REINHARDT, Circuit Judge:
Business Cards Tomorrow, Inc. (“BCT”) is a franchisor of printing shops that produce and sell business cards wholesale. In September 1983, a group of former BCT franchisees (hereinafter, “Murphy”) sued BCT and other corporate and individual defendants, alleging violations of the antitrust laws and a number of pendent state law claims. Most of the counts, including all the state law claims, were dismissed, leaving only two antitrust claims. Subsequently, the parties engaged in extensive discovery and, following its completion, the trial court granted defendants summary judgment on the remaining claims. Defendants Itek Corporation and Itek Leasing Corporation (jointly “Itek”) then moved for sanctions against plaintiffs under Rule 11. The district court denied the motion. Murphy appeals from the grant of summary judgment and Itek appeals from the denial of sanctions. We affirm.
Tying Arrangements
Murphy argues that BCT unlawfully tied the sale of BCT franchises to the purchase of equipment packages from BCT. The franchise agreement did not on its face require the purchase of the equipment package from BCT, and Murphy does not allege that BCT at any point informed potential franchisees of any such requirement. In fact, Murphy admits that none of the plaintiffs believed at the time they ob[1204]*1204tained a BCT franchise that they were not free to purchase the equipment package from someone other than BCT. Murphy alleges only that BCT had an unstated policy of not giving a franchise to anyone who would not also agree to buy the equipment package from it.1
The Supreme Court recently summarized the law prohibiting tying arrangements as follows:
[T]he essential characteristic of an invalid tying arrangement lies in the seller’s exploitation of its control over the tying product to force the buyer into the purchase of a tied product that the buyer either did not want at all, or might have preferred to purchase elsewhere on different terms. When such “forcing” is present, competition on the merits in the market for the tied item is restrained and the Sherman Act is violated.
Jefferson Parish Hosp. Dist. No. 2 v. Hyde, 466 U.S. 2, 12, 104 S.Ct. 1551, 1558, 80 L.Ed.2d 2 (1984).
In the present case, we agree with the district court that summary judgment for defendants was appropriate. As that court stated, “the uncontradicted evidence shows that no plaintiff was ‘forced’ to accept the tied product.” The essence of an antitrust tying violation is not the seller’s unilateral refusal to deal with a buyer who refuses to buy the tied product, cf. Monsanto Co. v. Spray-Rite Service Corp., 465 U.S. 752, 761-63, 104 S.Ct. 1464, 1469-70, 79 L.Ed.2d 775 (1984) (generally, a manufacturer may deal independently with any distributor it wishes), but the use by the seller of its “leverage” “to force a purchaser to do something that he would not do in a competitive market.” Jefferson Parish, 466 U.S. at 14 & n. 20, 104 S.Ct. at 1559 & n. 20. As Murphy neither asserts nor presents any evidence that would support an assertion that any persons, let alone plaintiffs, were persuaded by BCT’s control over its franchises to buy the equipment package from it rather than elsewhere, Murphy has not stated a claim under the antitrust rule against tying arrangements.
Exclusive Territories
Under its franchise agreements, BCT granted each franchisee a particular territory and agreed not to locate another franchise in the prescribed area. Murphy alleges that BCT read the franchise agreement as also providing that no other franchisee would be permitted to solicit sales in that area. Murphy contends that BCT regularly attempted to enforce these territorial restrictions.
Murphy characterizes BCT’s actions as a horizontal market allocations scheme, and thus per se illegal. However, it is clear that the agreement alleged is vertical, not horizontal; by Murphy’s own account, the territorial division was imposed on the franchisees by the franchisor, it was not created at the insistence or the initiative of the competing franchisees. See Business Electronics Corp. v. Sharp Electronics Corp., — U.S. -, 108 S.Ct. 1515, 1522 & n. 4, 99 L.Ed.2d 808 (1988). Vertical agreements to impose territorial restraints are not per se illegal, but are judged under a rule of reason analysis. Continental TV, Inc. v. GTE Sylvania, Inc., 433 U.S. 36, 97 S.Ct. 2549, 53 L.Ed.2d 568 (1977).
Murphy attempts to distinguish GTE Sylvania on the basis that it involved the distribution of products from a manufacturer through its retailers, while the present case does not. However, Murphy cites no authority — neither case nor commentator — and no persuasive policy reasons for his novel proposition that vertical non-price restrictions should be treated differently when they involve the use of business methods or processes developed by the franchisor rather than the distribution of the franchisor’s products. Therefore, we apply the rule of reason standard that [1205]*1205is customarily applied in vertical territorial restraint cases.
To establish a cause of action for unreasonable restraint of trade, the plaintiffs must show the following elements:
(1) an agreement among two or more persons or distinct business entities; (2) which is intended to harm or unreasonably restrain competition; and (3) which actually causes injury to competition.
Reid Brothers Logging Co. v. Ketchikan Pulp Co., 699 F.2d 1292, 1296 (9th Cir.), cert. denied, 464 U.S. 916, 104 S.Ct. 280, 78 L.Ed.2d 259 (1983). In meeting the third requirement, plaintiffs must show that the restrictions harmed competition in the relevant market. Aydin Corp. v. Loral Corp., 718 F.2d 897, 902 (9th Cir.1983); see McGlinchy v. Shell Chemical Co., 845 F.2d 802, 811-12 (9th Cir.1988).
Proof that the defendant’s activitiés had an impact upon competition in a relevant market is an absolutely essential element of the rule of reason case. It is the impact upon competitive conditions in a definable product market which distinguishes the antitrust violation from the ordinary business tort.
Kaplan v. Burroughs Corp., 611 F.2d 286, 291 (9th Cir.1979), cert. denied, 447 U.S. 924, 100 S.Ct. 3016, 65 L.Ed.2d 1116 (1980).
In the present case, the relevant market according to plaintiffs’ answers to defendants’ interrogatories is “the wholesale ther-mography market for business cards, letterheads and envelopes.” Yet, the plaintiffs contend only that the alleged antitrust violation caused some of their prices to be artificially high.
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REINHARDT, Circuit Judge:
Business Cards Tomorrow, Inc. (“BCT”) is a franchisor of printing shops that produce and sell business cards wholesale. In September 1983, a group of former BCT franchisees (hereinafter, “Murphy”) sued BCT and other corporate and individual defendants, alleging violations of the antitrust laws and a number of pendent state law claims. Most of the counts, including all the state law claims, were dismissed, leaving only two antitrust claims. Subsequently, the parties engaged in extensive discovery and, following its completion, the trial court granted defendants summary judgment on the remaining claims. Defendants Itek Corporation and Itek Leasing Corporation (jointly “Itek”) then moved for sanctions against plaintiffs under Rule 11. The district court denied the motion. Murphy appeals from the grant of summary judgment and Itek appeals from the denial of sanctions. We affirm.
Tying Arrangements
Murphy argues that BCT unlawfully tied the sale of BCT franchises to the purchase of equipment packages from BCT. The franchise agreement did not on its face require the purchase of the equipment package from BCT, and Murphy does not allege that BCT at any point informed potential franchisees of any such requirement. In fact, Murphy admits that none of the plaintiffs believed at the time they ob[1204]*1204tained a BCT franchise that they were not free to purchase the equipment package from someone other than BCT. Murphy alleges only that BCT had an unstated policy of not giving a franchise to anyone who would not also agree to buy the equipment package from it.1
The Supreme Court recently summarized the law prohibiting tying arrangements as follows:
[T]he essential characteristic of an invalid tying arrangement lies in the seller’s exploitation of its control over the tying product to force the buyer into the purchase of a tied product that the buyer either did not want at all, or might have preferred to purchase elsewhere on different terms. When such “forcing” is present, competition on the merits in the market for the tied item is restrained and the Sherman Act is violated.
Jefferson Parish Hosp. Dist. No. 2 v. Hyde, 466 U.S. 2, 12, 104 S.Ct. 1551, 1558, 80 L.Ed.2d 2 (1984).
In the present case, we agree with the district court that summary judgment for defendants was appropriate. As that court stated, “the uncontradicted evidence shows that no plaintiff was ‘forced’ to accept the tied product.” The essence of an antitrust tying violation is not the seller’s unilateral refusal to deal with a buyer who refuses to buy the tied product, cf. Monsanto Co. v. Spray-Rite Service Corp., 465 U.S. 752, 761-63, 104 S.Ct. 1464, 1469-70, 79 L.Ed.2d 775 (1984) (generally, a manufacturer may deal independently with any distributor it wishes), but the use by the seller of its “leverage” “to force a purchaser to do something that he would not do in a competitive market.” Jefferson Parish, 466 U.S. at 14 & n. 20, 104 S.Ct. at 1559 & n. 20. As Murphy neither asserts nor presents any evidence that would support an assertion that any persons, let alone plaintiffs, were persuaded by BCT’s control over its franchises to buy the equipment package from it rather than elsewhere, Murphy has not stated a claim under the antitrust rule against tying arrangements.
Exclusive Territories
Under its franchise agreements, BCT granted each franchisee a particular territory and agreed not to locate another franchise in the prescribed area. Murphy alleges that BCT read the franchise agreement as also providing that no other franchisee would be permitted to solicit sales in that area. Murphy contends that BCT regularly attempted to enforce these territorial restrictions.
Murphy characterizes BCT’s actions as a horizontal market allocations scheme, and thus per se illegal. However, it is clear that the agreement alleged is vertical, not horizontal; by Murphy’s own account, the territorial division was imposed on the franchisees by the franchisor, it was not created at the insistence or the initiative of the competing franchisees. See Business Electronics Corp. v. Sharp Electronics Corp., — U.S. -, 108 S.Ct. 1515, 1522 & n. 4, 99 L.Ed.2d 808 (1988). Vertical agreements to impose territorial restraints are not per se illegal, but are judged under a rule of reason analysis. Continental TV, Inc. v. GTE Sylvania, Inc., 433 U.S. 36, 97 S.Ct. 2549, 53 L.Ed.2d 568 (1977).
Murphy attempts to distinguish GTE Sylvania on the basis that it involved the distribution of products from a manufacturer through its retailers, while the present case does not. However, Murphy cites no authority — neither case nor commentator — and no persuasive policy reasons for his novel proposition that vertical non-price restrictions should be treated differently when they involve the use of business methods or processes developed by the franchisor rather than the distribution of the franchisor’s products. Therefore, we apply the rule of reason standard that [1205]*1205is customarily applied in vertical territorial restraint cases.
To establish a cause of action for unreasonable restraint of trade, the plaintiffs must show the following elements:
(1) an agreement among two or more persons or distinct business entities; (2) which is intended to harm or unreasonably restrain competition; and (3) which actually causes injury to competition.
Reid Brothers Logging Co. v. Ketchikan Pulp Co., 699 F.2d 1292, 1296 (9th Cir.), cert. denied, 464 U.S. 916, 104 S.Ct. 280, 78 L.Ed.2d 259 (1983). In meeting the third requirement, plaintiffs must show that the restrictions harmed competition in the relevant market. Aydin Corp. v. Loral Corp., 718 F.2d 897, 902 (9th Cir.1983); see McGlinchy v. Shell Chemical Co., 845 F.2d 802, 811-12 (9th Cir.1988).
Proof that the defendant’s activitiés had an impact upon competition in a relevant market is an absolutely essential element of the rule of reason case. It is the impact upon competitive conditions in a definable product market which distinguishes the antitrust violation from the ordinary business tort.
Kaplan v. Burroughs Corp., 611 F.2d 286, 291 (9th Cir.1979), cert. denied, 447 U.S. 924, 100 S.Ct. 3016, 65 L.Ed.2d 1116 (1980).
In the present case, the relevant market according to plaintiffs’ answers to defendants’ interrogatories is “the wholesale ther-mography market for business cards, letterheads and envelopes.” Yet, the plaintiffs contend only that the alleged antitrust violation caused some of their prices to be artificially high. The only evidence in the record regarding anticompetitive effects was testimony that two non-plaintiff BCT franchisees that operated outside their allotted territories were able to lower their prices due to economies of scale.2 Given the absence of any other relevant evidence, this is at most an argument that it would be in BCT and its franchisees’ economic interest to create larger franchisee territories; the evidence, standing alone, does not touch the question of how the restraints on competition among BCT franchisees affected the competitiveness of the wholesale thermography market in.general.
The district court granted summary judgment because plaintiffs had failed to raise a material issue of fact as to anticom-petitive effect. The court reasoned that the effect on intrabrand competition “is not relevant if there is intense interbrand competition, as shown by the testimony of plaintiffs in this ease.” As the district court noted, the evidence in the record was uncontroverted that BCT franchisees faced substantial competition in the local wholesale thermography market and that the barriers to entry into that market were low. Under those circumstances, we cannot assume, without more, that actions that may affect plaintiffs’ prices or profits will also affect the competitiveness of the relevant market. Plaintiffs have not offered more: therefore summary judgment was appropriate. See McGlinchy, 845 F.2d at 811-12.
Sanctions
Itek argues as its basis for Rule 11 sanctions against plaintiffs that two allegations in Murphy’s third amended complaint were plainly false, and that their falsity was or should have been apparent when the complaint was filed. Even if Itek’s contentions are true, Rule 11 sanctions are not appropriate in this case. We have held that Rule 11 permits sanctions only when the pleading as a whole is frivolous or of a harassing nature, not when one of the allegations or arguments in the pleading may be so characterized. Golden Eagle Distributing Corporation v. Burroughs Corporation, 801 F.2d 1531, 1540 (9th Cir.1986). Murphy’s complaint as a whole was not frivolous or of a harassing nature. Therefore the district court’s decision not to impose sanctions was correct.
For the reasons stated above, the judgment of the district court is AFFIRMED.