Academic journal article Economic Inquiry

Spatial Competition with Three Firms: An Experimental Study

Academic journal article Economic Inquiry

Spatial Competition with Three Firms: An Experimental Study

Article excerpt


This article reports the results of an experimental study of the three firm location problem. We compare the subjects' behavior in the experiments with the symmetric mixed strategy Nash equilibrium calculated by Shaked. Overall, the findings are consistent with the equilibrium prediction. However, the subjects' locations were significantly more dispersed than predicted by the theory. Three alternative explanations of this phenomenon--inexperience, approximate equilibrium behavior and risk aversion--are suggested and evaluated for their predictive power. Special attention is paid to risk aversion. (JEL C9, C72, D43)


This article reports the results of an experimental study of the three agent location problem. Starting with the works of Hotelling [1929] and Downs [1957], models of spatial competition have been widely studied in the economics and voting literature. In economics, such models are used to study both horizontal (or geographic) competition and vertical competition (or product differentiation); see Gabszewicz and Thisse [1992] for a review. In political science, spatial voting models are used to determine equilibrium outcomes of electoral competitions; see Enelow and Hinich [1990].

Hotelling's [1929] classic model of spatial competition predicts that, when two firms (or two political parties) compete for customers (voters) by choosing locations on a linear market (policy space), the only stable outcome is for both firms to locate at the center of the market. Hotelling used this result to explain the tendency for products to be very similar and political parties to become the same. He further conjectured that the tendency to cluster near the center of the market would persist in the case of more than two competing agents.

Contrary to Hotelling's conjecture, the literature that followed showed that the incentive for agents to disperse is strong in multiagent location models, as in Cox [1990]. In the case of three firms, no pure strategy location equilibrium exists, as was first noted by Lerner and Singer [1937] and formally shown by Eaton and Lipsey [1975]. Shaked [1982] characterizes the symmetric mixed strategy Nash equilibrium for the case of three firms and uniform distribution of buyers. He finds that the only symmetric Nash equilibrium is for each firm to locate randomly with equal probability at each point in the middle two quartiles of the market. [1] Osborne [1993] shows that if there are more than two political parties who choose their positions simultaneously, then pure strategy location equilibria fail to exist in a wide range of situations. He further notes that, in the case of mixed strategy equilibria, one aspect that may be essential for characterization of outcomes is uncertainty.

The purpose of this study is to test experimentally the theoretical breakdown of centrist tendencies in a multiagent spatial competition model. Further, we are interested in considering the effects of uncertainty on the behavior of agents when no pure strategy location equilibrium exists. As argued by Osborne and Pitchik [1986], a mixed strategy equilibrium can, under certain circumstances, be viewed as a pure strategy equilibrium in a game of incomplete information. Consideration of location models where no pure strategy equilibrium exists is therefore useful for understanding the behavior of firms or political parties in an uncertain world.

The majority of existing experimental literature on spatial competition is based on voting models and considers the behavior of both candidates and voters in a spatial context. Studies of two-candidate elections indicate that, even with limited information of candidates and voters, candidates converge to the median voter ideal point, as in McKelvey and Ordeshook [1985] and Collier, McKelvey, Ordeshook, and Williams [1987]. McKelvey and Ordeshook [1982] also find evidence that subjects use mixed strategies in two-candidate elections set in two-issue voting space when a majority rule equilibrium does not exist. …

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