Learning and Noisy Equilibrium Behavior in an Experimental Study of Imperfect Price Competition

This paper considers a duopoly price-choice game in which the unique Nash equilibrium is the Bertrand outcome. Price competition, however, is imperfect in the sense that the market share of the high-price firm is not zero. Economic intuition suggests that price levels should be positively related to the market share of the high-price firm. Although this relationship is not predicted by standard game theory, it is implied by a generalization of the Nash equilibrium that results when players make noisy (logit) best responses to expected payoff differences. This logit equilibrium model was used to design a laboratory experiment with treatments that correspond to changing the market share of the high-price firm. The model predicts the final-period price averages for both treatments with remarkable accuracy. Moreover computer simulations of a naive learning model were used, ex ante, to predict the observed differences in the time paths of average prices.