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This paper studies how firms use their number of franchises as a strategic tool. Firms can commit to high output by creating many franchises. However, signing a single franchise contract with a low wholesale price is an equally effective way to generate output. The value of granting many franchises is undercut when firms can sign contracts afterwards, so firms place only a single franchise in a market. This finding reverses previous results which did not model contracts. The same issues arise in international competition policy, where countries use anti-trust policy to affect their number of exporters and use subsidies to affect the choices of exporters.

Economists have long been interested in how a firm contracts with its franchisees. But a firm chooses how many franchises with which to contract as well. Recognizing that firms pick their number of franchises in conjunction with franchise contracts has important implications both for market outcomes and for the design of observed contracts. This paper presents a simple model which explores how the choice over the number of franchises interacts with the contracting choice. This paper analyzes a situation where two firms choose how many franchises to use in a Cournot game under perfect information. The firms use franchises to implement strategies which the firms could not commit to on their own. The paper considers the case in which firms can also set up two-part tariffs (a fixed fee and a per-unit wholesale price) in order to change the incentives of the franchisees. Choosing a high number of franchises or a low wholesale price are two ways for the firm to elicit high output. The central result is that the choice over the number of franchises and the choice of contract are interchangeable in the sense that each tool can be used to produce almost any quantity, including the optimal quantity. When one tool is set optimally, there is no gain to adjusting the other. This result is important for solving for equilibrium. This paper studies a sequential game, where firms choose the number of franchises before the two-part tariff. The sequential game reflects the fact that it is easier to change a wholesale price than it is to develop a franchise location. When firms choose the number of franchises first, they recognize that their choice affects their opponent’s choice of two-part tariff. Choosing a large number of franchises is no longer an effective way to capture market share because the opponent can respond with an aggressive contract. In fact, because any level of output which the firm can achieve through the choice of the number of franchises can also be achieved through the choice of the two-part tariff, the only effect of picking a large number of franchises is to commit the opponent to a low per-unit price – the opposite of what the firm wants to happen. In equilibrium, both firms choose to have one franchisee and use the two-part tariff to induce the franchisee to produce high output. The result that firms choose to have one franchise is very different from results found by other researchers. Polasky (1992) considers a model in which firms choose the number of agents to play a Cournot game under a linear demand curve. Polasky’s game is similar to the one in this paper but without the choice over a two-part tariff. Polasky interprets the set-up as a model of divisionalization, divestiture or franchising – any act which credibly creates independent business ventures. He shows that in order to commit to high output, the best response for each principal is to pick more agents than the opponent. When principals simultaneously play such a strategy, there is no equilibrium. Baye et al. (1996) generate an equilibrium in Polasky’s model by introducing a per-agent fixed cost. Under this assumption, firms do not want to choose an arbitrarily high number of divisions or franchises. Baye et al. (1996) show that in the limit as the fixed cost goes to zero, the equilibrium number of agents goes to infinity. Polasky (1992) and Baye et al. (1996) suggest that if fixed costs are low, we should expect to see firms choose a very large number of franchises. I show that in a richer contracting environment, the firm’s optimal choice of the number of franchises is to choose as low as possible. This paper presents a strategic reason, as opposed to a market friction, why we might expect a low number of franchises in a market. By generalizing the previous models in a logical way, the predictions from those studies are reversed. The general question of a principal which chooses both how to contract with agents and how many agents with which to contract arises in a number of economic settings. For instance, Brander and Spencer (1985) analyze a model of countries setting subsidy levels for exporters. It is well known that their result depends on the number of exporters in each country. This paper recognizes that the number of exporters is not exogenous. A country can affect its number of exporters by enforcing or not enforcing anti-trust measures. A model in which principals choose their number of agents can be used to study how countries use competition policy as a tool for strategic trade. This paper interprets the model along the lines of Brander and Spencer (1985) in order to analyze this issue. Efforts to subject competition policy and trade policy to formal economic analysis are recent and rare. However, a number of models which endogenize the choice over the number of agents have appeared under the competition-policy interpretation. Like this paper, Horn and Levinsohn (1997) and Richardson (1997) model competition policy as a country choosing the specific number of domestic exporters, as well as tariffs and (in the case of Horn and Levinsohn) production subsidies. Their papers analyze a range of more complicated situations than this one, notably home consumption and per-exporter fixed costs.1 Many aspects of this paper draw on older results in the economics literature. The fact that there is no equilibrium in the game where two principals choose only the number of agents is closely related to Reynolds et al. (1983). Those authors show computationally that in a Cournot game, firms will gain from a merger only if the merging firms represent a very large share of the market. Clearly, if firms do not want to merge together, then they can gain from splitting themselves up. As suggested above, the presentation of the two-part tariff game draws from Brander and Spencer, 1983 and Brander and Spencer, 1985. My paper extends Brander and Spencer by allowing countries to choose the number of domestic exporters before choosing subsidies. Gaudet and Salant (1991a) present very similar intuition to Brander and Spencer in a more general setting. Fershtman and Judd (1997) allow a firm to determine a managers’ salary as a function of sales and profits. They find similar results to those presented in this paper in the sense that firms use pre-production strategies to commit to the Stackelberg output in the production stage.2 Section 2 considers the two-stage game, where firms choose the number of franchises and then the franchisees set quantity. Section 3 introduces the two-part tariff and shows that the two-part tariff and the number of agents are interchangeable tools by which to elicit high output. Section 4 solves for equilibrium in the sequential game, in which firms choose their number of franchises and then choose their two-part tariff. In order to understand the model better, Section 4 also discusses a simultaneous game, where firms select the number of franchises and the two-part tariff simultaneously, as well as the reversed sequential case, where firms choose wholesale prices first, then their number of franchises. Section 5 reinterprets the model as one of national governments using competition policy as a tool for strategic trade. A final section summarizes the paper and offers some concluding thoughts.

This paper recognizes that in many important principal–agent situations, principals choose how many agents with which to deal in addition to how to contract with the agents. Building on previous work by Polasky (1992) and Brander and Spencer (1985), this paper presents a model which endogenizes the choice over the number of agents in an environment in which principals can write non-linear contracts with their agents. The paper first analyzes a game where principals choose the number of agents but are restricted to being unable to adjust their per-unit price or their fixed fee. Both principals want to have more agents than the other in order to succeed in the quantity-setting game in the final stage. Next, the paper introduces a two-part tariff and shows that setting a two-part tariff and setting the number of agents are interchangeable ways to elicit high production from agents, thereby gaining surplus for the principal. When one tool is set optimally, there is no gain to adjusting the other tool. This feature generates multiple equilibria in the game where principals choose the number of agents and the two-part tariff simultaneously. However, equilibrium is unique in the game where principals choose their number of agents before choosing two-part tariffs. In this case, principals pick only one agent. The reason for this result is that a principal which picks a high number of agents in the first stage simply adjusts its two-part tariff (which is always being set optimally) in the second stage so that there is no direct effect of the choice over number of agents. But choosing a high number of agents does lead the competitor to choose a low per-unit price, which hurts the principal’s profit. This paper presents two interpretations. The paper interprets the model as one of franchisors choosing how many franchises to set up in a given market, and one of governments using competition policy as a tool for a strategic trade. Under both of these interpretations, this paper makes many simplifying assumptions which deserve further research. By taking a simple demand function as given, this paper abstracts from any issues of location and of how a market is defined. An interesting extension of the franchising interpretation would be to explore how issues of two-part tariffs and outlet-number would interact in an address model, where geography and ‘market scoping’ could be modeled explicitly. Under the competition-policy interpretation, allowing the domestic government to choose exactly the number of domestic competitors is useful as a first pass at this question but is obviously too crude. In practice, a government can choose to implement tough anti-trust laws or choose not to enforce existing laws, but it cannot select the precise number of domestic firms. A logical next step is to develop a more textured model of how a government can affect the number of domestic firms.