A contract with an arbitration clause referred to certain parties, including an entity called “Town & Country Auto.” An arbitral panel resolving a payment dispute determined that this referred to a particular car dealership, Town & Country Salida, Inc., and entered an award against it. In the district court below, Town & Country Salida, Inc., sought to vacate or modify the arbitral award on the ground that Town & Country Salida, Inc., was not an entity referred to or bound by the contract con*471taining the arbitration clause. The district court, without deferring to the arbitrators’ determination that Town & Country Sali-da, Inc. was in fact a party to the contract, proceeded to find that it was not. Because the district court’s factual determination in this respect was not clearly erroneous, we have no basis to reverse the district court’s partial vacatur of the arbitral award so as not to apply to Town & Country Salida, Inc.
Defendant-appellant Dealer Computer Services, Inc. (“DCS”) — a company that provides and services computer hardware and software for car dealerships — entered into a series of agreements with car dealerships in Colorado owned by J. Michael Goodart. The original 1995 agreement between DCS and Gunnison Ford, Inc. included an arbitration provision. Through a series of assignments, Town & Country Autoplex-Gunnison, Inc. (“T & C Gunni-son”) became a party to the agreement in 2001.
A February 2008 amendment to the contract included a reference not only to T & C Gunnison, but also to “Town & Country Auto” (“ ‘T & C Auto’ ”), a dealership with a different billing-identification number. Contract Amendment Number 37, ¶ 3, provided that “DCS agrees to grant a 100% discount on the Total Initial License Fees ... when licensed by Dealer at Town & Country Autoplex-Gunnison (806295) and Town & Country Auto (A06295).... ” See Appl. and Mot. to Vacate Arbitration Award Ex. B-2. Goodart signed this amendment as president of T & C Gunni-son. Throughout the rest of the agreement, the only other reference to “T & C Auto” is an amendment which acknowledges that DCS temporarily installed some equipment at “T & C Auto.”
There are two provisions in the agreement that are relevant to the legal duties of dealerships affiliated with T & C Gunni-son. The software-license terms of the original 1995 agreement contemplate that affiliated companies at other locations may use the software, but that such dealerships must agree in writing to be bound by the agreement and that T & C Gunnison guarantees the affiliated dealership’s performance:
Dealer may use the Licensed Software for the internal requirements of an affiliated company at another location by paying an additional initial Software License Fee and an additional Application Consulting Service Fee in the amounts specified in Schedule D for each Application Program so utilized. Dealer’s “affiliated companies” shall mean corporations or entities in which Dealer owns at least a majority of the outstanding capital stock or equity interest and which have agreed, in writing, to be bound by the terms of this Agreement and for which Dealer guarantees the performance thereof.
Appl. and Mot. to Vacate Arbitration Award Ex. B-l, Agreement, § 5(A). Contract Amendment Number 37, which first referred to “T & C Auto,” also contains a similar provision that purports to create joint and several liability for related dealerships:
The parties acknowledge and agree that each individual dealership location that Licenses Application Programs under this Agreement is jointly and severally liable for the entire contractual obligation. Dealer represents that the person executing the Amendment on behalf of Dealer is authorized to bind Dealer and each dealership location to this [acknowledgment] of joint and several liability, and that no further signatures are required.
Appl. and Mot. to Vacate Arbitration Award Ex. B-2, Contract Amendment No. 37, ¶ 61. At no point did Goodart explicit*472ly agree to anything as a signatory for “T & C Auto.”
There is a factual dispute about which dealership received services from DCS following this agreement. Goodart owns and operates two Town & Country dealerships in Salida, Colorado: Town & Country Sali-da, Inc. (“T & C Salida”) and Town & Country C.G., Inc. (“T & C C.G.”).1 Both are on the same road, with T & C Salida located at 1520 East Highway 50 and T & C C.G. located at 943 East Highway 50. Without citing facts in the record, DCS alleges that it provided services to the plaintiff-appellee in this case, T & C Sali-da. T & C Salida, on the other hand, points to affidavits by Goodart which say that DCS provided services to another entity, T & C C.G., and that “T & C Auto” is not T & C Salida. See Mot. for Leave to File Sur-Reply Ex. 1, Supp. Aff. of Michael Goodart Feb. 21, 2012, ¶4 (“[T & C C.G.], a separate corporate entity which is located in Salida at 943 E. Highway 50, did receive services from [DCS].”); T & C Salida’s Resp. to DCS’ Mot. to Confirm Arbitration Award Ex. H, Aff. of Michael Goodart, Jan. 31, 2012, ¶3 (“‘[T & C Auto]’ is not a former name, assumed name, or trade name of [T & C Salida].”).
The current dispute began in 2008 when, apparently due to economic difficulties, T & C Gunnison stopped paying DCS. On March 26, 2009, DCS filed a demand for arbitration with the American Arbitration Association. This demand was directed only to T & C Gunnison. An August 18, 2010 prehearing order by the arbitrators reflects that T & C Gunnison was being represented by counsel, but there is no mention of Goodart’s other entities.
On February 1, 2011, DCS amended its demand for arbitration to add “T & C Auto” as a party to the proceedings. This amended demand was served on T & C Gunnison’s counsel of record. On March 21, 2011, James Blume, a lawyer with the same firm that was representing T & C Gunnison, responded to this demand by objecting on behalf of “T & C Auto” to the arbitration in its entirety and reserving the right to have the issue of arbitrability determined by a court.
On August 12, 2011, DCS made the first filing in the record that links “T & C Auto” to T & C Salida. In its prehearing brief to the arbitrators, DCS repeatedly refers to “Town & Country Auto a/k/a Town & Country Salida, Inc.” See T & C Salida’s Resp. to DCS’ Mot. to Confirm Arbitration Award Ex. F, DCS’ Pre-Hearing Br., 1, ¶¶ 8, 19. However, it does not appear that DCS provided any evidence that “T & C Auto” was the same entity as T & C Salida.
On October 3, 2011, the arbitrators conducted the final arbitration hearing. DCS appeared and presented evidence. No representatives from any of Goodart’s entities attended. On November 18, 2011, the arbitrators issued an award in favor of DCS. In this award, the arbitrators identified T & C Salida as an alias of “T & C Auto,” which they considered to be a party to the contract and the arbitration proceedings.
T & C Salida subsequently filed a complaint in the U.S. District Court for the Eastern District of Michigan seeking to vacate or modify the arbitration award pursuant to the Federal Arbitration Act, 9 U.S.C. §§ 10(a)(4), 11(b). T & C Salida argued that it was never a party to the contract and claimed that “T & C Auto” is “not a former name, assumed name or *473trade name” of T & C Salida and that DCS never provided goods or services to T & C Salida. See Appl. and Mot. to Vacate Arbitration Award, ¶¶ 12-13. In response, DCS filed an answer and a cross-motion to confirm the arbitration award. This motion added T & C Gunnison as a third-party defendant. On March 26, 2012, DCS requested that the clerk enter default judgment against T & C Gunnison, and the clerk did so the following day.
The district court vacated the arbitration award insofar as it bound T & C Salida. The district court found that there was not sufficient evidence to conclude that “T & C Auto” was T & C Salida, and therefore there was no agreement compelling T & C Salida to arbitrate the dispute. The district court also found that despite the arbitrators’ references to T & C Sali-da, there was no evidence that T & C Salida acquiesced in the arbitration. The district court said that even if there was some activity on the part of “T & C Auto” and this dealership was in Salida, this did not necessarily mean that this activity was by T & C Salida. In support of this finding, the district court noted that Goo-dart testified that T & C C.G. was in Salida, received services, and employed Dave Bratton as the general manager — a fact relevant because DCS provided the district court with letters addressed to Dave Bratton as general manager of “T & C Auto.”2 In addition, the district court cited a newspaper article submitted by DCS, which stated that Goodart had two dealerships in Salida. The district court, however, stopped short of finding that “T & C Auto” was T & C C.G. See Town & Country Salida, Inc. v. Dealer Computer Servs., Inc., No. 11-15430, 2012 WL 1964106, at *5-11 (E.D.Mich. May 31, 2012). DCS appeals from this judgment.
On the record, the district court did not clearly err in finding that T & C Salida was not bound to arbitrate by the agreement between DCS and T & C Gunnison. Because T & C Salida did not agree to arbitration, the arbitrators had no authority to issue an award against T & C Salida.
If, as it appears, “T & C Auto” referred to an entity other than T & C Gunnison, it could plausibly refer to either T & C Sali-da or T & C C.G. DCS argues that “T & C Auto” refers to T & C Salida, while T & C Salida, on the other hand, suggests the possibility (but carefully does not admit) that “T & C Auto” is T & C C.G.
It was not clear error for the district court to find that there was not sufficient evidence to establish that “T & C Auto” was T & C Salida. The district court based its finding in part on Goodart’s affidavit, which plainly stated that “[T & C Auto] is not a former name, assumed name, or trade name of [T & C Salida].” T & C Salida, 2012 WL 1964106, at *7 (quoting T & C Salida’s Resp. to DCS’ Mot. to Confirm Arbitration Award Ex. H, Aff. of Michael Goodart, Jan. 31, 2012, ¶ 3). DCS does not point to anything in the record that contradicts Goodart’s affidavit. Even if DCS provided services to a dealership owned by Goodart in Salida, Colorado, this does not necessarily mean that T & C Salida is “T & C Auto” because, as the district court recognized, Goodart had two dealerships in Salida. Although the corre*474spondence between DCS and Dave Brat-ton, ostensibly T & C C.G.’s general manager, used T & C Salida’s address, the letters may have reflected DCS’s confusion rather than T & C Salida’s receipt of services. See supra, n. 2. Strongly supporting the district court’s factual determination is the statement in Goodart’s affidavit that services were supplied to 943 East Highway 50, the address of T & C C.G.
It is true that T & C Salida, owned by Goodart, could have made things much clearer in the court below, and here, by taking a straightforward position on what entity was referred to as “T & C Auto.” T & C Salida did not do so, apparently with a view toward preserving an argument that T & C C.G. is also not bound by the DCS contract. In any event, the affidavit evidence that T & C Salida was not serviced by DCS, and that T & C C.G. was so serviced, could certainly be credited as weightier evidence than the addresses in the DCS-Bratton letters. The district court thus did not clearly err in finding that “T & C Auto” was not T & C Salida.
Neither party sought a jury trial of any disputed factual issues, see Fed.R.Civ.P. 38(d), and neither party argues, assuming that the district court had factual issues to resolve independently of the arbitrators’ findings, that we should review such independent factual determinations other than under a deferential “clearly erroneous” standard. See Fed.R.Civ.P. 52(a)(6); First Options of Chi., Inc. v. Kaplan, 514 U.S. 938, 947-48, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995); Uhl v. Komatsu Forklift Co., Ltd., 512 F.3d 294, 303 (6th Cir.2008).
DCS does argue that the district court erred in deciding the question of whether T & C Salida was “T & C Auto” without deferring to the arbitrators’ finding that it was. This argument is without merit. Where arbitrators allegedly “exceeded their powers,” 9 U.S.C. § 10(a)(4), or “awarded upon a matter not submitted to them,” 9 U.S.C. § 11(b), due to the absence of a party’s consent, courts need not defer to the arbitrators, because if a party did not agree to arbitration, the arbitrators have no authority to issue an award.
It is well settled in both commercial and labor cases that whether parties have agreed to submit a particular dispute to arbitration is typically an issue for judicial determination. It is similarly well settled that where the dispute at issue concerns contract formation, the dispute is generally for courts to decide.
Granite Rock Co. v. Int’l Bhd. of Teamsters, — U.S.-, 130 S.Ct. 2847, 2850-51, 177 L.Ed.2d 567 (2010) (internal quotation marks and citations omitted).
DCS argues that Equitable Resources v. United Steel, 621 F.3d 538, 545-49 (6th Cir.2010), controls this case and requires this court to treat the interpretation of “T & C Auto” as a typical instance of an arbitrator’s interpretation of a contract, entitling the arbitrator’s conclusion to deference. Equitable does not control this case because Equitable voluntarily submitted to arbitration before the arbitrator engaged in any interpretation. See id. at 541. Equitable could perhaps affect this case if T & C Salida had clearly submitted to arbitration and an arbitrator had found that T & C Salida was in fact “T & C Auto.” But this is not what happened; Equitable clearly consented to arbitration pri- or to the arbitrator’s interpretation of the contract. When an arbitrator finds consent to arbitration based on the arbitrator’s findings of facts or interpretation of a contract, these findings and interpretations are not accorded deference when a party challenges the arbitrator’s authority. Indeed, a court must find “clear and unmistakable evidence” that the parties agreed to arbitrate the issue of arbitrability. *475First Options, 514 U.S. at 944, 115 S.Ct. 1920.
Moreover, the district court properly found that T & C Salida was not bound to arbitrate as a nonsignatory to the contract. DCS argues two of the theories that this court has acknowledged under “ordinary contract and agency principles,” to provide a basis for binding a nonsigna-tory to an arbitration agreement: agency and estoppel. See Javitch v. First Union Secs., 315 F.3d 619, 629 (6th Cir.2003) (citing Thomson-CSF v. Am. Arbitration Ass’n, 64 F.3d 773, 776 (2d Cir.1995)). Neither provides a basis in this case to require T & C Salida to arbitrate.
First, when Goodart agreed to Contract Amendment Number 37, there is no indication that Goodart was acting as the agent of T & C Salida. DCS proffers two theories about Goodart’s role: either Goo-dart acted as president of T & C Gunnison, which was somehow an agent of T & C Salida, or Goodart acted as president of T & C Salida and thus was an agent of T & C Salida. DCS argues that T & C Salida was in either event an undisclosed principal, and accordingly, DCS can hold it to account for its agent’s actions.
As a factual matter, there is no basis to argue that Goodart — either as president of T & C Gunnison or as president of T & C Salida — acted on behalf of T & C Salida. The contract refers to “T & C Auto” and, as the district court found, this was not T & C Salida. While both Michigan and Colorado agency law allow for undisclosed principals to be liable in contract to those who contract with their agents, see Timmerman v. Bultman, 243 Mich. 344, 220 N.W. 754, 755 (1928); McCreery v. Morrison, 46 Colo. 533, 105 P. 876, 877 (1909), the question of whether an agent was acting on behalf of a principal is generally a factual question. See, e.g., Lenart v. Ragsdale, 148 Mich.App. 571, 385 N.W.2d 282, 284 (1986); Socomet, Inc. v. City of Detroit, 33 Mich.App. 626, 190 N.W.2d 551, 554 (1971); McCreery, 105 P. at 877. In the absence of evidence that Goodart in either alleged capacity was acting on behalf of T & C Salida, the district court did not clearly err in finding otherwise.
While this factual finding dooms DCS’s agency argument, there are also strong policy arguments against accepting DCS’s broad view of principal liability. DCS’s argument would create widespread alternative liability when any individual who happens to serve as a corporate officer of multiple corporations signs a contract. While this would create problems for the corporations, it would also leave third parties contracting with such individuals unsure with which corporations they have formed a contractual relation. DCS’s agency argument fails.
Second, DCS’s estoppel argument also does not warrant reversal. DCS argues that T & C Salida received the benefits of the contract for five years and is thus estopped from disavowing the arbitration provision. However, as T & C Salida points out, DCS did not raise its estoppel argument before the district court and it is therefore waived. Moreover, DCS cites no evidence that it provided T & C Salida with benefits for five years. In fact, there is evidence in the record that directly contradicts DCS’s assertion. See Mot. for Leave to File Sur-Reply Ex. 1, Supp. Aff. of Michael Goodart Feb. 21, 2012, ¶ 2 (“[T & C Salida] never received services from [DCS].”).
DCS also argues that the district court erred in finding that T & C Salida did not receive notice of the arbitration proceedings. However, even if T & C Salida properly received notice, the more important point is that T & C Salida did not consent to arbitration and cannot be bound *476as a nonsignatory. DCS does not explain what difference notice would make, so DOS’s notice argument does not warrant reversal.
We need not address the cases relied upon by DCS dealing with whether an arbitral decision may be challenged as a manifest disregard of the law. Although the district court referred to the manifest disregard standard, see T & C Salida, 2012 WL 1964106, at *7, the reference was not necessary to the district court’s analysis, and we need not rely upon it. The district court’s judgment is best understood as arising under the statutory bases for challenging arbitration awards.
Neither party challenges the district court’s action in partially vacating the award while leaving the award against T & C Gunnison in place. Accordingly, we do not address the concern mentioned by the district court that a partial vacatur — as opposed to a modification — may not be proper under the Federal Arbitration Act.
Finally, we acknowledge DC S’s general concern that because the principal of all the similarly named T & C’s is Goodart, DCS is the victim of some “shell game.” But the law respects the separate nature of different corporations, and a business wanting to rely on a contract with other businesses is well-advised to ensure that the contract clearly indicates who the contracting parties are. The creditors and equity holders of T & C Salida should not be harmed because Goodart has a similarly named business down the highway and has been less than eager to admit that he or T & C C.G. owes DCS. Moreover, our opinion in no way addresses DCS’s ability to recover from T & C Gunnison, against which DCS has an arbitral award, or from T & C C.G., which is not a party to this appeal, and which did receive services from DCS according to Goodart’s affidavit.
The judgment of the district court is affirmed.
. At oral argument, DCS agreed that Goodart has two dealerships in Salida. See Oral Arg. at 8:40-9:15. The court understands this as a withdrawal of DCS's previous argument that T & C C.G. is located in Alamosa, Colorado.
. Although the district court did not acknowledge so, the letters involving Dave Bratton introduce further ambiguity about which Sali-da dealership was "T & C Auto.” The four letters from 2003 are addressed to Dave Brat-ton at "T & C Auto" but the inside address used is 1520 East Highway 50. 1520 East Highway 50 is the address that T & C Salida identifies as its address rather than the 943 East Highway 50 address that Goodart says is the location of T & C C.G. This suggests that either DCS had the wrong address for Dave Bratton’s place of work, or Dave Bratton was actually working at T & C Salida.