The Continuous Logit Dynamic and Price Dispersion

We define the logit dynamic for games with continuous strategy spaces and establish its fundamental properties, i.e. the existence, uniqueness and continuity of solutions. We apply the dynamic to the analysis of the Burdett and Judd (1983) model of price dispersion. Our objective is to assess the stability of the logit equilibrium corresponding to the unique Nash equilibrium of this model. Although a direct analysis of local stability is difficult due to technical difficulties, an appeal to finite approximation techniques suggest that the logit equilibrium is unstable. Price dispersion, instead of being an equilibrium phenomenon, is a cyclical phenomenon. We also establish a result on the Lyapunov stability of logit equilibria in negative definite games.