Welfare effects of tying arrangements in franchise contracts : a game theoretical analysis of the Chicken Delight case

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Welfare Effects of Tying

Arrangements in Franchise

Contracts

A game theoretical analysis of the Chicken Delight

case

FACULTY OF ECONOMICS AND BUSINESS

MSc. Economics

Track: Markets and Regulation

Student: Aristeidis Kontopoulos

Student ID: 11374896

Supervisor: Professor Dr. Sander Onderstal

Date: 15 August 2018

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Statement of Originality

The work contained in this thesis was conducted between March 2018 and August 2018. It is an original work except where due reference is made. It has not been and shall not be submitted for the award of any degree or diploma to any other institution of higher learning except from the University of Amsterdam.

Abstract

In this paper I develop a game theoretical model of vertical markets in order to examine the welfare effects of tying arrangements in franchise contracts. The main finding of the analysis is that a tying arrangement in a franchise contract need not harm consumers per se. Thus, while tying might be profitable for an upstream firm, it also constitutes a solution for some of the agency problems that franchise firms face, particularly free riding, in which a tying arrangement benefits consumers. Finally, I argue that tying should be approached with rule reason.

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I. Introduction

Franchise networks are an important aspect of the economy in many countries. A manufacturer has to decide whether to distribute its products to the end consumers with its own means of distribution, or to outsource the distribution to a franchise network of retailers that will purchase the product from it and then sell it to the consumers i.e. vertical separation. A franchise network is composed by an upstream firm, the franchisor, which in many cases is also the manufacturer or the importer of the main product or services and the downstream firm(s) or the franchisee(s). The downstream firm is the retailer bound by a contract with the upstream firm (franchisor) to sell the main product to the final consumer. The downstream firm(s) is (are) obligated by contract to pay the upstream firm either a fee or royalties on sales that it did. The most common is for the downstream firm(s) to pay a fee –the franchise fee– to the upstream firm.

European and United States antitrust policy diverge in the way in which they deal with illegal practices in franchise contracts. The European Commission treats tying in the context of the abuse of dominance (Article 102(d), TFEU)1, although tying may also fall within the scope of the control of anti-cartel law. First, the European courts adopted a “unified” approach to the different forms of tying. Contractual tying (including the tying of inputs and consumables) and the integration of products has been assessed in the same way, without considering the different underlying effects on competition and efficiency. Second, the formal framework of the tying analysis consists of a four-step approach that has many similarities to the U.S. per

se approach and to the second modified per se approach. Those steps are: “1) To establish

market power or dominance of the seller in relation to the tying product. 2) To identify tying which means to demonstrate that (a) customers are forced (b) to purchase two separate products (the tying and the tied product). 3) To assess the effects of tying on competition. 4) To consider whether any exceptional justification for tying exists” (Ahlborn, Evans and Padilla 2004).

The U.S. antitrust law has undergone significant changes over the years. In 1962, the period when the Chicken Delight case was examined, the U.S. courts were following a per se illegal approach. The early cases reflected a great hostility against tying arrangements that were regarded as having no extenuating features. At a later stage, there was a modified per se illegality approach. Specifically, in the Jefferson Parish case the criteria for tying were used as measures to determine possible harm to competition. Finally, the Microsoft III case introduced a rule of reason approach towards tying (Ahlborn, Evans and Padilla 2004). I will elaborate more in regards to the treatment of tying cases, in in Section II.1.

1_{Any abuse by one or more undertakings of a dominant position within the internal market or in a substantial}

part of it shall be prohibited as incompatible with the internal market in so far as it may affect trade between Member States. Such abuse may, in particular, consist in: (d) making the conclusion of contracts subject to acceptance by the other parties of supplementary obligations which, by their nature or according to commercial

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The Chicken Delight case described in the following lines was treated as per se illegal by the U.S. courts. When Chicken Delight commenced operation in 1952, it was in the avant garde of the fast food franchise industry. Quite surprising Chicken Delight did not charge a franchise fee or royalties to the members of the franchise network, a practise that is not followed by its contemporaries. Instead, “the only quid pro quo of the agreements was the obligation of the franchisees to purchase certain cooking equipment, dip and spice mix and certain trademark-bearing paper products exclusively from the upstream firm”. The necessary inputs purchased by the retailers were priced above the market value, but “the prices were specified in the agreement” (Bates 1972).

In 1962 a class action representing approximately 700 retailers, the Chicken Delight arrangement was regarded as an illegal tie-in under Section 1 of the Sherman Act2. The alleged tying product was the trademark license. The tied items were the products that downstream firms were required to purchase from the upstream firm. “The district court determined as matters of law that i) a tie-in existed, ii) that sufficient market power in the tying market was present and that iii) sufficient commerce was affected in the tied market to invoke the per se rule of illegality. Also, the court determined that with respect to the paper products, no justifications existed for the tie-in” (Bates 1972).

A verdict was directed for the defendants on all the above issues. The jury was questioned on whether the purchase of inputs could be justified as “quality control devices” and decided that they could not. The court found that as a “matter of law”, that damages existed but it did not estimate the amount of it. “The measure of damages was held to be the amount of the price for the tied items in excess of their fair market value” (Bates 1972).

As said, both courts that handled the case, being the lower court and the appellate court, recognised that consumers were harmed. The court determined that an illegal tie-in existed. The decision was based on the necessary market power in the tying market that was sufficient for Chicken Delight, “that commerce was affected in the tied markets and regarding paper products no reason for tying existed”. All the above reasons were regarded to suffice in order for the tie in to be per se illegal (Bates 1972).

The practise of tying is regarded to harm consumers, since it can achieve price discrimination. According to Whinston (1990), tying has the ability to “foreclose competition in the tied good market” and according to Huschelrath (2003) “tying can be used to preserve and extend a monopoly position in tying market by deterring the entry of efficient producers”. On the other hand, a franchise contract without any exclusionary arrangements, such as exclusive territories and exclusive dealing and with only a franchise fee does not

2_{Every contract, combination in the form of trust or otherwise, or conspiracy, in restraint of trade or commerce}

among the several States, or with foreign nations, is declared to be illegal. Every person who shall make any contract or engage in any combination or conspiracy hereby declared to be illegal shall be deemed guilty of a felony and on conviction thereof, shall be punished by fine not exceeding one million dollars if a corporation, or if any other person, one hundred thousand dollars or by imprisonment not exceeding three years, or by both said punishments, in the discretion of the court (economics.fundamentalfinance.com n.d.).

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seem to harm competition. Practises like tying, are regarded as vertical restraints and according to the European Competition Commission are harming consumers. While franchise contracts entailing only a franchise fee are in fact vertical separation which according to Bonnano and Vickers (1988) are beneficial to manufactures.

In this thesis, I will attempt to answer the following research question and sub-question:

What are the welfare effects of tying arrangements in franchise contracts and under which conditions an upstream firm (franchisor) prefers a tying arrangement over charging only a franchise fee?

The purpose of this paper is to answer the above question.

I will base the analysis of the model on the Siegel v. Chicken Delight Inc. tying case. The methodology that I will be following in this paper consists of a literature review and a game theoretical model. In Chapter II, I will start by introducing the definition of tying arrangements in franchise networks and then discuss how the E.U. and the U.S. are treating illegal cases of tying arrangements in franchise contracts. In addition to that, I will refer in more detail to a paper by Ahlborn, Evans and Padilla (2004) that presents the treatment and a critique of tying cases in the U.S. and E.U. Following that I will present certain reasons that justify tying by upstream firms. Furthermore, I shall be referring to some data concerning the opinions that downstream firms have about their existing franchise contracts. Finally, I shall provide an overview of theoretical models in the past literature concerning tie-in sales and relevant papers that addressed the matter.

In Chapter III, I will analyse the welfare effects of such tying arrangements through the use of a game theoretical model. I begin by assuming a risk neutral downstream firm to depict the benchmark case and the standard case. In the standard case there are two upstream firms the franchisor which the incumbent and the competitor. The upstream incumbent does not implement a tying arrangement and charges a franchise fee to the downstream firm. The upstream competitor supplies the inputs to the downstream firm and in the downstream market there is a monopoly situation. I will also be introducing the quality control aspect, in the form of a demand function that will be interpreting the upstream firm’s argument, stating that in the presence of a tying arrangement, increased demand is driven by the better quality of the final product. The framework of the model will be based on the discussion of the case by Bates (1972) and the court proceedings of that case. A further development of the model will be the assumption of a risk averse downstream firm to further examine the standard case under a different risk environment.

I begin the analysis by considering a general model of a vertical market. The upstream firm is the franchisor and the downstream firm is the franchisee. The upstream firm sells inputs to the downstream firm, which in the Chicken Delight case include cooking equipment, dip and spice mix and trademark-baring paper products. I will start by examining two main demand cases that the vertical chain faces.

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In all cases of the model, consumers have a linear demand for the final product provided by the franchise chain. In the Benchmark case I introduce the model of a two-part tariff, where the upstream firm sells the inputs to the downstream firm. Both firms are monopolists in their markets. In the Standard case, there are two upstream firms, the incumbent and the competitor. The incumbent charges a franchise fee to the downstream firm and sells its inputs at a wholesale price, while the competitor simply sells the inputs to the downstream firm. The two upstream firms engage in competition á la Bertrand. If the incumbent’s wholesale price is equal to the competitor’s wholesale price, then the downstream firm buys from the supplier with the lowest marginal cost. The market will be modelled as a two-stage game.

In the Quality improvement case3, with a tying arrangement in the franchise contract, the upstream firm is considered to be offering two products to the downstream, the trademark and the inputs. The downstream firm cannot purchase the inputs from a competitor, due to the tying arrangement, but solely from the upstream firm. Additionally, it cannot use the trademark if it does not purchase the inputs from the upstream, or the franchise contract will be terminated. In order to proceed to the welfare analysis of the tying arrangement I have to define the market for the products and the license. The market for the trademark (A) is monopolised by the upstream firm, but the market for the inputs (B) is served by two upstream firms the incumbent and the competitor.

Finally, I will perform an analysis of the free riding problem. In that case I introduce three demand cases with linear functions that will depict the decrease in demand through the deterioration of quality caused from free riding. In that case at least one of the downstream firms will buy the inputs from the upstream firm and the other will try to offer a cheaper (lower quality) version of the product to the consumers. I wish to investigate, from the point of welfare, if a tying arrangement used as a solution to the free riding problem will benefit consumers.

II. Literature Review

The aim of this section is to present the treatment of tying arrangements under the law of competition and to mention and discuss the reasons that a firm might engage in tying. I will also present an empirical analysis on the effects that tying arrangements have in franchising and mention the works on the theory of industrial organisation that describes tying. In section II.A I present the legal background of tying arrangements for the United States and the European Union. In II.B I briefly mention some reasons that justify a tying arrangement from a firm’s side. In the next section II.C I present an empirical analysis on the effects of tying in franchising. In the final section of Chapter II I will refer to the works of economists regarding the theory of tying in industrial organisation.

3_{I will be following the Chicken Delights’ argument presented in the court, that tie-in sales secure the quality of}

the offered final product and therefore the demand from the consumers’ side.

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II.A. Competition Law

Huschelrath (2003) defines a tie-in as such: “A tie-in results when a franchisor sells a good or a service to a franchisee on the condition that the franchisee purchases a second good from the franchisor, that it does not need or it could purchase it by another seller”. This definition is particularly relevant to the case examined in this thesis as it is mentioned in the introduction. According to Huschelrath (2003) tie-ins are responsible for potential harm to the consumers. That is the reason for the United States and the European Union to have legislature for treating such cases.

The European Union and United States legislature have been treating tying cases differently. The European Commission intervenes significantly more compared to the Federal Trade Commission. One can look in history to comprehend the differences. U.S. antitrust law since its establishment, is dedicated to protect competition and to prevent monopolies so that consumers are not harmed. On the opposing side, since the late 1950s, the European Commission was viewing strict competition policy as a means to market integration. It should be kept in mind though, that national European markets were protected by barriers to entry that translates to a larger degree of dominant positions compared to the U.S. The differences in competition policy between the E.U. and U.S. can be attributed to the former European business environment (Belleflamme and Peitz 2015).

In the European legislature, cases of tying arrangements are treated under Article 102(d)4 (TFEU) (ex Article 82 TEC) and Article 1015 since tying might constitute a vertical restraint

4_{Any abuse by one or more undertakings of a dominant position within the internal market or in a substantial}

part of it shall be prohibited as incompatible with the internal market in so far as it may affect trade between Member States. Such abuse may, in particular, consist in: (d) making the conclusion of contracts subject to acceptance by the other parties of supplementary obligations which, by their nature or according to commercial usage, have no connection with the subject of such contracts (European Union, 2013).

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1. The following shall be prohibited as incompatible with the internal market: all agreements between undertakings, decisions by associations of undertakings and concerted practices which may affect trade between Member States and which have as their object or effect the prevention, restriction or distortion of competition within the internal market, and in particular those which: (a) directly or indirectly fix purchase or selling prices or any other trading conditions; (b) limit or control production, markets, technical development, or investment; (c) share markets or sources of supply; (d) apply dissimilar conditions to equivalent transactions with other trading parties, thereby placing them at a competitive disadvantage; (e) make the conclusion of contracts subject to acceptance by the other parties of supplementary obligations which, by their nature or according to commercial usage, have no connection with the subject of such contracts.

2. Any agreements or decisions prohibited pursuant to this Article shall be automatically void.

3. The provisions of paragraph 1 may, however, be declared inapplicable in the case of: (i) any agreement or category of agreements between undertakings, (ii) any decision or category of decisions by associations of undertakings, (iii) any concerted practice or category of concerted practices, which contributes to improving the production or distribution of goods or to promoting technical or economic progress, while allowing consumers a fair share of the resulting benefit, and which does not:

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(European Commission 2010). In the U.S. tying agreements are treated under Section 1 of the Sherman Act6. Particularly, in the U.S. the Sherman Act can work in conjunction with the Section 3 of the Clayton Act7. Also the Federal Trade Commission has the power to take action under Section 5 of the Federal Trade Commission Act8 to eliminate tying arrangements where they are deemed to be “unfair methods of competition” (Bates 1972). There are three important tying cases in the E.U. The first one was the Hilti case in which “the sale of nail cartridge strips (for nail guns) was conditional upon the customer buying a corresponding complement of nails”. The Commission ruled that Hilti’s practices “leave the consumer with no choice over the source of its nails and as such abusively exploit it (IV/30.787 and 31.488 – Hilti, para 75)”. Another case was Tetra Pak II which it contained the “obligation that only Tetra Pak cartons were to be used in Tetra Pak packaging machines and that cartons were to be obtained exclusively from Tetra Pak”. The court ruled that “when an undertaking in a dominant position directly or indirectly ties its customers by an exclusive supply obligation, that constitutes an abuse since it deprives the customer of the ability to choose its sources of supply and denies other produces access to the market”. The third case concerned Microsoft and was about the “technological integration of Windows operating system and Windows Media Player”. The Commission decided on a five-step test to determine the abuse of dominance: “a) Dominance in the tying market, b) the tying and tied goods must constitute two separate products, c) coercion: Customers have no choice of obtaining the tying product without the tied product, d) foreclosure effect on competition and e) no objective justification”. The court confirmed the decision (Østerud n.d.).

(a) impose on the undertakings concerned restrictions which are not indispensable to the attainment of these objectives;

(b) afford such undertakings the possibility of eliminating competition in respect of a substantial part of the products in question. (European Union 2008)

6_{Every contract, combination in the form of trust or otherwise, or conspiracy, in restraint of trade or commerce}

among the several States, or with foreign nations, is declared to be illegal. Every person who shall make any contract or engage in any combination or conspiracy hereby declared to be illegal shall be deemed guilty of a felony, and, on conviction thereof, shall be punished by fine not exceeding one million dollars if a corporation, or, if any other person, one hundred thousand dollars or by imprisonment not exceeding three years, or by both said punishments, in the discretion of the court(economics.fundamentalfinance.com n.d.).

7_{It shall be unlawful for any person engaged in commerce, in the course of such commerce, to pay or grant, or}

to receive or accept, anything of value as a commission, brokerage, or other compensation, or any allowance or discount in lieu thereof, except for services rendered in connection with the sale or purchase of goods, wares, or merchandise, either to the other party to such transaction or to an agent, representative, or other intermediary therein where such intermediary is acting in fact for or in behalf, or is subject to the direct or indirect control, of any party to such transaction other than the person by whom such compensation is so granted or paid (Clayton Act, 15 U.S.C. §§ 12-27, 29 U.S.C. §§ 52-53 n.d.).

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The treatment of tying cases under U.S. antitrust law has undergone significant changes over time. There are three main approaches. In the early period there was the per se approach. That was changed to a modified per se illegality approach and thirdly, the Microsoft III case introduced a rule of reason approach towards tying (Ahlborn, Evans and Padilla 2004).

Under the per se illegality approach, the courts accepted that some form of economic or market power was a necessary condition for harmful tying. Based on their assumption that tying did not have any extenuating features, they did not address whether market power was also a sufficient condition. Additionally, they did not appear to have recognised that tying was a common practise among firms with little or no market power and therefore must have served some “purpose beyond the suppression of competition”. Regarding the situation in the E.U., the issue of tying law has been addressed largely in the context of the control of abusive behaviour of dominant firms and in the scope of the control of exclusionary agreements. Although, the United States and the European Union have different policy instruments to treat illegal tying arrangements, the two analytical frameworks are similar to each other (Ahlborn, Evans and Padilla 2004).

Quaintly, the fact that the United States and the European Union have used different policy instruments to deal with tying has led to a parallel path for the two frameworks. This is partly because the requirement of “sufficient market power” of the tying firm under the U.S. law matches closely the “standard of dominance” under E.U. law. Compared to the concept of monopoly power under Section 2 of the Sherman Act9_{. Both systems investigate tying} arrangements, when the level of sufficient market power is surpassed by a firm. It is difficult to compare the treatment of tying arrangements in U.S. and E.U. competition law, due to the fact that the European Commission and the European Court have dealt with a small number of old tying cases. Finally, the E.U. competition policy has not involved much in assessment of tying over the last 40 years, while the U.S. antitrust law was on the heels of economic thinking (Ahlborn, Evans and Padilla 2004).

II.B. Reasons for a Tying Arrangement

In this section I shall be outlining some arguments and reasons in support of tying arrangements and ultimately some proposed remedies for antitrust. Some reasons for a tying arrangement are: a) The absence of a rival firm. b) Tying a complementary product when its competitors sell superior complementary products. c) Product specific scale economies make

9_{Every person who shall monopolise, or attempt to monopolize, or combine or conspire with any other person}

or persons to monopolise any part of the trade or commerce among the several States, or with foreign nations shall be deemed guilty of a felony, and, on conviction thereof, shall be punished by fine not exceeding one million dollars if a corporation, or, if any other person, one hundred thousand dollars or by imprisonment not exceeding three years, or by both said punishments, in the discretion of the court (economics.fundamentalfinance.com n.d.).

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tying efficient. d) Control of uniform quality throughout the franchise network. e) The downstream firm can purchase the necessary inputs at a lower price.

The first reason for tying is efficiency, as far as physical ties are concerned. A physical tie is when a product is physically and not contractually linked. Such as, cars and shoes. It is impossible to imagine a car being sold as a group of separate products: tires, wheels, radio, engine e.t.c. Also, a pair of shoes is usually sold along with shoe laces and not separately. “Transactions costs are reduced since consumers want to purchase the product as a whole” (Viscusi, Harrington, Jr and Vernon 2005).

Carlton and Gans (2010) focus on the more realistic case of reversible ties10 and develop a new rationale for the practice in which a monopolist ties a complementary product to alter the outcome of the pricing game between itself and the rival producer of the complementary good. They find that the motive for tying in that case is the absence of a rival firm.

However, this type of tying is not efficient when a competitor is in the market. It is made clear that a firm ties a complementary product when its competitors sell superior complementary products. This example of tying can be seen in Microsoft’s behaviour of tying several complementary goods such as instant messaging, movie and photo editing and security programs. They note that while tying is welfare decreasing, the results do not justify antitrust intervention. They point out that antitrust policy, under certain circumstances, should not be hostile on certain types of vertical contracting and mergers, as they might prove to be welfare improving (Carlton and Gans 2010).

A further reason that tying occurs, is that product specific scale economies make tying efficient. When a firm limits product selection, “e.g. refusal to sell the tied good without the tying good”, firms can reduce total costs. Although, product specific scale economies, are able to motivate tying in a competitive market they can also lead to tying when firms have sufficient market power to do so (Evans and Salinger 2005).

Another important factor that supports tying arrangements is the quality control argument. It appears reasonable for upstream firms to specify the quality of inputs to be used by downstream firms, rather than force them to purchase the inputs from a particular supplier. However, even if the quality of the input is specified in the contract, the tie could be characterised as a “contract enforcing mechanism”. Due to the incentive to “shirk” on quality, that a franchise contract creates, “tie-in contracts are likely to be sufficient policing devices” (Klein and Saft 1985).

Hunt and Nevin (1975) state two primary justifications that upstream firms give in favour of tying arrangements. The first one is that the downstream firm can purchase the necessary inputs at a lower price, using volume purchases and the second reason is that the

10_{“A reversible tie means that a consumer who purchases a tied product from the monopolist can add the}

alternative producer’s complementary product to its system, although it cannot return (as a refund) the tied product. The consumer has both, but utilises one” (Carlton and Gans 2010).

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requirements are necessary to insure uniform quality throughout the franchise network. There are examples of upstream firms, which indicate their mass purchasing power in their brochures as an advantage of joining a franchise network. One of such brochures states: “Negotiate volume contracts with all purveyors and suppliers. These contracts are based on high quality and low prices. The upstream firm makes all items available to the individual operator at the exact price of the contract. The overall advantage of this centralised buying power reflects a saving to the operator of approximately 4 percent of his gross, for which he is paying only 2.5 percent”.

Many upstream firms also argue that purchasing requirements is the only effective means of ensuring quality control. According to William Sandberg, contributing editor of the

Franchise Journal, “there are numerous cases where downstream firms have completely

ignored quality standards when the upstream firm forgoes strict control over the franchisees' purchasing procedures”. A. L. Lapin, Jr., past president of the International Franchise

Association, “contends that upstream firms, downstream firms and American consumers are

all harmed when quality control cannot be assured”. He highlights that: “The upstream firm, which cannot be assured of its ability to direct the uniformity and preserve the quality of its product, will simply choose to cease franchising. The downstream firm, that cannot be assured that the consumer acceptance of its franchised goods or services can be protected by the franchisor, will have lost much of the value of its investment. The American consumer cannot be but harmed, by the impairment in quality and the decrease in confidence of the individual outlet which will inevitably flow from the atrophy of the franchising system” (Hunt and Nevin 1975).

An additional argument for tying is that it is away to avoid price regulation. For instance, “in the 1970s, when gasoline was under maximum price control, the excess demand was great”. Since the prices could not be increased in order for the market to clear, a gasoline station could tie its gasoline to other products or services to avoid the price regulation. It was alleged that one station has offered gasoline at the controlled price to anyone who bought a rabbit’s foot worth 5$ (Viscusi, Harrington, Jr and Vernon 2005).

In specific cases tying could serve as a benefit to consumers. Schwartz and Werden (1996) developed a model in which consumers cannot observe the quality of a durable good before purchasing it and they are vulnerable to monopoly pricing of tied complements. “Only if there is a way for the sellers to signal its high quality to consumers, then the product is offered”. They assume that while “a high price cannot adequately signal quality, tying can achieve that, provided that demand for the complements is sufficiently greater with the high-quality good than with the low-high-quality good”. Under this framework tying is permitted “only if consumers are benefited”. Thus, tying is not used “to exploit informational imperfections, to the detriment of consumers on the contrary, it serves to overcome informational imperfections, so that consumers are benefited”. They also note, that the quality signalling rationale for tying does not explain the majority of tying cases. However, “it provides a plausible rationale for efficiency regarding tying that should be considered before tying is condemned”. In Kodak, “where the market for the durable good appears to be competitive

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and consumers do not have sufficient information about the quality of the product, this rationale might help to explain tying”.

Finally, I will refer to some antitrust remedies that have been proposed, regarding tying arrangements. According to Grimes (1996) “it is very important to have a balanced and grounded in economics antitrust policy toward franchising that can be a constructive force for others systems to follow”. The approach that is proposed is the incorporation of economic learning with regards to market power in the relationship between an upstream firm and a downstream firm. This insight is consistent with traditional antitrust case law. “The possibilities regarding antitrust remedies for disgruntled franchisees are limited by a discrete set of precedents that, for the most part, limit the availability of antitrust relief”. “Such disturbing precedents are those that insist that market power in the franchise context must be proven by a surrogate relevant market definition” This definition, “ignores the real source of most upstream firm’s market power, that the downstream firm has high sunk costs”. With the passing of time, sound economics, supported by antitrust policies that recognise the potential anticompetitive injury from abuses of single brand market power, will prevail (Grimes 1996). My analysis supports the rule of reason approach for tying arrangements in franchise contracts. Through the use of a game theoretical model I show that tying should not be regarded as per se illegal. I present two cases in the following model where tying arrangements can be regarded beneficial for downstream firms and consumers. Those instances in which tying arrangements are not harming competition are: a) When a downstream firm is highly risk averse and b) when free riding occurs in a franchise chain. In the former case, tying is used a means of risk sharing between an upstream firm and a downstream firm, when the market environment that the downstream firm is called to operate is risky. In the latter case, tying is used as a way of ensuring the upstream firm’s profits and the uniform quality of the final product which is offered to consumers.

II.C. An Empirical Analysis on the Effects of Tying in Franchise

Contracts

Hunt and Nevin (1975) collected data from a national sample of 664 completed questionnaires from downstream firms’ in the fast-food restaurant industry, to better understand how tying arrangements in franchise contracts affect franchising. The sample was drawn from the yellow pages of telephone directories.

Regarding the extent of the practice, the results of the survey indicated that about 70% of the responding downstream firms were required to purchase at least some of their operating supplies from their upstream firms. Additionally, 50% of the supplies purchased by upstream firms were necessary for the operation of the downstream firm. So, tying arrangements affect a great majority of downstream firms, which are obligated to purchase at least some of their supplies from their upstream firms. As far as the prices charged for supplies, the results showed that only a “24.8% of the downstream firms thought that they paid lower prices to the

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upstream firms than they would pay to a competitor”. However, “47.0% believed that they paid higher prices when they were buying from the upstream firm, while 28.2% perceived that the prices they paid to their upstream firms were about the same as in a competitive market”. Moreover, “the effects of purchase requirements were determined with the use of an F test”. They determined that downstream firms that were required to purchase inputs from upstream firms had “significantly lower incomes than downstream firms not required to purchase their inputs from their upstream firms”. In this study, the downstream firms’ “income included profit plus owner's salary and any salaries paid to spouse and unmarried children”. The results also indicate that the proportion of supplies downstream firm were required to purchase from their upstream firms “was negatively related to both measures of downstream firm satisfaction”. Downstream firms “that did not plan to renew their contracts were required to purchase a significantly higher percentage of their supplies from their upstream firms than downstream firms that planned to renew their contracts”. Likewise, “downstream firms which were very dissatisfied with the profitability of their business were required to purchase a high percentage of their inputs from the upstream firm, while downstream firms that were very satisfied with the profitability their franchises purchased a smaller proportion from their upstream firms”. The results also show “that the prices that a downstream firm paid for inputs were negatively related to both measures of downstream firm satisfaction”. Downstream firms that “did not plan to renew their contracts reported paying higher prices” to their upstream firms for supplies than “downstream firms that did plan to renew their contracts”. Downstream firms that “indicated dissatisfaction with the profitability of the franchise also reported paying higher prices to their upstream firms for supplies than downstream firms that indicated satisfaction with the profitability of their upstream firms” (Hunt and Nevin 1975).

II.D. Industrial Organisation Theory

In this part I will be discussing some works of the economists who dealt with the practise of tying in franchise contracts and I will be briefly mentioning some of the benefits that vertical separation offers to upstream firms.

The practise of franchising is in fact vertical separation. The paper of Bonnano and Vickers (1988) develops a simple duopoly model to show “the advantage that a manufacturer has when selling its product through an independent retailer (vertical separation) rather than directly to consumers (vertical integration)”. Amongst others they consider the case where “franchise fees can be used to extract retailers' surplus”. An intuitive approach is that “vertical separation is profitable as it induces more friendly behaviour from the rival manufacturer”. In the oligopolistic market, where the model is developed, “the disharmony of interests between the upstream firm and the downstream firm entailed by vertical separation may be used to the advantage of the manufacturer”. The results of their study show that “vertical separation with wholesale prices in excess of production costs is profitable when franchise fees are fully extracted”. Additionally, they have proved that “vertical separation, alongside with an appropriate contract between the upstream firm and the downstream firm,

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can be a profitable strategic move”. They conclude by stating that, vertical separation and vertical arrangements in general require more consideration.

There are many papers that have been engaged in developing and analysing a model for tying. I shall present those that I consider most useful and close to the topic of the analysis that will be presented in this thesis. Burstein (1960) developed a model of tying by assuming that the tying and tied goods are independent in demand and concludes amongst others that the complementarity of the tying and the tied good is not essential to the rationale of a tie-in sale. The tying arrangement is seen as way of extracting the profit in an “all or nothing”11 selling arrangement. The model that is used in the paper is static but tying arrangements can also be viewed dynamically. Additionally, Burstein shows that “tying arrangements can be viewed in a context apart from extension of monopoly or exclusion of entry”.

Blair and Kaserman (1978), developed a simple formal model to provide a formal proof of Burstein’s proposition12, that “the upstream monopolist could obtain identical results by tying the purchase of non-monopolised substitutable inputs to the purchase of the intermediate product over which the monopolist exercises control” and to briefly determine the antitrust issues raised. The intuition behind the aforementioned proposition is that the monopolist of an intermediate product, has an alternative to the strategy of vertical integration which may be employed in circumstances where ownership integration is either feasible or unattractive. The main result is, that the firm holding monopoly power over an input for which substitutes exist must select between alternative strategies, on the basis of factors that lie outside the simplified model discussed. It was also demonstrated that vertical integration and tying arrangements are “alternative paths to obtain exactly the same result”. Finally, they conclude by arguing that while “vertical integration by a merger receives a rule of reason approach by the court, tying arrangements are treated severely as per se violations of Section 1 of the Sherman Act or Section 3 of the Clayton Act”. This treatment seems dangerous as a similar economic result can be obtained at a higher cost for welfare.

Another important paper is by Whinston (1990), in which he develops a theoretical model to depict the leverage of tied sales and argues that tying can serve as a mechanism for leveraging market power13_{. The intuition is that tying can indeed serve as leverage for market} power. He concludes by saying, that “if someone allows for scale economies and strategic interaction to exist, tying can make continued operation by a monopolist’s tied market rival, unprofitable by leading to the foreclosure of the tied good sales”. The models used indicated

11_“_{An all-or-nothing demand curve can be explained by determining the maximum amount a consumer would}

pay for x units of a good if confronted with the choice, of purchasing x units or none at all. It is, of course, true that, if we observe a consumer purchasing x units in an unrestricted market at the going price p, he would generally be willing to pay more than $xp on an all-or-nothing basis for the x units. The difference is the consumer surplus” (Burstein 1960).

12_{“Theory of Full-Line Forcing, Northwestern University Law Review, March/April 1960-1961, 55, 62-95”.} 13_{“Tying provides a mechanism whereby a firm with monopoly power in one market can use the leverage}

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that such a strategy can be profitable for a monopolist, due to its exclusionary effect on market structure.

An additional paper by Choi and Christodoulos (2001), developed a simple formal model to “depict the way that tying affects the investment incentives of entrants, strengthening the monopoly position of an incumbent”. A very important addition to the model is a risky upfront investment in research and development. A potential entrant can enter the market if it succeeds in innovating and obtaining a superior technology. The probability of the entrant to success depends on the amount of money spent for research and development. The intuition is, that in this framework, “the tying of two complementary components by a monopolist credibly makes entry in one component completely dependent upon success in the other”. The paper showed that tying may lead to less certain prospects of entry, discouraging the incumbent’s rivals from investing and innovating. Under these circumstances tying might lead to lower total welfare. The above argument “is only applicable when the prospects of investment are uncertain”. “In practise, the threat of entry in one of the components may not exist, so the incumbent might not use tying to defend its position”.

All the aforementioned papers proved that tie-in sales reduced consumers’ surplus in the markets.

III. Theory

In this chapter, I will be developing the model and the theory in order to answer my research question. The chapter is divided in three main sections. In section III.A I examine the topic by assuming a risk neutral retailer that operates in four different types of frameworks. The first one is the Benchmark case where I present the notion of two-part tariffs as a solution to the double marginalisation problem. I call the second case, Standard case, because I present the simple case of franchise contract with a franchise fee. The third one is the Quality Improvement case where the upstream firm imposes a tying arrangement in the franchise contract with the downstream firm and charges a zero franchise fee. I also present a hybrid case of a tying arrangement in a franchise contract with a franchise fee.

In section III.B. I make a new assumption regarding the downstream firm in which I assume to be risk averse. This section includes only the Standard case with a franchise fee and without a tying arrangement, as the analysis shows no need for an additional case. Finally, I present and discuss the results of both sections in section III.C.

The last section of the model is devoted to the free riding problem that is inherent in franchise networks. I show, through the use of game theory, that free riding does happen in franchise networks. Furthermore, through the use of a game theoretical model I analyse the effects that free riding has on the welfare. I present the results in section III.E. I also propose some

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solutions to the problem, in particular how and why tying can solve the problem of free riding.

I begin the analysis by considering a simple model of a vertical market. The market consists of two upstream firms (the franchisor and a competitor), one downstream firm (the franchisee), and consumers. The upstream firm sells inputs to the downstream firm and the downstream firm to the consumers.

If the downstream firm uses an upstream competitor’s input, consumers have a demand of: 𝑑(𝑃) = 𝑎 − 𝑃, 𝑎 > 0.

In the case of a tying arrangement when the downstream firm uses the franchisor’s input, consumers have an increased demand of:

𝐷 𝑃 = 𝑏 − 𝑃, 𝑏 > 𝑎.

III.A. Risk Neutral Retailer

III.A.a. The Benchmark Case

In the vertical market of figure 1, the upstream firm, is the monopolist. The downstream firm, which is also a monopolist in its own market, distributes the product to the consumers. The upstream firm with marginal cost of 𝑐_/ sets the wholesale price 𝑃₀ for the inputs that sells to the downstream firm and the franchise fee 𝐹 which is a payment to the upstream firm by the downstream firm. The downstream firm with marginal costs of 𝑐₂ sells the final product to the consumers at a retail price of 𝑃₂ and pays the franchise fee to the upstream firm. The total marginal cost of the chain is: 𝑀𝐶₆ = 𝑐_/+ 𝑐₂. In this type of market structure an inherent issue exists, the so-called double marginalisation problem14. Figure 1 depicts the resulting Benchmark case.

14_{The inefficiency arises because he retailer does not take into account the externality exerted on the upstream}

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Figure 1, Benchmark case

List of Variables 𝑃₀: Wholesale price. 𝑃2: Retail price.

𝑃₈: Competitor’s wholesale price.

𝐹: Franchise fee (payment to the upstream by the downstream firm). 𝑐_/: Marginal costs of the upstream firm.

𝑐₈: Marginal costs of the competitor firm. 𝑐₂: Marginal cost of the downstream firm. 𝑀𝐶₆: Total marginal cost of the chain. The market is modelled as a two stage game.

Stage 1: The upstream firm determines the wholesale price for the inputs 𝑃₀.

Stage 2: The downstream firm chooses the price 𝑃₂ for the final product that is going to be sold to the consumers.

An obvious solution to double marginalisation problem would be vertical integration. In this paper though I will be looking at the alternative solution, because it corresponds better to the Chicken Delight case, which is a two-part tariff in the form of a franchise fee 𝑇(𝑞) = 𝐹 + 𝑃₀. The interpretation of this solution is to sell the whole business to the downstream firm for a price equal to the monopoly profit and then the downstream firm becomes the “residual claimant”.

Assumption 1: One-to-one production technology, i.e., for every meal sold the downstream

firm uses one item of the tied product.

Upstream

F, P

_w

Downstream

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Proposition 1:

A two-part tariff in the form of a franchise fee maximises the profit of the vertical chain. An intuitive approach, would be that when the upstream firm sets the wholesale price equal to its marginal costs, it profits from the franchise fee that is levied from the retailer. As a result, the profit maximising level equals to the profit of the downstream firm, so that the upstream firm receives all the profits.

Proof:

In Appendix A

III.A.b. The Standard Case

First, I will perform a welfare analysis of the case by assuming no tying between the upstream firm and the downstream firm. The upstream firm charges a franchise fee 𝐹 to the downstream firm. The upstream with marginal cost 𝑐_/, sells the inputs to the downstream firm at a wholesale price of 𝑃₀ and charges a franchise fee 𝐹 to the downstream firm. The downstream firm with marginal cost of 𝑐₂, sells the final product to consumers at a retail price of 𝑃₂ and pay its franchise fee to the upstream firm. In the market for inputs there is also a competitor with marginal costs of 𝑐_/ > 𝑐₈ which offers them to the downstream at a wholesale price of 𝑃₈. The downstream firm with marginal costs of 𝑐₂, 𝑐_/ > 𝑐₈ > 𝑐₂ sells the final product to the consumers at the price of 𝑃2.

The two upstream firms engage in competition 𝑎 la Bertrand. If 𝑃₀ = 𝑃₈ the downstream firm buys from the lowest cost supplier, 𝑐_/ > 𝑐₈.

Assumption 2: 𝑏 = 𝑎.

The market is modelled as a two stage game.

Upstream

_Competitor

Downstream

Consumers

Figure 2, Standard case

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Stage 1: The upstream firm chooses the franchise fee 𝐹 and the wholesale price for the inputs 𝑃₀. The competitor chooses the price 𝑃₈. Both firms choose their prices independently.

Stage 2: The downstream firm chooses the price 𝑃₂ for the final product and pays the franchise fee 𝐹.

Proposition 2:

A franchise contract with a franchise fee yields higher welfare and profits than of a franchise contract with a tying arrangement and without a franchise fee.

That might be true, because a tying arrangement has the ability to foreclose the efficient competitor from the market and it allows the upstream firm to set a price for inputs, higher than the marginal costs and close or equal to the monopoly price.

Proof:

In Appendix A.

III.A.c. The Quality Improvement Case

Second, I will analyse the welfare effects of the quality improvement case. In that case I will be looking at a market where consumers have demand of 𝐷 𝑃 = 𝑏 − 𝑃, 𝑏 > 𝑎. Consumers’ demand is depended on the quality that the brand name carries, which depends on the Chicken Delight meals. Now the upstream firm is considered to be offering two products to the downstream, the trademark and the inputs. The downstream cannot purchase the inputs from a competitor, due to the tying arrangement, but solely from the upstream and it cannot use the brand name if it does not purchase the inputs from the upstream, or the franchise contract will be terminated.

However, in order to proceed to the welfare analysis of the tying arrangement we have to define the market for the products and the license. The market for the trademark (A) is monopolised by the franchisor, but the market for the inputs (B) is served by two upstream firms the franchisor and a competitor firm.

The upstream firm in my model, as in the Chicken Delight case will not charge a franchise fee, sales royalties or similar franchise charges. The marginal costs for the upstream firm that provides the inputs are 𝑐_/ and for the competitor 𝑐₈ < 𝑐_/. The upstream firm offers the inputs to the downstream at the price of 𝑃₀<_{and the competitor at}_𝑃

8<. Since there is a tying

arrangement in the contract, the upstream firm can set a price for the inputs that is above the marginal costs and can be regarded equal to the monopoly price. The downstream firm has marginal costs 𝑐₂ and sells the final product to the consumers at the price of 𝑃₂<_.

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Now the downstream firm is faced with an all or nothing choice. It can either a) accept the tying arrangement in the franchise contract and purchase the inputs only from the upstream firm or b) reject the tying arrangement and as a result lose the franchise contract. If the downstream firm accepts the contract, we have monopolisation in both markets and if it rejects it, we return to the previous case. When the contract with the tying arrangement is accepted the competitor is unable to sell products to the downstream firm.

The market can be modelled as a two stage game in the case where the franchise contract with the tying arrangement is accepted by the downstream firm.

Stage 1: The upstream firm chooses the wholesale price for the inputs 𝑃₀<_.

Stage 2: The downstream firm chooses the price 𝑃₂<_{for the final product that is going to be}

sold to the consumers.

III.A.d. The Standard Case with a Tying Arrangement

After the analysis of the above major cases I look at the case in which along with the standard franchise contract offered to a downstream firm (including a franchise fee), there is the addition of a tying arrangement in it. I will not engage in lengthy calculations as this case can be modelled as a synthesis of the III.A.b and III.A.c cases. As a result, the relations for profits in case III.A.c can be altered to depict this case, with the addition of the franchise fee. In that case welfare is the same with case III.A.c, because the franchise fee in the profits of the upstream and downstream firm cancels out in the welfare relation.

Proposition 3:

A franchise contract with a franchise fee and a tying arrangement yields lower welfare than a franchise contract entailing only a franchise fee.

The effect that the tying arrangement in the franchise contract has on competition can not be offset by the presence of the franchise fee. The tying arrangement between the upstream firm and the downstream firm forecloses the upstream competitor from the market and this results in lower welfare. Proof: In Appendix A.

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III.B. Risk Averse Retailer

III.B.a. The Standard Case

Now, I will consider a risk-sharing case, between the upstream and the downstream. I will estimate the risk premium that the upstream firm offers to the downstream in order for the second to enter the franchise network. To achieve this, I will first have to derive the expected profits of the downstream as a function of the demand factor 𝛾, which is not random.

In that case the game evolves as follows:

Stage 1: The upstream firm offers a franchise contract to the downstream (𝐹, 𝑃₀>?₎

Stage2: The downstream firm accepts or rejects the contract

Stage 3: If the contract is accepted, the downstream firm chooses the retail price, 𝑃₂>?_.

If the contract is rejected, the profit of the downstream firm is Π₂>? _{= 0.}

Stage 4: Nature draws 𝛾~𝑁(𝜇, 𝜎E₎

Demand from the consumers’ side is formed as: 𝐷>? 𝑃2>? = 𝛾(1 − 𝑃2>?)

Assumption 4: Utility of the downstream firm is u x = −𝑒JKL _with

x: profit of the downstream firm.

Proposition 4:

If a downstream firm is highly risk averse, then the upstream firm prefers a contract with a tying arrangement over a contract that includes only a franchise fee.

This is might be the case because the downstream firm is called to operate in a risky environment, where it has to pay the upstream firm a large amount of money in the form of a franchise fee, while facing a random demand with uncertain profits for itself. Thus, the prospective downstream firm will accept the contract if the fee is low enough. So, the upstream imposes a tying arrangement in the contract and charges a zero franchise fee, in order to mitigate the risk for the downstream firm through sharing it. This case could also be approached as the principal agent problem, where the principal being the upstream firm would like to offer a franchise contract to a downstream firm in order to share the risk of distributing the final product with its own means. The agent, being the downstream firm, is risk averse and wants to be reassured of its “investment”, so the downstream firm requests a contract that will be able to provide it with enough profit to allow it to operate in a high risk environment.

Proof:

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III.C. Results of sections III.A. and III.B.

I will compare the profits of the upstream firm and the welfare in the market for the two aforementioned cases. From relations (12) and (25) in Appendix A we can see that the retail price in the quality improvement case is higher than the retail price in the standard case. This is true, because in the quality improvement case where the upstream firm engages in tying it acquires more market power and is able to set a higher price than the price it charged without the tying arrangement. As a result, consumer surplus for the case with the tying arrangement is less than the consumer surplus in the case with the simple franchise contract.

The relations (9) and (10) in Appendix A posit that the profit of the upstream firm is lower or equal to the profit of the retailer. The intuition behind it is that the upstream firm leaves a part of the profit to the downstream in order to have an incentive to operate.

Furthermore, from relations (27) and (28) in Appendix A it is shown that the profit of the upstream firm is higher than the profit of the downstream firm.

Consequently, from relations (15) and (27) in Appendix A, the profit of the upstream firm in the standard case is lower than the profit of the upstream firm in quality improvement case. Moreover, regarding the profits of the retailer, from relations (14) and (28) in Appendix A I found that the profit of the retailer in the standard case is lower than the profit of the retailer in the quality improvement case. It should also be noted that in the quality improvement case the profit of the competitor is zero due to the tying agreement that does not permit the downstream firm to purchase inputs from it.

Regarding welfare, from all the above comparisons it can be deducted, that welfare for the standard case is greater than the welfare of the quality improvement case. This seems to create a dent in the argument of upstream firms, that tying increases the quality of the offered product or service and therefore the welfare.

Finally, in section II.A.d. it can be seen from looking at the relations of profits, consumer’s surplus and welfare that a contract with a franchise fee and a tying arrangement delivers the same results, as far as welfare in concerned, as a contract with only a tying arrangement. As a result, when a tying arrangement is present in a franchise contract, the downstream firm and the market environment are risk neutral, then tying has deleterious effects for the consumers in that market.

Additionally, in order to acquire a more holistic picture of the topic, I further proceeded into examining the above cases when the downstream firm or the market environment is risk averse. In Appendix B and from relation (47) the franchise fee might also be negative. If the franchise fee is negative, then the upstream firm has to pay the downstream firm in order to join its franchise network. This means possibly that the downstream firm is highly risk averse or that is asked to operate in a high risk environment. So, if the downstream firm becomes more risk averse (𝜌 ↑) then the franchise fee decreases (𝐹 ↓) or if the market environment becomes more risky (𝜎E _{↑) then the franchise fee decreases too (𝐹 ↓). To sum up, the results}

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firm when the first is highly risk averse or the market environment that has to operate is highly risk averse, is for the upstream firm to charge a zero franchise fee. The upstream firm is possible to attract the downstream firm into participating in the network profits if it offers a tying arrangement. This of course will affect the welfare of consumers, but it will solve the upstream firm’s problem. Other solutions include sales royalties and profit sharing.

III.D. The Free Riding Problem

Finally, I will perform an experiment of the free riding problem, which will be developed as a “prisoners’ dilemma” type of game, where at least one of the downstream firms will buy the inputs from the upstream firm and the other will try to offer a cheaper (lower quality) version of the product to the consumers. I wish to investigate from the point of welfare, whether a tying arrangement is beneficial and can solve the free riding problem.

It is recognised though, that tying as a form of vertical restraint solves several incentive problems and agency costs, every franchise network might face. An example of it would be that tying assists into solving or even eliminating the free riding on the inputs purchased by the downstream firms. Since downstream firms purchase all the inputs exclusively from the upstream firm. “An essential aspect of a franchise network is to create a standardised product. By expanding the standardisation in a franchise network, the consumers expect the same level of quality at various retail locations and create valuable information”. “Standardisation allows the consumer to transfer the information it possesses on all its previous experiences on a franchise chain”. The consumer also expects the upstream firm to standardise and control the quality across outlets and is willing to pay a price for this service (Klein and Saft 1985). It is evident that as the quality information applies to a franchise network of downstream firms using the same name, a free riding problem is created. Consumers cannot normally detect the quality of the product before they purchase it. So if each downstream firm is supplied with inputs that significally influence the quality of the offered product, then it will have an incentive to reduce costs, offer a lesser quality product and have increased profits. This will result to the consumer blaming the entire franchise network baring the same trademark and the other downstream firms will share the losses caused by a decrease in the demand, while the individual downstream firm that free rode will be directly benefited from the lower quality product (Klein and Saft 1985).

According to Mathewson and Winter (1985) there are two kinds of free riding: The first is when an agent can free ride on the national brand name (vertically) and the second when an agent can free ride on the local quality of other agents (horizontally). “With national brand names created and leased by the franchisor, vertical externalities are always present, horizontal externalities are not necessary to explain franchise contracts and restrictions as these arise even with a single franchisor an agent”.

Additionally, another way that the free riding problem is revealed in a franchise network is through the use of a national brand name by a local franchise network of downstream firms.

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After the two parties agree on a franchise contract the downstream firms must make decisions on prices, “sales effort” and any “contribution into the quality of the final product”. It should be mentioned that the “manufacturer continues to invest in advertising, product quality and the product’s brand name”. In theory, it would be possible to completely specify all decisions in the contract and “efficient (joint profit-maximising) choices could be guaranteed”. However, the costs of enforcing a contract such as the above, specifically the costs of monitoring the decisions of the contractual parties, lead to an incomplete contract. In such a contract, decisions of principal’s or agent’s in the contract will be “undertaken ex post on the basis of the unconstrained self-interest of the decision-maker given the incentives provided by the contract, to the extent that this self-interest deviates from the collective interest of all parties to the contract an agency cost in incurred” (Mathewson and Winter 1985).

III.D.a. Theory

In this section and in the following subsections, I will develop a model to underpin the profits of the free riding experiment of section III.D.c. The section is divided in three main subsections. In subsection III.D.a.1 I examine the case in which no free riding takes place in the network as a tying arrangement is in place. In the second case, section III.D.a.2, I assume that downstream firm 2 free rides and purchases the inputs from an upstream competitor, while downstream firm 1 does not free ride and continues to purchase the inputs from the upstream firm. The third case, section III.D.a.3, is when all firms in the network free ride and purchase their inputs from the upstream competitor, while paying the franchise fee to the upstream incumbent. In section III.D.b. I present the free riding problem as a “prisoners dilemma” type of game, to show that free riding leads to less profits when all downstream firms in the network free ride. Finally, I present and discuss the results from the analysis of the above cases in section III.D.b.

I begin the analysis by considering a simple model of a vertical market. The market consists of two upstream firms (the franchisor and a competitor), two downstream firms (the franchisees), and consumers. The incumbent upstream firm sells inputs to the downstream firms and the downstream firms sell the final product to the consumers.

Consumers’ demand in the market when neither downstream firm free rides is: 𝐷_{__} = 2 − 𝑃₂__

Consumers’ demand in the market when at least one, but not all, downstream firm free rides is:

𝐷_{_a} = 1 − 𝑃₂_a_{, 𝑑𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚 𝑓𝑖𝑟𝑚 1}

𝐷a_= 1 − 𝑃2a_, 𝑑𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚 𝑓𝑖𝑟𝑚 2

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𝐷_aa = 0.5 − 𝑃₂aa

The downstream firms pay a fixed franchise fee, which is the same for both of them, to the upstream incumbent and they have a tying arrangement so they purchase the inputs from the upstream firm at a wholesale price of 𝑃₀___{. The downstream firms have symmetric marginal}

costs of 𝑐₂, 𝑐_/ > 𝑐₈ > 𝑐₂. The downstream firms sell the final product to the consumers at a retail price of 𝑃₂___.

When downstream firm 2 decides to free ride on the good reputation of the brand name of the incumbent, it purchases the inputs from the competitor at a price of 𝑃_la__{, pays the franchise}

fee and sells the final product to consumers at a price of 𝑃2a_. The two upstream firms engage

in competition 𝑎 la Bertrand. If the wholesale price of the incumbents’ is the same to the competitors’ the downstream firm buys from the lowest cost supplier, 𝑐_/ > 𝑐₈. The downstream firm that does not free ride, continues to purchase the inputs from the upstream firm at the same price as before and sells the final product at consumers at a price of 𝑃₂_a_.

Finally, when both firms free ride they purchase the inputs from the competitor at a price of 𝑃_laa_{, pay the franchise fee and sell the final product to the consumers at a price of 𝑃}

2aa.

List of variables: 𝐹: Franchise fee.

𝑃₀___{: Wholesale price when no downstream firm free rides.}

𝑃0_a: Wholesale price when one downstream firm free rides.

𝑃₂___{: Retail price when no downstream firm free rides.}

Upstream Firm Competitor Downstream Firm 1 Downstream Firm 2 Consumers 𝑃la_ Figure 3, The Free Riding case.

Welfare effects of tying arrangements in franchise contracts : a game theoretical analysis of the Chicken Delight case