Defendants Brown and Tobey appeal their jury convictions for conspiracy to suppress competition for billboard sites in violation of the Sherman Antitrust Act, 15 U.S.C. § 1 (1988). We affirm.

FACTS

Appellant Brown is senior vice president for public affairs in a division of Gannett Company, Inc. that includes fifteen separate billboard advertising companies. One of these companies is Gannett Outdoor Company, Inc. of Southern California, an original defendant in this case and the descendant of a company that Brown’s father founded in the early 1930s. Brown himself started working part-time in the family company in 1954, and in late 1968 or early 1969 he became the company’s president and chief operating officer. He left the billboard advertising business in 1973, but returned two years later to become president and chief executive officer of the company. In 1984 he was promoted from these positions to his current, national management position. Gannett Outdoor Company, Inc. of Southern California and its predecessors will be referred to collectively as “Gannett”.

Appellant Tobey is a senior executive in Foster & Kleiser Corp. (“F & K”), a subsidiary of Metromedia, Inc. and the other orig[*1044] inal defendant in this case. F & K has been a dominant force in the billboard advertising business since the 1920s, when it controlled a monopolistic share of billboard sites in California and three other western states. Tobey joined F & K as a lease representative in 1963, and worked his way into management. In 1971 he became vice-president and executive vice-president in charge of public relations, and in 1984 he assumed control of F & K’s leasing department.

Gannett and F & K are the two largest billboard advertising companies in California and have been dominant for some time. In 1964 they entered into a written agreement, a portion of which provided that the companies would refrain from bidding on each other’s former leaseholds for a period of one year after the space was lost or abandoned by the lessee-company. ^[1] To implement this “one-year rule”, the agreement established a notification procedure whereby each company would send written notice to the other when it either leased a new billboard site or removed a billboard from an existing site. Although this explicit written agreement was terminated sometime in 1969 and the notification procedures abandoned, the one-year rule was honored by both companies for fifteen more years.

On December 12, 1988, the government filed a one-count felony information against both companies and against appellants Brown and Tobey, charging them with conspiring to restrain trade in violation of the Sherman Antitrust Act, 15 U.S.C. § 1 (1988). The information alleged that the defendants participated in an ongoing conspiracy to suppress competition for billboard sites from 1964 until 1984. Gannett and Metromedia, F & K’s corporate parent, entered pleas of nolo contendere, and F & K was dismissed in conjunction with Me-tromedia’s plea, but the case against Brown and Tobey went to trial.

Much testimony was presented at trial regarding the agreement and appellants’ participation in it. Joseph Cubiero, a subordinate of Brown’s, testified that the agreement was in effect from 1975 until sometime in 1984. He also testified that Brown confronted him at least a half dozen times about “violations” of the no-compete aspects of the agreement and informed him that such transgressions would make Brown’s life miserable in negotiating with F & K on other issues. Cubiero also testified that when he approached Brown in 1984 regarding investigation of the companies, Brown simply stated that he had terminated the agreement.

Witnesses gave similar testimony about Tobey’s involvement. Cubiero testified that Tobey complained about violations of the agreement to appellant Brown. Bart Browne, a subordinate of Tobey’s at F & K, testified that he informed Tobey of violations of the agreement and urged him to contact Gannett to resolve the problem. He also testified that Tobey contacted Cu-biero at Gannett and, after conversing with him, decided that “all deals are off.” To-bey then asked Browne to inform other F[*1045] & K employees. Finally, Drake Kennedy, the president of a competing billboard company, testified that Tobey stated that if Cubiero would not honor the agreement, he would not do so either.

At the conclusion of the trial, the jury convicted both Brown and Tobey. They now appeal.

DISCUSSION

Brown and Tobey raise seven issues on appeal: 1) whether the district court’s classification of the agreement between the companies as a per se antitrust violation was correct; 2) whether the court’s mens rea instruction was adequate; 3) whether the court’s exclusion from evidence of a 1931 consent decree involving F & K was proper; 4) whether the jury instruction on appellants’ liability for the illegal conduct of their subordinates was proper; 5) whether the jury instruction relating to the statute of limitations was proper; 6) whether the district court’s limitations on Brown’s cross-examination of government witnesses violated his sixth amendment rights; and 7) whether the evidence was sufficient to support the appellants’ convictions.

1. Classification of the Agreement as a Per Se Violation

Brown and Tobey claim that the district court erred in determining as a matter of law that the companies’ agreement was a per se antitrust violation. We review this determination de novo. United States v. McConney, 728 F.2d 1195, 1201 (9th Cir.) (en banc), cert. denied, 469 U.S. 824, 105 S.Ct. 101, 83 L.Ed.2d 46 (1984).

The Sherman Act prohibits unreasonable restraints of trade. Business Electronics Corp. v. Sharp Electronics Corp., 485 U.S. 717, 723, 108 S.Ct. 1515, 1519, 99 L.Ed.2d 808 (1988). Whether a restraint of trade is unreasonable generally turns on “the facts peculiar to the business, the history of the restraint, and the reasons why it was imposed.” National Soc’y of Professional Eng’rs v. United States, 435 U.S. 679, 692, 98 S.Ct. 1355, 1365, 55 L.Ed.2d 637 (1978). However, this case-by-case analysis is unnecessary when the restraint falls into a category of agreements which have been determined to be per se illegal. Such agreements are those that “always or almost always tend to restrict competition and decrease output.” Northwest Wholesale Stationers, Inc. v. Pacific Stationery & Printing Co., 472 U.S. 284, 289-290, 105 S.Ct. 2613, 2617, 86 L.Ed.2d 202 (1985) (quoting Broadcast Music, Inc. v. Columbia Broadcasting System, Inc., 441 U.S. 1, 19-20, 99 S.Ct. 1551, 1562, 60 L.Ed.2d 1 (1979)).

We agree with the district court that the agreement in this case should be characterized as per se illegal. The agreement restricted each company’s ability to compete for the other’s billboard sites. It clearly allocated markets between the two billboard companies. A market allocation agreement between competitors at the same market level is a classic per se antitrust violation. United States v. Topco Assocs., Inc., 405 U.S. 596, 608, 92 S.Ct. 1126, 1133, 31 L.Ed.2d 515 (1972).

Appellants contend that the agreement should not be classified as a per se antitrust violation because it was intended to comply with a 1931 consent decree to which F & K was a party. Although the terms of a consent decree can militate against the application of the per se rule, see Broadcast Music, 441 U.S. at 12-13, 99 S.Ct. at 1559-60, the consent decree in this case governed only the actions of F & K. Because it neither mandated nor permitted the reciprocal agreement between F & K and Gannett, the 1931 consent decree is not relevant to the determination of whether the agreement constituted a per se violation of section one of the Sherman Act.

2. Jury Instruction on Mens Rea

Appellants, relying on United States v. United States Gypsum Co., 438 U.S. 422, 98 S.Ct. 2864, 57 L.Ed.2d 854 (1978), argue that the district court should have instructed the jury that an intent to produce anti-competitive effects is an element of a criminal antitrust offense. We review de novo whether the jury was properly instructed on all the elements of the charged offense.[*1046] United States v. Stenberg, 803 F.2d 422, 433 (9th Cir.1986).

Gypsum involved a criminal prosecution for a price-fixing conspiracy in violation of section one of the Sherman Act. The district court had instructed the jury that if the defendants’ exchanges of pricing information had the effect of raising or fixing prices, they could be presumed to have intended that result. The Supreme Court rejected this instruction, holding that intent is an element of a criminal antitrust offense that cannot be presumed, but rather “must be established by evidence and inferences drawn therefrom.” 438 U.S. at 435, 98 S.Ct. at 2872. In giving content to the intent requirement, the Court announced that “action undertaken with knowledge of its probable consequences and having the requisite anticompetitive effects can be a sufficient predicate for a finding of criminal liability under the antitrust laws.” Id. at 444, 98 S.Ct. at 2877. The Court in Gypsum also noted that the anticompeti-tive effects need not have come to pass if it is proven that the defendants undertook the conduct with the purpose of producing an anticompetitive effect. Id. at 444 n. 21, 98 S.Ct. at 2877 n. 21.

In the present ease, the district court held that the intent requirement of Gypsum does not apply to charges of per se violations of the antitrust laws, such as the agreement between Gannett and F & K. Accordingly, the court held that it was not necessary to instruct the jury that it had to find that the defendants acted with the purpose of achieving anticompetitive effects or with the knowledge that such effects likely would result. The district court’s ruling accords with the express holdings of six other circuits, and the intimations of another, that Gypsum does not require proof of a defendant’s intent to produce anticompetitive effects where the defendant is charged with a per se violation of the Sherman Act. ^[2] We agree with the conclusion of the district court and the other circuits that have addressed the issue. The reasoning of the Second Circuit is particularly cogent:

Where per se conduct is found, a finding of intent to conspire to commit the offense is sufficient; a requirement that intent go further and envision actual anti-competitive results would reopen the very questions of reasonableness which the per se rule is designed to avoid.

United States v. Koppers Co., 652 F.2d 290, 296 n. 6 (2d Cir.), cert. denied, 454 U.S. 1083, 102 S.Ct. 639, 70 L.Ed.2d 617 (1981). The district court did not err by following this reasoning and holding that it was unnecessary to instruct the jury that intent to produce anticompetitive effects is an element of the offense of which Brown and Tobey were convicted. ^[3]

[*1047] 3. Exclusion of the 1931 Consent Decree

Tobey further argues that the court erroneously excluded evidence based on its determination that Gypsum’s intent requirements did not apply. Specifically, he asserts that the excluded 1931 consent decree, to which F & K was a party, was relevant to F & K’s intent in entering into the agreement with Gannett and would have supported Tobey’s claim of a lack of criminal intent. We review a district court’s determination of relevance for an abuse of discretion. United States v. Kessi, 868 F.2d 1097, 1107 (9th Cir.1989). We will reverse only upon the firm conviction that the district court committed a clear error of judgment. Fjelstad v. American Honda Motor Co., 762 F.2d 1334, 1337 (9th Cir.1985).

We conclude that the district court properly could exclude the decree on either of two bases: first, in light of its ruling with regard to the Gypsum intent requirement, any purported reliance on the decree was not relevant to Tobey’s defense; second, the government presented persuasive evidence that the decree neither addressed nor permitted the type of agreement at issue. The decree restrained F & K from certain methods of expansion into certain market areas because of its predominant role in the industry. It stretches credulity for Tobey even to suggest that the decree authorized F & K to enter into the agreement with Gannett, a competitor and not a party to the decree, that would force a division of markets between the two. The district court did not err in excluding the consent decree.

4. Jury Instruction on Liability for the Illegal Conduct of Subordinates

The district court instructed the jury that appellants could be held criminally liable for the illegal actions of subordinates if they knowingly authorized or consented to such behavior. ^[4] Appellants timely objected to the instruction; they argue that it erroneously permitted the jury to convict them for merely knowing about the illegal conduct of others and failing to stop it, even if they were not wrongdoers themselves. Questions as to whether the instructions properly state the elements of an offense are reviewed de novo. United States v. Stenberg, 803 F.2d 422, 433 (9th Cir.1986).

In United States v. Wise, 370 U.S. 405, 416, 82 S.Ct. 1354, 1361, 8 L.Ed.2d 590 (1962), the Supreme Court held:

a corporate officer is subject to prosecution under § 1 of the Sherman Act whenever he knowingly participates in effecting the illegal contract, combination, or conspiracy—be he one who authorizes, orders, or helps perpetrate the crime—re[*1048] gardless of whether he is acting in a representative capacity.

Although Wise does not define “knowingly participates,” we agree that it requires more than purely passive behavior. However, we reject appellants’ premise that the instructions in this case allowed conviction based on mere knowledge of the wrongdoing of others. The charge asked the jury to determine whether the appellants knowingly consented to their subordinates’ participation in the conspiracy. Further instructions defined “knowingly” as “voluntarily and intentionally”, and defined “participating knowingly” as “encouraging, advising or assisting for the purpose of furthering the conspiracy.” These instructions and definitions adequately reflect the standard established in Wise.

5. Jury Instructions Regarding the Statute of Limitations

An important issue in the case was whether the five-year statute of limitations barred prosecution. Because the government’s information was filed on December 12,1988, the jury was instructed that it had to find that the conspiracy was in existence after December 12, 1983. Appellants contend that the district court confused the jury through the use of contradictory instructions on this issue and failed to include a mens rea element in the last overt act instruction. Since a proper objection to these instructions was not made below, we review for plain error. United States v. Ramos, 861 F.2d 228, 230 (9th Cir.1988). We will reverse for plain error only in exceptional circumstances; the error must have affected substantial rights, and it must be highly probable that the error materially affected the verdict. Id.

The allegedly inconsistent portions of the jury charge deal with two separate issues. First, the jury was asked to determine whether a conspiracy existed at all. Correctly summarizing the law in this area, the court instructed the jury that a finding of an overt act is not necessary to a finding that a Sherman Act conspiracy has been formed. See, e.g., Nash v. U.S., 229 U.S. 373, 378, 33 S.Ct. 780, 782, 57 L.Ed. 1232 (1913). I rors were asked to determine whether the conspiracy existed after December 12, 1983. The jury was told that, assuming the conspiracy was formed before December 12, 1983, it had to find that a member committed an overt act in furtherance of the conspiracy after that date. See United States v. Inryco, Inc., 642 F.2d 290, 294 (9th Cir.1981), cert. dismissed, 454 U.S. 1167, 102 S.Ct. 1045, 71 L.Ed.2d 324 (1982). Although the jury was told in one instance that an overt act was not necessary and in another that it was necessary, the law was correctly stated. We find no plain error in these instructions.

We also reject appellants’ claim that the last overt act instruction failed to include a mens rea element. The jury was asked to determine whether “one or more members of the conspiracy performed some act after December 12, 1983 in furtherance of the purposes and objectives of the conspiracy.” Thus, a member, defined in the charge as an individual who voluntarily and intentionally joined the conspiracy, was required to commit an overt act in furtherance of the conspiracy. Read in context, the instruction does not give the impression that a conviction could be based on an innocent act which inadvertently furthered the conspiracy. The jury would not have been misled or confused. Certainly there was no plain error.

6. Limitations on Cross-Examination of Government Witnesses

Brown argues that the district court, in limiting the scope of his cross-examination of government witnesses, violated his sixth amendment rights. The sixth amendment right to cross-examine adverse witnesses does not empower a defendant to pursue irrelevant inquiries or exercise complete control over the extent of the cross-examination. The district court is responsible for determining the relevance of a given topic and the extent of cross-examination to be permitted on that topic. Skinner v. Cardwell, 564 F.2d 1381, 1388-89 (9th Cir.1977), cert. denied 435 U.S. 1009, 98 S.Ct. 1883, 56 L.Ed.2d 392 (1978). We review the district court’s decision to limit[*1049] cross-examination for an abuse of discretion, considering whether the “jury is otherwise in possession of sufficient information upon which to make a discriminating appraisal of the subject matter at issue.” Id. at 1389.

Brown contends that his cross-examination was limited improperly in three instances. The first two instances involved inquiries into two memoranda circulated within Gannett. One memorandum referred to the “gentlemen’s agreement” between Gannett and F & K, while the other referred to the “intended spirit” between the companies. Gannett employees, called by the government, testified that these phrases referred to the illegal agreement between Gannett and F & K. Brown, on cross-examination, sought to elicit the fact that much of the content of the two memo-randa dealt with completely legal aspects of Gannett’s operations and relationship with F & K. Brown argues that this testimony could have been used to negate the government’s assertion that Brown had knowledge of the illegal agreement, and that his efforts in this regard were foiled when the district court limited the scope of his cross-examination.

With regard to the first memorandum, the district court did not permit inquiry into the meaning and origin of the terms and phrases used in the document. In Brown’s cross-examination on the second memorandum, the district court refused to permit inquiry into the details of the lawful activities referred to in the document. In neither instance did the district court abuse its discretion. Brown was permitted to convey to the jury the fact that both documents dealt in part with lawful concerns of Brown’s company. He simply was not permitted to develop testimony on the definitions of specific terms and practices employed in the billboard business—matters which were essentially irrelevant to his defense.

The third instance occurred when the district court limited Brown’s development of testimony on the business challenges the billboard industry faced during the conspiracy period. Brown argues that the testimony was necessary to show that joint meetings between the companies addressed lawful concerns rather than the illegal one-year rule. The district court has wide discretion to limit the admission of what is essentially background information. Admittedly, such evidence may be relevant when it is directly related to a defendant’s specific conduct, and the court must be careful not to inhibit the development of a defense. The record here, however, reveals that the district court did not limit specific questions regarding the companies’ cooperation and discussions held at meetings. Brown was permitted to elicit testimony concerning the problems facing the billboard industry and the need for cooperation between the companies in the context of specific behavior. Only when the cross-examination went further afield was it curtailed. We find no abuse of discretion by the district court.

7. Sufficiency of the Evidence

Finally, both defendants contend that the evidence was insufficient to support their convictions. Specifically, they contend that the evidence was insufficient for the jury to have found that they knowingly participated in the conspiracy and that the conspiracy was in existence during the statute of limitations period. In reviewing these claims, we “must examine the evidence in the light most favorable to the government and determine whether any rational trier of fact could have found the essential elements of the offense beyond a reasonable doubt.” United States v. Little, 753 F.2d 1420, 1449 (9th Cir.1984) (citing Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979)).

The record contains a substantial amount of evidence that Brown was a knowing, active participant in the conspiracy. The most damaging testimony was given by Joseph Cubiero, a Gannett executive who supervised the leasing department from late 1975 until 1986. Cubiero testified that Brown would fill him in on complaints made by F & K regarding violations of the one-year rule. He also testified that he was warned by an F & K employee that complaints regarding the agreement would be relayed to Brown by F & K executives. Finally, Cubiero testified that he was confronted by Brown, who complained several[*1050] times that Cubiero was violating the agreement. This testimony, combined with evidence of Brown’s active involvement in all aspects of his company’s operations, was sufficient for a reasonable jury to conclude beyond a reasonable doubt that Brown knew about and actively participated in the conspiracy.

That Tobey knew about and participated in the agreement is similarly well supported by the evidence. Bart Browne provided the most incriminating testimony. He testified that he informed Tobey of several Gannett violations of the one-year rule and urged Tobey to contact Gannett regarding the agreement in early 1984. He further testified that Tobey made such a call and, when he did not receive Cubiero’s support on the companies’ understanding, cancelled the agreement. This testimony was corroborated by Cubiero, who further testified that Tobey was involved in relaying complaints regarding Gannett’s violation of the one-year rule. Tobey’s arguments regarding the sufficiency of the evidence, like Brown’s, must fail.

Our review of the record also leads us to reject the appellants’ assertions that there is no evidence of their knowing participation in the conspiracy within the statute of limitations period. The government presented evidence that the appellants and various employees discussed enforcement activity after December 12, 1983. The conversation between Tobey and Cubiero about Tobey’s dissatisfaction with the companies’ cooperation, for example, occurred in 1984. This evidence, when considered in the light most favorable to the government, supports the conclusion that the appellants participated in the conspiracy within the statute of limitations period.

CONCLUSION

The convictions of Brown and Tobey are AFFIRMED.