Consumer Rationing and Cournot Outcomes: Experimental Evidence

Abstract

[Author Affiliation]Jason J Lepore, * Department of Economics, Orfalea Business College, California Polytechnic State University, San Luis Obispo, CA 93407, USA; E-mail: jlepore@calpoly.edu .Aric P Shafran, [dagger] Department of Economics, Orfalea Business College, California Polytechnic State University, San Luis Obispo, CA 93407, USA; E-mail: ashafran@calpoly.edu ; corresponding author.[Acknowledgment]The authors acknowledge the Orfalea College of Business for financial support. We thank Blake Allison for assistance running the experiments and the anonymous reviewers and conference participants at the North American Economic Science Association Meetings for helpful comments.1. IntroductionThis article reports the results of duopoly market experiments where firms first commit to capacities and then compete in prices. The theoretical literature pertaining to these duopoly models suggests that the way residual demand is rationed is fundamental to the character of equilibrium outcomes. The goal of this study is to test the impact of residual demand rationing on the behavior of subjects in an experimental environment.In a two-stage game, where firms first commit to capacities and then compete in prices, Kreps and Scheinkman (1983; hereafter K&S) prove that the unique Nash equilibrium outcome coincides with the Cournot equilibrium outcome with efficient rationing of residual demand. Efficient rationing means that the higher-priced firm is left with the worst possible residual demand curve. If demand is composed of many similar consumers that each demand multiple units and we construct aggregate demand by way of a representative consumer, then efficient rationing is imposed by the model. On the other hand, if demand is instead composed of a mass of consumers with unit demand and varied willingness to pay, then the efficient rationing rule imposes the restriction that the highest-valued consumers buy from the firm with the lower price. Davidson and Deneckere (1986) make a compelling argument that proportional rationing is a more appropriate assumption in the latter case. Proportional rationing means that a uniform distribution of possible consumers buy from the firm with the lower price. Davidson and Deneckere show that under proportional rationing (as well as any rationing rule other than the efficient rule), the Cournot outcome is not necessarily the unique equilibrium of the two-stage game. The Davidson and Deneckere result is problematic for the K&S model because it deflates the generality of their theoretical result.1Lepore (2009) further clarifies the relationship between proportional rationing and the Cournot outcome. In the K&S game with proportional rationing, the Cournot outcome is the unique Nash equilibrium only when capacity cost is greater than a threshold level. The purpose of our experiments is to assess if the play of experimental subjects in the two-stage game is sensitive to the rationing scheme in the way that theory predicts. To do this, we construct an experimental design with four treatments. The treatments vary by two controls: the demand-rationing scheme and the cost of capacity. We conduct two efficient rationing treatments, one with a high capacity cost and one with a low cost. For both costs, theory predicts that the outcome coincide with the Cournot model. We also conduct two treatments using proportional rationing, one with each of the capacity costs used in the efficient rationing treatments. With a high cost, theory predicts the outcome should coincide with the Cournot model, as in the case of efficient rationing. However, theory predicts that the Cournot outcome should not occur when the cost of capacity is low, and prices should not clear the market.Recently several authors have used laboratory experiments as a means to empirically test the predictions of the K&S model. …