffs’ counsel still had time remaining, but explicitly declined the opportunity to cross-examine Erreearte.
Plaintiffs were not “denied” the opportunity to cross-examine witnesses. Indeed, the district court allowed both sides additional time for cross-examination by allowing them to use their commentary time for cross-examination. Cf. General Signal Corp., 66 F.3d at 1508 (citing Harries v. United States, 350 F.2d 231, 236 (9th Cir.1965) (stating that a limitation on cross-examination denies due process only if it is “so severe as to constitute a denial” of the right to cross-examine)). Plaintiffs, though cognizant of the time limitations, used their supplemental time for other things, such as to recall their expert witness.
The record indicates that throughout the trial, plaintiffs’ counsel was acutely aware that he would have limited time to cross-examine defendants’ witnesses. Even before the trial got underway, plaintiffs’ counsel predicted that under the forty-hour limit, “there will be virtually no time left when we come to cross-examine the defendants.” Just one week after the district court had granted the parties additional time, plaintiffs’ counsel complained that the five hours he then had remaining would force him to choose between conducting further examination of his expert and cross-examining defendants’ witnesses, and notified the court that he would ask the court for “proper cross-examination time” after he finished direct examination of his expert. The next day, when plaintiffs’ counsel had virtually depleted his time, the district court offered to let counsel use his remaining commentary time for witness cross-examination. The court refused to grant plaintiffs’ counsel additional time, however, explaining:
The defendants have abided by the time rules that have been set down, and the court makes the finding that for me to give you additional time other than your commentary time would be injust [sic] to them, as they have also shortcircuited some things in order to live up to their own estimate of the time.
Plaintiffs are mistaken in their contention that the time limits deprived them of their due. process right to confront witnesses. The case law makes clear that where a district court has set reasonable time limits and has shown flexibility in applying them, that court does not abuse its discretion. Moreover, to overturn a jury verdict based on a party’s failure to use its limited time for witness cross-examination.would be to invite parties to exhaust their time limits without completing cross-examination, then appeal on due *1515process grounds. Such a result would undermine the discretion of district courts to manage time during trials.
III. Evidentiary Rulings
A. Admission of Defense Expert Testimony
Plaintiffs challenge Judge Caulfield’s decision to allow testimony by defense expert Dr. Merrill Bateman, which contravened Judge Henderson’s earlier order sanctioning defendants’ repeated discovery. We review for abuse of discretion a district judge’s decision to reconsider an interlocutory order by another judge of the same court. Zipfel v. Halliburton Co., 832 F.2d 1477, 1481 (9th Cir.1987) (citation omitted), cert. denied, 486 U.S. 1054, 108 S.Ct. 2819, 100 L.Ed.2d 921 (1988).
We begin by acknowledging that “the interlocutory orders and rulings made pre-trial by a district judge are subject to modification by the district judge at any time prior to final judgment, and may be modified to the same extent if the ease is reassigned to another judge.” In re United States, 733 F.2d 10, 13 (2nd Cir.1984). There is “ ‘no imperative duty to follow the earlier ruling— only the desirability that suitors shall, so far as possible, have reliable guidance how to conduct their affairs.’” Id. (citing Dictograph Products Co. v. Sonotone Corp., 230 F.2d 131, 134-35 (2nd Cir.), petition for cert. dismissed, 352 U.S. 883, 77 S.Ct. 104, 1 L.Ed.2d 82 (1956)).
Moreover, a district court is vested with “broad discretion to make discovery and evidentiary rulings conducive to the conduct of a fair and orderly trial.” Campbell Industries v. M/V Gemini, 619 F.2d 24, 27 (9th Cir.1980). Within a district court’s broad discretion “lies both the power to exclude or admit expert testimony,” and “to exclude testimony of witnesses whose use at trial is in bad faith or would unfairly prejudice an opposing party.” Campbell Industries, 619 F.2d at 27 (citations omitted). In addition, the district court has broad discretion over the admission of rebuttal evidence. Trust Services of America, Inc. v. United States, 885 F.2d 561, 569 (9th Cir.1989) (citation omitted). In Campbell Industries, for example, we upheld a district court’s order—much like Judge Henderson’s order in this case—that sanctioned a party’s “flagrant violation” of the discovery rules by barring the testimony of that party’s witness. Campbell Industries, 619 F.2d at 27.
We are confronted here with the delicate problem of two district court judges exercising their “broad discretion” over evidentiary rulings in different phases of the same case and reaching contradictory results. Judge Henderson exercised his discretion in sanctioning defendants’ discovery violations by prohibiting defendants from introducing expert testimony. The propriety of that decision is uncontested here. See id. Judge Caulfield exercised her discretion to allow rebuttal testimony by the excluded defense expert.
In evaluating whether Dr. Bateman’s testimony should have been admitted, we are guided by other limitations on the district court’s rulings. We have made it clear that district courts “should generally allow amendments of pre-trial orders” provided three criteria are met: (1) “no substantial injury will be occasioned to the opposing party,” (2) refusal to allow the amendment “might result in injustice to the movant,” and (3) the “inconvenience to the court is slight.” Id. at 27-28 (internal quotation and citation omitted); see also United States v. First Nat’l Bank of Circle, 652 F.2d 882, 887 (9th Cir.1981) (factors- to consider in deciding whether to modify pre-trial order include: prejudice to movant of a refusal to modify; prejudice to non-movant of modification; impact of modification on orderly conduct of case; and degree of wilfulness, bad faith, or excusable neglect on the part of the movant).
We have applied this principle to a district court’s decision to amend a pre-trial order to allow parties to add witnesses. The factors a district court must consider where a party seeks to call a witness who does not appear on the witness list are: (1) the prejudice or surprise of the party against whom the excluded witness testifies; (2) the ability of that party to cure the prejudice; (3) the extent to which calling the witness would *1516disrupt the orderly and efficient trial; and (4) bad faith or wilfulness in failing to comply with the court’s order. Price v. Seydel, 961 F.2d 1470, 1471 (9th Cir.1992) (citations omitted).
Applying that authority to the facts of this case, we conclude that Judge Caulfield’s decision to allow Dr. Bateman to testify was not error. Judge Caulfield apparently concluded that the reference to a writing by Dr. Bate-man during the examination of plaintiffs’ own expert constituted a sufficiently changed circumstance as to justify a limited response. We will not second guess the exercise of the considerable discretion allowed her, particularly where the result was to allow limited testimony on an issue (plaintiffs’ damages) which the jury never reached.
B. Admission of Defendants’ Summary Exhibits
Plaintiffs challenge the admission of two of defendants’ summary exhibits on grounds that defendants failed to provide plaintiffs with the materials underlying those exhibits. Evidentiary rulings are reviewed for an abuse of discretion and should not be reversed absent some prejudice. City of Long Beach v. Standard Oil Co., 46 F.3d 929, 936 (9th Cir.1995).
Federal Rule of Evidence 1006 governs the admissibility of summary exhibits. It provides in relevant part:
The contents of voluminous writings, recordings, or photographs which cannot conveniently be examined in court may be presented in the form of a chart, summary, or calculation. The originals, or duplicates, shall be made available for examination or copying, or both, by other parties at reasonable time or place.
Fed.R.Evid. 1006.
A proponent of a summary exhibit must establish a foundation that (1) the underlying materials on which the summary exhibit is based are admissible in evidence, and (2) those underlying materials were made available to the opposing party for inspection. Paddock v. Dave Christensen, Inc., 745 F.2d 1254, 1259 (9th Cir.1984). The purpose of the availability requirement is “to give the opposing party an opportunity to verify the reliability and accuracy of the summary prior to trial.” Id. at 1261. Accord Intel Corp. v. Terabyte Int’l, Inc., 6 F.3d 614, 623 (9th Cir.1993) (under adversary system, opposing party entitled to see materials that form basis for summary). Where a party fails to make available materials underlying a summary exhibit, that summary exhibit is inadmissible. United States v. Miller, 771 F.2d 1219, 1238 (9th Cir.1985) (summaries inadmissible under Federal Rule of Evidence 1006 where government failed to provided defendants with copy of underlying documents before summary was introduced into evidence).
Defense Exhibit 781A summarized two types of price information: California rice prices that had been adjusted by defendants’ expert, and Thai rice prices. Additionally, it summarized defendants’ expert’s regression analysis of that price information. During his testimony, defendants’ expert used Defense Exhibit 781A to criticize plaintiffs’ expert’s study, which contained a similar regression analysis but relied on different data: round grain rice prices from the Food and Agricultural Organization (“FAO”) and unadjusted California rice prices.
Defense Exhibit 529A was a graph comparing a price-to-loan ratio to a stocks to use ratio for California rice. In preparing Defense Exhibit 529A, defendants’ expert used a formula contained in a graph offered by plaintiffs’ expert, but used “different values of the stocks-to-use ratio and different values of the farm price-to-loan ratio.”
Plaintiffs urge that the admission of Defense Exhibit 781A and Defense Exhibit 529A violated Federal Rule of Evidence 1006 because defendants allegedly “never produced the underlying data or computations” relating to those summary exhibits.
When plaintiffs objected at trial to the admission of Defense Exhibit 781A on grounds they were not furnished with the underlying information, the district court overruled plaintiffs’ objection, finding that Exhibit 781A
is the same analysis that your expert went through, except they’re using a different *1517price, which is the Thai price instead of the FAO price. So it’s exactly your model, alternatively presented in surrebuttal on the issue of credibility of the expert as well as authenticity of methodology.
Although plaintiffs failed to object when defense counsel questioned defendants’ expert about Defense Exhibit 529A they raised a blanket objection when defense counsel moved for admission of all the exhibits defendants’ expert discussed in his testimony. Plaintiffs objected on grounds that “they were summary exhibits for which none of the underlying materials were ever provided.” The district court overruled plaintiffs’ blanket objection to the admission of defendants’ summary exhibits, however, explaining:
[A]ll of the calculation testimony testified to by [defense expert] Dr. Bateman was testimony derived from the expert testimony of [plaintiffs’ expert] Dr. Knut-son and [ ] the testimony is clear that it is the same calculations done with different foundational numbers.
The district court’s explanations unfortunately ignore the requirement—embodied in the mandatory language of Federal Rule of Evidence 1006 and explicitly required by our Paddock decision, that a party must make available to the opposing party the materials that have gone into preparing the summary exhibit. Under Federal Rule of Evidence 1006, defendants had an obligation to make available to plaintiffs the information relied on in Defense Exhibit 781A (the adjusted California prices and the Thai prices) and the information relied on in Defense Exhibit 529A (defendants’ values for the stocks-to-use ratio and for the price-to-loan ratio). Admission of these summary exhibits violated this mandatory provision.
Defendants defend the admission of Exhibit 781A by insisting that “the underlying materials upon which the summaries were based were formulae used by plaintiffs’ own expert.” This argument, however, ignores that the summary exhibit contained raw data —Thai prices and adjusted California prices— never provided to plaintiffs. Although defendants insist that this information was made available to plaintiffs “in [defendants’ pretrial motion and in their exhibits,” they offer no support from the record as to the former and cite only to unadmitted exhibits as to the latter.
Our ultimate question, however, is whether the erroneous admission of these summary exhibits was prejudicial, since evidentiary rulings should not be reversed absent some prejudice. City of Long Beach, 46 F.3d at 936. We conclude under the unusual circumstances here, including impeaching evidence given by plaintiffs expert in rebuttal, that the error was not prejudicial and therefore does not require reversal.15
IY. Application of the Noerr-Pennington Doctrine
Plaintiffs challenge the district court’s application of the Noerr-Pennington doctrine and its . evidentiary rulings with respect to conduct of defendants alleged to underlie plaintiffs’ antitrust injury. We review de novo the district court’s grant of directed verdict.16 Berry v. Bunnell, 39 F.3d 1066, 1057 (9th Cir.1994). A directed verdict is proper when the evidence permits only one reasonable conclusion. “The evidence must *1518be viewed in the light most favorable to the nonmoving party,” and “all reasonable inferences must be drawn in favor of that party.” Id.
The Noerr-Pennington doctrine provides that “[t]hose who petition government for redress are generally immune from antitrust liability.” Professional Real Estate Investors, Inc. v. Columbia Pictures Industries, Inc., 508 U.S. 49, 56, 113 S.Ct. 1920, 1926, 123 L.Ed.2d 611 (1993). This general rule encompasses private actions that “attempt to persuade the legislature or the executive to take particular action with respect to a law that would produce a restraint or a monopoly,” id. (citing Eastern R.R. Presidents Conf. v. Noerr Motor Freight, Inc., 365 U.S. 127, 136, 81 S.Ct. 523, 529, 5 L.Ed.2d 464 (1961)), as well as “‘the approach of citizens ... to administrative agencies ... and to courts,’ ” id. (citing California Motor Transport Co. v. Trucking Unlimited, 404 U.S. 508, 510, 92 S.Ct. 609, 611-12, 30 L.Ed.2d 642 (1972)).
Noerr-Pennington antitrust immunity does not apply, however, when the activity “is a mere sham to cover ... an attempt to interfere directly with the business relationships of a competitor.” Eastern R.R. Presidents Conf. v. Noerr Motor Freight, Inc., 365 U.S. 127, 144, 81 S.Ct. 523, 533, 5 L.Ed.2d 464 (1961). The Supreme Court’s latest articulation of the parameters of the “sham” litigation exception to Noerr-Pennington immunity is contained in its Professional Real Estate Investors decision.17 There, the Court held that “an objectively reasonable effort to litigate cannot be sham regardless of subjective intent.” Professional Real Estate Investors, 508 U.S. at 60, 113 S.Ct. at 1928. The Court outlined a two-part definition of “sham” litigation:
First, the lawsuit must be objectively baseless in the sense that no reasonable litigant could realistically expect success on the merits. If an objective litigant could conclude that the suit is reasonably calculated to elicit a favorable outcome, the suit is immunized under Noerr, and an antitrust claim premised on the sham exception must fail. Only if challenged litigation is objectively baseless may a court examine the litigant’s subjective motivation.
Id. at 60, 113 S.Ct. at 1928 (emphasis added).
In formulating the standard, the Court made clear that in the first step, the litigant’s subjective purpose is irrelevant, explaining that “the legality of objectively reasonable petitioning ... is not at all affected by any anticompetitive purpose [the litigant] may have.” Id. at 59, 113 S.Ct. at 1927 (citing Noerr, 365 U.S. at 140, 81 S.Ct. at 531). Indeed, the Court stated that “[t]he existence of probable cause to institute legal proceedings precludes a finding that an antitrust defendant has engaged in sham litigation,” and is an “absolute defense” to allegations of “sham litigation.” Professional Real Estate Investors, 508 U.S. at 62-63, 113 S.Ct. at 1929. It defined “probable cause to institute civil proceedings” as the mere “reasonable] belie[f] that there is a chance that [a] claim may be held valid upon adjudication.” Id. (citations omitted).
If the plaintiff succeeds in establishing that the lawsuit is “objectively baseless,” as required in the first step of Professional Real Estate Investors, then a court “may ... examine the litigant’s subjective motivation.” Id. This second step requires the court to determine “whether the baseless lawsuit conceals ‘an attempt to interfere directly with the business relationships of a competitor ... ’ through the ‘use [of] the governmental process ... as an anticompetitive weapon.’ ” Id. (citations omitted).
Plaintiffs urge that Professional Real Estate Investors is an inappropriate test to apply in this case, insisting that the proper test is set forth in our recent decision in USS-POSCO Industries v. Contra Costa County Bldg. and Constr. Trades Council, 31 F.3d 800 (9th Cir.1994). In USS-POSCO Industries, we recognized that “where the defendant is accused of bringing a whole *1519series of legal proceedings” as opposed to a “single action,” as was the ease in Professional Beal Estate Investors, the analysis is different. As we explained in USS-POSCO Industries, “[t]he question is not whether any one of [the legal proceedings] has merit ... but whether they are brought pursuant to a policy of starting legal proceedings without regard to the merits and for the purpose of injuring a market rival.” In other words, we must ask, “[w]ere the legal filings made, not out of a genuine interest in redressing grievances, but as part of a pattern or practice of successive filings undertaken essentially for purposes of harassment.” USS-POSCO Industries, 31 F.3d at 811. In USS-POSCO Industries, we held that the plaintiff could not substantiate its “sham” litigation claim because more than half of the twenty-nine lawsuits and arbitration actions filed by the defendants were successful. Given that success rate, we concluded that the plaintiff could not establish that the defendants “were filing lawsuits and other actions willy-nilly without regard to success.” Id.
The distinction we drew in USS-POSCO Industries reflects the distinction alluded to by the Supreme Court in Professional Real Estate Investors. There, the Court explained that in determining whether a challenged action falls within the “sham” exception, “a reviewing court [must] ‘diseern[ ] and draw[]’ the ‘difficult line’ separating objectively reasonable claims from ‘a pattern of baseless, repetitive claims ... which leads the factfinder to conclude that the administrative and judicial processes have been abused.’” Professional Real Estate Investors, 508 U.S. at 58, 113 S.Ct. at 1926-27 (citing California Motor Transport, 404 U.S. at 513, 92 S.Ct. at 613) (emphasis added). This distinction may be traced back to California Motor Transport Co. v. Trucking Unlimited, 404 U.S. 508, 92 S.Ct. 609, 30 L.Ed.2d 642 (1972), which fell within the latter category: the “abuse of [ ] proeess[ ] [that] effectively barr[ed] [the plaintiffs] from access to the agencies and courts.” California Motor Transport, 404 U.S. at 513, 92 S.Ct. at 613.
This case does not concern “a whole series of legal proceedings,” USS-POSCO Industries, 31 F.3d at 811, or a “ ‘pattern of baseless, repetitive claims,’ ” Professional Real Estate Investors, 508 U.S. at 58, 113 S.Ct. at 1927 (citing California Motor Transport, 404 U.S. at 513, 92 S.Ct. at 613), that would require us to apply the standard set forth in USS-POSCO Industries. Here, plaintiffs cite only two lawsuits, not a “series” or a “pattern” of them. Although we do not attempt to define here the number of legal proceedings needed to allege a “series” or “pattern” of litigation as required in USS-POSCO Industries, 31 F.3d at 811, we distinguish this case from USS-POSCO Industries, which involved twenty-nine legal proceedings. We do not consider the third “sham” litigation alleged, since that was simply a counterclaim in this litigation, and contained essentially the same allegation as one of the two alleged “sham” lawsuits.
Plaintiffs next argue that, even if USS-POSCO Industries is inapposite, the district court erred when it ruled that plaintiffs failed to meet “the standard [for a] baseless lawsuit [brought] without probable cause.” With this contention in mind, we examine the legal and administrative proceedings plaintiffs insist fell within the “sham” exception to the Noerr-Pennington antitrust immunity doctrine. We note that to invoke the “sham” exception, “th[e] two-tiered process [in Professional Real Estate Investors ] requires the plaintiff to disprove the challenged lawsuit’s legal viability.” Professional Real Estate Investors, 508 U.S. at 61, 113 S.Ct. at 1928.
A. The Alleged “Sham” Lawsuits
Plaintiffs alleged that in 1981, defendants Connell Rice, Grover Connell, and Joseph Alioto instituted a “sham” lawsuit against PIRMI in the name of Louisiana rice farmer Larry Lyons. See Lyons v. PIRMI Delta, No. 811951 (W.D.La. October 28, 1981). The complaint in that suit alleged that PIRMI had violated United States Department of Agriculture (“USDA”) reporting regulations pertaining to rice sales and had violated various antitrust laws. Plaintiffs alleged defendants surreptitiously sponsored the lawsuit “for the purpose of harassing and embarrassing actual and potential purchasers of California paddy rice and California milled rice who were defendants in that action.” *1520Connell Rice and Joseph Alioto denied having had any involvement with the Lyons suit before it was filed, although Alioto’s law firm subsequently represented Lyons in the suit. The Lyons suit was subsequently dismissed on a motion for summary judgment.
The next “sham” litigation plaintiffs alleged was a lawsuit brought by FRC and RGA, but allegedly sponsored by Connell Rice. That lawsuit accused PIRMI and Agro-prom, a Swiss company, of bribing Korean officials to secure rice contracts. See Rice Growers Ass’n and Farmers Rice Cooperative v. Pacific Int’l Rice Mills, Inc., et al., No. C-82-0872 SC (N.D.Cal.1982). Plaintiffs alleged that the suit was instigated by Grover Connell and Joseph Alioto, who acted “with knowledge that the suit lacked merit,” and was financed in part by Connell Rice. Plaintiffs claimed the suit was commenced “for the purpose of embarrassing actual and potential purchasers of California paddy rice and California milled rice.” That suit eventually settled without compensation.
The third “sham” litigation plaintiffs allege is defendant Connell Rice’s counterclaim against PIRMI in separate litigation, the essential allegations of which were repeated in the instant lawsuit. Connell Rice’s counterclaim, like the Rice Growers complaint, alleged that PIRMI had engaged in commercial bribery.
We conclude that plaintiffs failed to establish that the lawsuits were “objectively baseless” under the Professional Real Estate Investors standard, since they have not adduced evidence to “disprove the challenged lawsuit[s’] legal viability.” Professional Real Estate Investors, 508 U.S. at 61, 113 S.Ct. at 1928.
We first note that the plaintiff in Lyons alleged defendants had violated USDA reporting requirements. Although the court handling the litigation later held that the plaintiff there lacked standing to sue for USDA regulatory violations, nonetheless there was evidence in the record tending to show PIRMI’s failure to comply with USDA reporting regulations.
Next, we note that defendants’ involvement in the Rice Growers lawsuit was based on their suspicion that PIRMI was bribing Korean officials to secure an exclusive opportunity to bid on the limited quota of rice sales to Korea. Although there was no direct evidence of such bribery, the absence of direct evidence does not preclude probable cause to institute litigation. They relied instead on circumstantial evidence — the price differential between PIRMI’s bid prices and Connell Rice’s bid price. Moreover, given defendants’ concerns that PIRMI was on the verge of blocking them out of bidding, defendants had good reason to expedite the litigation. We conclude that defendants had probable cause to bring the Rice Growers suit, and for the same reasons had probable cause to bring the similar counterclaim in the instant litigation.
B. The Alleged “Sham” Administrative Proceedings
Plaintiffs also accused defendants of petitioning State Department officials and Korean officials in an effort to influence rice exports to Korea. In our view, defendants’ efforts to influence various American and Korean officials — from State Department officials to members of Congress-was legitimate private action in response to defendants’ suspicions of bribery. The NoerrPennington doctrine shields from antitrust liability efforts to influence legislators and members of the executive branch. Noerr, 365 U.S. at 136, 81 S.Ct. at 528-29.
Y. Refusal to Instruct Jury on the Law of Service of Subpoenas on Foreign Government Officials
Plaintiffs appeal the district court’s refusal to adopt plaintiffs’ proposed instructions to the jury with respect to the serving of subpoenas on foreign diplomatic officials. We review for abuse of discretion a district court’s formulation of civil jury instructions. Fikes v. Cleghorn, 47 F.3d 1011, 1013 (9th Cir.1995).
Although the district court did not adopt plaintiffs’ proposed jury instructions with respect to the law of subpoenaing diplomatic officials, the district court’s instructions to the jury did not constitute an abuse of discretion. By the time it instructed the *1521jury, the district court had already entered judgment as a matter of law for defendants on plaintiffs’ claims of “sham” litigation, meaning the district court’s instructions to the jury on this peripheral question were of little or no import.
VI. The District Court’s Judgment as a Matter of Law on Plaintiffs’ Section 1 and California Cartwright Act Claims
Plaintiffs contend it was error for the district court to enter judgment for defendants on the claims on which the jury was hung: claims brought under Section 1 of the Sherman Act and the California Cartwright Act. We review de novo the district court’s decision to enter judgment as a matter of law, and must “view conflicting evidence in the light most favorable to the non-movant, and determine whether the proffered result is the only reasonable conclusion.” Forro Precision, Inc. v. International Business Machines Corp., 673 F.2d 1045, 1058 (9th Cir.1982).
Federal Rule of Civil Procedure 50(b) provides that “[i]f no verdict was returned, the court may, in disposing of the renewed motion [for judgment as a matter of law] direct the entry of judgment as a matter of law.” We have held that in directing the entry of judgment in the wake of a jury’s failure to return a verdict, a district court “must accept as true facts that necessarily were established” by the jury’s verdict.
The district court’s entry of judgment as a matter of law is premised on the district court’s characterization of plaintiffs’ theory of the case. The district court interpreted plaintiffs’ complaint and “their presentation to the jury” to articulate the following theory of the case: that “it was defendants’ attempt to conspire to monopolize that allegedly restrained trade in the relevant market.” Amarel, 1993 WL 515885, * 2.
An examination of plaintiffs’ claims suggests, however, that the jury’s verdict for defendants as to the Section 2 monopoly claim does not, standing alone, preclude plaintiffs’ Section 1 restraint of trade claim.
First, as a general matter, Section 1 and Section 2 of the Sherman Act proscribe two separate and distinct statutory offenses: Section 1 prohibits restraints of trade and Section 2 prohibits monopoly.
Significantly, Section 2 claims tend to encompass a narrower range of anticompetitive behaviors specifically defined as monopolization and attempts to monopolize. Section 2 of the Sherman Act provides that “[e]very person who shall monopolize, or attempt to monopolize, or combine or conspire with any person or persons, to monopolize ... trade shall be guilty” of an antitrust violation. 15 U.S.C. § 2. Claims for violation of Section 2 must allege two key elements: (1) the possession of monopoly power in the relevant market and (2) the willful acquisition or maintenance of that power. United States v. Grinnell Corp., 384 U.S. 563, 570-71, 86 S.Ct. 1698, 1703-04, 16 L.Ed.2d 778 (1966). Because Section 2 claims require proof of a defendant’s market power in the form of monopolistic control, they inevitably encompass a smaller pool of anticompetitive conduct. To establish a Sherman Act Section 2 violation for attempted monopolization, a private plaintiff seeking damages must demonstrate four elements: (1) specific intent to control prices or destroy competition; (2) predatory or anticompetitive conduct directed at accomplishing that purpose; (3) a dangerous probability of achieving ‘monopoly power’: and (4) casual antitrust injury. Rebel Oil Co., Inc. v. Atlantic Richfield Co., 51 F.3d 1421, 1432-33 (9th Cir.1995) (citing McGlinchy v. Shell Chem. Co., 845 F.2d 802, 811 (9th Cir.1988)).
Section 1, in contrast, broadly prohibits concerted action that “unreasonably”. restrains trade. Section 1 has been construed to encompass a wide variety of anticompetitive practices, including horizontal and vertical price fixing, horizontal and .vertical restraints on such non-price factors as territories and customers, tying agreements, exclusive dealing agreements, and, finally, anticompetitive boycotts or concerted refusals to deal, as plaintiffs alleged in this *1522case. William C. Holmes, Antitrust Law Handbook 188 (Clark Boardman Callaghan: 1996). Unlike Section 2 claims, Section 1 restraint of trade claims need not establish the threshold showing of monopoly control over a relevant market. To show a violation of Section 1, a plaintiff “must establish a contract, conspiracy or combination intended to restrain competition and which actually has an anticompetitive effect.” City of Vernon v. Southern California Edison Co., 955 F.2d 1861, 1365 (9th Cir.), cert. denied, 506 U.S. 908, 113 S.Ct. 305, 121 L.Ed.2d 228 (1992).
Second, in this particular case, plaintiffs’ theory of the case, though inartfully pleaded, does not condition recovery under Section 1 on recovery under Section 2. Although plaintiffs pleaded the two claims within a single cause of action, plaintiffs’ complaint alleges several other instances of anticompet-itive conduct in addition to the monopolistic behavior alleged. In particular, plaintiffs alleged defendants engaged in boycotts and refusals to deal in order to restrain trade in the markets for milled rice as well as for paddy rice.
For these reasons, it was improper for the district court to enter judgment for defendants on the restraint of trade claims under Section 1 of the Sherman Act and the California Cartwright Act. We therefore reverse the district court’s judgment for defendants as to plaintiffs’ restraint of trade claims and remand for a new trial as to these claims only.
VII. Antitrust Immunity for Defendant Joseph Alioto
Plaintiffs challenge the district court’s entry of judgment as a matter of law for defendant Joseph Alioto, which accorded him antitrust immunity on the ground that he was defendants’ lawyer. We review de novo the district court’s judgment as a matter of law, and thus must “view conflicting evidence in the light most favorable to the non-movant, and determine whether the proffered result is the only reasonable conclusion.” Forro Precision, Inc., 673 F.2d at 1058.
We outlined the test for determining whether a lawyer is entitled to antitrust immunity in Pinhas v. Summit Health, Ltd., 894 F.2d 1024, 1033 (9th Cir.1989), aff'd, 500 U.S. 322, 111 S.Ct. 1842, 114 L.Ed.2d 366 (1991). In Pinhas, we held that “an attorney is not immune from antitrust liability if he becomes an active participant in formulating policy decisions with his client to restrain competition.” Pinhas, 894 F.2d at 1033 (citing Tillamook Cheese and Dairy Ass’n v. Tillamook County Creamery Ass’n, 358 F.2d 115, 118 (9th Cir.1966)) (emphasis added).
Implicit in this rule is a corresponding requirement: Where a plaintiff seeks to impose antitrust liability on an attorney, that plaintiff must establish that the attorney “exerted [his] influence over [a client] so as to direct [the client] to engage in the complained of acts for an anticompetitive purpose.” Pinhas, 894 F.2d at 1033. As the Sixth Circuit recently explained,
Individual liability under the antitrust laws can be imposed only where corporate [attorneys] are actively and knowingly engaged in a scheme designed to achieve anticompetitive ends. To support a determination of liability under this standard, the evidence must demonstrate that a defendant exerted his influence so as to shape corporate intentions.
Brown v. Donco Enterprises, Inc., 783 F.2d 644, 646 (6th Cir.1986).
In bringing their lawsuit, plaintiffs alleged Alioto masterminded and perpetrated defendants’ alleged conspiracy to monopolize and restrain trade in the rice industry for over thirty years, and, in particular, orchestrated the anticompetitive activities in 1981 in an attempt to prevent PIRMI and Comet from competing in the market for the export of California rice to Korea. On appeal, plaintiffs repeat these allegations, placing special emphasis on Alioto’s role in defendants’ alleged “sham” litigation. However, plaintiffs offer no evidence from the record to support *1523such accusations, and therefore fail to establish that Moto “exerted [his] influence over [his clients] so as to direct [the clients] to engage in the complained of acts for an anti-competitive purpose.” Pinhas, 894 F.2d at 1033. We therefore conclude that Joseph Moto was entitled to judgment as a matter of law on grounds of attorney immunity from antitrust liability.
VIII. Award of Costs to Defendants-Ap-pellees
Plaintiffs appeal the district court’s award of costs to defendants. Because “the decision to award costs ordinarily resides in the district court,” we review such decisions for an abuse of discretion. National Information Services, Inc. v. TRW, Inc., 51 F.3d 1470, 1471 (9th Cir.1995).
Federal Rule of Civil Procedure 54(d)(1) provides that costs “shall be allowed as of course to the prevailing party unless the court otherwise directs.” We have construed Federal Rule of Civil Procedure 54(d)(1) to create a presumption in. favor of awarding costs to the prevailing party. National Information Services, 51 F.3d at 1471.
Where a reviewing court reverses a district court’s judgment for the prevailing party, however, both the underlying judgment and the taxation of costs undertaken pursuant to that judgment are reversed. Farmer v. Arabian American Oil Co., 379 U.S. 227, 85 S.Ct. 411, 13 L.Ed.2d 248 (1964), disapproved of on other grounds by Crawford Fitting Co. v. J.T. Gibbons, Inc., 482 U.S. 437, 443, 107 S.Ct. 2494, 2498, 96 L.Ed.2d 385 (1987). In Farmer, the district court entered a directed verdict for the defendant when the jury could not reach a decision as to the plaintiffs wrongful discharge claim. When the'defendant, as the prevailing party, moved for an award of costs, the district court approved the clerk’s taxation of costs against the plaintiff. The Second Circuit subsequently reversed the directed verdict and remanded for a new trial. In describing the Second Circuit’s decision to reverse the directed verdict and remand for a new trial, the Supreme Court noted that the Second Circuit’s decision to reverse the judgment “thereby upset[] the judgment and the taxation of costs.” Farmer, 379 U.S. at 229, 85 S.Ct. at 413 (emphasis added). Similarly, our reversal of the district court’s judgment as a matter of law with respect to plaintiffs’ claim under Section 1 of the Sherman Act therefore operates to reverse the district court’s award of costs incurred in defending against that claim.
We acknowledge that our decision to reverse the district court’s judgment for defendants on plaintiffs’ Section 1 claim does not affect the jury verdict for defendants as to plaintiffs’ Section 2 claim. In view of their success in defending against plaintiffs’ Section 2 claim, defendants may very well be entitled to an award of the costs they incurred defending the Section 2 claim. On remand, however, we direct the district court to await resolution of plaintiffs’ Section 1 claim before determining whether an award of costs is appropriate for either claim.
Our rationale is two-fold: First, the outcome of plaintiffs’ Section 1 claim will bear on whether an award of costs is appropriate, since it will influence the district court’s determination of whether defendants are the “prevailing parties” in the overall action. We have explained that “[a] party in whose favor judgment is rendered is generally the prevailing party for purposes of awarding costs under Rule 54(d).” d’Hedouville v. Pioneer Hotel Co., 552 F.2d 886 (9th Cir.1977). In the event of a mixed judgment, however, it is within the discretion of a district court to require each party to bear its own costs. Testa v. Village of Mundelein, 89 F.3d 443 (7th Cir.1996) (requiring each party to bear its own costs where plaintiff prevailed on one claim and defendant prevailed on federal claim) (citations omitted). In the event that plaintiffs prevail on their Section 1 claim on remand, the resultant mixed judgment may warrant that each party bear its own costs. We express no opinion on this matter, which will fall within the discretion of the district court following the new trial.
*1524Second, it would be difficult at this juncture to separate the costs incurred on the Section 1 claim from those incurred on the Section 2 claim: In awarding costs below, the district court did not distinguish the costs incurred in defending the Section 1 claim from the costs incurred in defending the Section 2 claim, since defendants prevailed on both claims., Instead of attempting to award partial costs at this juncture, the district court should await the outcome of the Section 1 claim to ascertain whether allocation of costs is necessary. See Farmer, 379 U.S. at 232-33, 85 S.Ct. at 415 (dicta stating that where the district court’s judgment and taxation of costs were both upset by the Court of Appeals’ reversal of the first trial judgment, “it became the duty of the clerk to tax costs for both trials only when judgment was finally entered for the [defendant].”) (emphasis added).
CONCLUSION
We affirm the judgment for defendants on plaintiffs’ monopolization claims under Section 2 of the Sherman Act and the California Unfair Practices Act. We reverse the judgment for defendants on plaintiffs’ restraint of trade claims under Section 1 of the Sherman Act and the California Cartwright Act, and we remand the case for a new trial solely on the restraint' of trade claims. We reverse the district court’s award of costs and direct the district court to await resolution of plaintiffs’ restraint of trade claims before determining whether an award of costs is appropriate.
. Because the district court ordered separate trials of plaintiffs’ claims and defendants' counterclaims, defendants' counterclaims remain pending in district court. Jurisdiction is nonetheless appropriate because the district court entered final judgment for defendants as to plaintiffs’ claims, and certified the judgment for appeal pursuant to Federal Rule of Civil Procedure 54(b).
. Southern short grain rice is grown in the southern United States and resembles the "japó-nica" rice grown in California and Japan and preferred by Korean consumers.
. "California” rice is a variety of "japónica” rice.
. Although both parties number plaintiffs at eighteen, nineteen plaintiffs are named, both in the second amended complaint and in the briefs on appeal. This discrepancy apparently stems from the second amended complaint, which lists a husband and wife as one plaintiff.
. None of the independent rice mills are parties to this action.
. RGA was voluntarily dismissed from this action, and FRC was never served and was dismissed.
. Connell Rice apparently provided the $260 price quote in response to OSROK's January 19, 1982 request, by telephone, for a price quote from RGA. Because Connell Rice is RGA’s export marketing agent, RGA directed OSROK to contact Connell about the quote.
. Several members of Congress apparently took seriously the charge that Korea had paid inflated prices for U.S. rice: 111 members of Congress signed a letter to the president of Korea, accusing the Korean government of "improprieties in the purchase of U.S. rice.”
. The sole defendants to go to trial were Connell Rice, Grover Connell, and Joseph Alioto. RGA and Errecarte were voluntarily dismissed with prejudice in 1986. FRC was apparently never served and was dismissed in 1986.
. Plaintiffs accused Alioto of masterminding and perpetrating the alleged monopolization conspiracy for over thirty years, and alleged Alioto had orchestrated defendants' alleged anticompet-itive activities in 1981-82. Particular allegations were that Alioto attempted to obstruct Korean contracts with the independent mills by allegedly lying to Korean officials about the price of rice; falsely accusing independent mill PIRMI of bribery of Korean officials; knowingly serving illegal subpoenas on Korean diplomats to deter them from contracting with the independent rice mills; masterminding the alleged sham litigation and sham administrative proceedings aimed at obstructing the independent mills' efforts to sell rice to Korea; and concealing the nature of RGA's attempted purchase of the PIRMI mill in an attempt to evade U.S. Department of Justice antitrust review.
. The United States Department of Justice, Antitrust Division, filed suit under Sections 7 and 15 of the Clayton Act, 15 U.S.C. §§ 18 and 25, seeking to enjoin RGA's acquisition of PIRMI assets. The district court entered judgment for the United States in 1986, finding that the at*1504tempted acquisition would result in a market concentration that could “substantially ... lessen competition in the market for the purchase or acquisition for milling of paddy rice grown in California,” and thus would violate Sections 7 and 15 of the Clayton Act. United States v. Rice Growers Ass’n of California, 1986-2 Trade Cases (CCH) [para] 67,287, 1986 WL 12562, * 12 (E.D.Cal.1986). The district court found that the transaction, which was directed to some extent by Joseph Alioto, appeared “structured so as to avoid the reporting requirements of the Hart-Scott-Rodino Antitrust Improvement Act of 1976, 15 U.S.C. § 18(a)." Id. at* 13.
. Plaintiffs also brought monopoly and restraint of trade claims under the Cartwright Act, Calif. Bus. & Prof.Code § 16790 and the California Unfair Practices Act, Calif. Bus. & Prof.Code §§ 17045-17048 and 17200. Additionally, plaintiffs brought a claim suit under Section 7 of the Clayton Act, 15 U.S.C. § 18, alleging defendants' actions “Iessen[ed] competition or [] tendfed] to create a monopoly in a line of commerce in a section of the country.”
. Connell Rice's counterclaims allege plaintiffs and the independent rice mills conspired to monopolize the California rice market through commercial bribery, and engaged in abuse of process in bringing their antitrust claims.
. On two occasions below, the district court denied similar motions by defendants-appellees. First, in a pre-trial ruling in response to defendants' motion for summary judgment, which was based on plaintiffs’ purported lack of standing and was therefore treated as a motion to dismiss, the district court held that plaintiffs had standing. Amarel v. Connel, 1986-2 Trade Cases ¶ 67,-233, 1986 WL 10613, * 2-3 (N.D.Cal. Aug. 8, 1986). Second, in a post-trial order in response to defendants’ motion for judgment as a matter *1507of law, the trial judge summarily rejected defendants' contention that plaintiffs jacked standing.
. Under Federal Rule of Evidence 703, these exhibits were inadmissible "as general proof of the truth of the underlying matter,” Paddack, 745 F.2d at 1261 (internal quotations and citations omitted). Nonetheless, even had the district court not admitted Defense Exhibit 781A and Defense Exhibit 529A into evidence, defendants' expert could have discussed the information contained in Defense Exhibits 781A and 529A as a basis for criticizing plaintiffs' expert's analysis under Federal Rule of Evidence 703. Actually admitting the data into evidence was therefore not prejudicial. We disagree, moreover, with plaintiffs’ contention that their expert was "unable to respond” to defendants’ expert’s testimony. This argument mischaracterizes the record. In fact, plaintiffs’ expert did offer specific arguments to rebut defendants' expert's criticism of his models.
. Plaintiffs characterize the district court's Noerr-Pennington rulings as a judgment as a matter of law pursuant to Federal Rule of Civil Procedure 50(a). Because it appears from the record that the district court ruled during trial that defendants failed to meet the legal standard necessary to invoke the “sham” litigation exception to the Noerr-Pennington doctrine, we analyze the rulings under the standard of review for a directed verdict.
. The district court made its ruling before the Supreme Court had issued its decision in Professional Real Estate Investors. We must apply that decision to this appeal, since a federal civil rule of law applies retroactively to appeals pending at the time the rule is announced. Harper v. Virginia Dept. of Taxation, 509 U.S. 86, 113 S.Ct. 2510, 125 L.Ed.2d 74 (1993).