Fouraker and Siegel’s oligopoly markets

148 A. Muren J. of Economic Behavior Org. 41 2000 147–157 degree of competition increases from zero to its maximum level already when the number of firms increases from one to two. In the Cournot model, where quantity of output is the strategic variable, the number of firms plays a role in that the equilibrium price goes down when additional firms enter, which seems intuitively reasonable. The problem lies in the theoretical motivation for the equilibrium — it would seem appropriate for any oligopoly model to let firms set prices rather than just output levels. Kreps and Scheinkman 1983 formulated a two stage model where firms first choose production capacity and then, in stage two, set their prices. Under certain circumstances the equilibrium in this model will be identical to the Cournot equilibrium. Kreps and Scheinkman’s theoretical result integrates the Bertrand price setting model with the Cournot model of quantity competition, and provides a rationale for using the Cournot model to de- scribe an industry with steeply increasing marginal costs, i.e. where the capacity choice is a binding constraint for the firm, while the Bertrand model would be more suitable for an industry with a technology such that the marginal cost of production increases slowly with output. 1 Testing the Kreps and Scheinkman model could provide useful information for policy makers on the appropriateness of the Cournot model. One experimental test of the Kreps and Scheinkman hypothesis is provided by Mestelman and Welland 1988, who study the effects of advance production on the relative performance of posted offer and double auction markets. They find that advance production, which is essentially the same as capacity precommitment, leads to competitive outcomes under both trading institutions. However, as noted by Holt Holt, 1995, p. 376, the design used by Mestelman and Welland does not distinguish well between competitive outcomes and Cournot outcomes nor is that the purpose of their study. The experiment described in this paper was designed to test whether the Kreps and Scheinkman results emerge in an experimental market organized according to the assump- tions of that model. To achieve this end we have followed the assumptions of the Kreps and Scheinkman model closely. In particular, we have used efficient rationing, which is a crucial assumption of the model, as demonstrated by Davison and Deneckere 1986 who show that under other rationing mechanisms, e.g. proportional rationing, the Kreps and Scheinkman result may not emerge. Since the Kreps and Scheinkman model combines the two opposites of quantity-setting and price-setting, it is also interesting to compare the experimental performance of the model with those of the Cournot and Bertrand models. This is done using the Fouraker and Siegel 1963 results for the two market forms. After the presentation of Fouraker and Siegel’s results in Section 2, there follows a description of the experimental formulation and the set-up of the experimental sessions in Section 3. Section 4 derives equilibrium predictions. Section 5 analyzes the outcome of the experiment and Section 6 concludes.

2. Fouraker and Siegel’s oligopoly markets

Experimental investigations of quantity competition markets are reviewed by Holt Holt, 1995, pp. 403–404, who concludes that the outcomes of Cournot experiments with more 1 This argument is formulated in some detail e.g. in Tirole 1988, p. 224. A. Muren J. of Economic Behavior Org. 41 2000 147–157 149 than two sellers tend to be more competitive than is predicted by the Cournot model. The results reached by Fouraker and Siegel provide a standard of comparison for both the price setting and the quantity setting cases. Fouraker and Siegel report results from two triopoly quantity competition experiments, which differ with respect to the amount of information provided to subjects. In the incom- plete information formulation, sellers know only their own profits for each quantity choice, as dependent on the combined quantities of the other two sellers. In the complete infor- mation formulation, sellers know also the effect of their and the sum of their competitors’ quantity choices on the combined profits of the other sellers. In our capacity precommit- ment experiment the information to sellers is cast in terms of costs and demand instead of profit tables, and sellers have identical costs, which means that they can infer the effects on other sellers’ profits. This suggests that of Fouraker and Siegel’s two Cournot triopoly ex- periments, the complete information formulation would provide our most relevant Cournot outcome comparison. Fouraker and Siegel summarize the results of their quantity competition experiments in terms of the support for each of three types of equilibria: cooperative, Cournot and competitiverivalistic see Table 9.10, p. 150. 2 Their definition of ‘support’ is that the outcome supported an equilibrium solution if it was closer to the corresponding numerical quantity prediction than to any other. There were 11 triopoly markets in their complete information experiment. The cooperative solution was supported by 0 markets, the Cournot solution was supported by 5 markets, and the competitive solution was supported by 6 markets. Thus, the competitive solution was just dominant over the Cournot solution. In the Bertrand competition case in Fouraker and Siegel there are also two experimental formulations of triopoly markets, differing in informational structure. In both formulations the market outcome was strongly competitive, with the ruling price being equal to the Bertrand price in every market. 3

3. Experimental formulation