Price Competition under Cost Uncertainty: A Laboratory Analysis

By Abbink, Klaus; Brandts, Jordi | Economic Inquiry, July 2005 | Go to article overview

Price Competition under Cost Uncertainty: A Laboratory Analysis


Abbink, Klaus, Brandts, Jordi, Economic Inquiry


I. INTRODUCTION

In markets with posted price competition sellers independently choose prices, which are publicly communicated to buyers on a take-it-or-leave-it basis. Such posted pricing is common in retail markets as well as in industries in which regulatory agencies require that prices be filed with them and that discounts not be granted. This type of competition has been studied both theoretically and experimentally. The theoretical work by Bertrand (1883) gave rise to what is known as the Bertrand paradox: If marginal costs are constant, then two firms are enough for equilibrium prices to equal marginal cost; beyond monopoly, there is no inverse relation between prices and the number of firms in the market. Subsequent theoretical work has consisted in proposing price competition models that "resolved" this paradox. Vives (1999) discusses the theoretical work on price competition in detail.

The experimental work in the area--surveyed in Holt (1995)--has contributed data about behavior in various price competition environments. Early experimental studies on posted prices, like those of Williams (1973) and Plott and Smith (1978), were not based on formal models of price competition. Instead, they took the Walrasian outcome as the natural benchmark for evaluating behavior. More recently, a number of experimental studies have investigated price competition on the basis of designs more closely connected to theoretical models.

Davis and Holt (1994) and Kruse et al. (1994) study price competition in environments in which the equilibrium prediction involves a price distribution with average prices above marginal cost in the spirit of the first theoretical resolution of the Bertrand paradox proposed by Edgeworth (1925). Both studies find price dispersion distinct but qualitatively similar to those predicted by Nash equilibrium. The study by Morgan et al. (2001) experimentally examines a model on price competition with informed and uninformed consumers. Informed consumers search for the best price, but uninformed consumers are captive to a firm. As a result, pure strategy equilibria do not exist. The authors find observed price distributions to be different from the prediction but the comparative statics of the strategic equilibrium to be supported.

Some studies deal with how the number of firms affects prices. Dufwenberg and Gneezy (2000) address this question in what can be seen as the first direct test of the Bertrand paradox as such. They study the effects of market concentration in a one-shot price competition framework with constant marginal cost and inelastic demand. In their experiments, price is above marginal cost for the case of two firms but equal to that cost for three and four firms. (1) In their results, two firms are not enough to get prices down to marginal cost, but three firms are. In a sense, the Bernard paradox remains, because the experimental results do not exhibit the intuitively expected negative relation between the number of firms and the price-cost margin.

Selten and Apesteguia (2002) experimentally study price competition in a model of spatial competition. Their setting involves positive profit margins in the Cournot equilibrium, but these margins are constant in the number of firms. In line with this prediction, they find very little difference in average prices across their treatments with three, four, and five firms, and average prices are close to but slightly above those chosen in equilibrium. In the spatial competition game experimentally studied by Orzen and Sefton (2003), pure strategy equilibria do not exist. Predictions for the expected price involve decreasing prices for increasing firm numbers; a prediction that is met in the experimental data.

Abbink and Brandts (2002) examine the effects of the number of firms in an experimental design in which price competition can lead to positive equilibrium price-cost margins. Their design is based on the theoretical model by Dastidar (1995) in which there are multiple equilibria in pure strategies, compatible with price-cost margins being decreasing in the number of firms. …

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