On the dynamic Stability of a Price Dispersion Model

This paper studies the evolutionary stability of a unique Nash equilibrium in a price dis-persion model (Burdett and Judd, 1983) using gradient dynamics. The numerical solution tothe partial differential equation that governs the evolution of prices shows that the stationaryequilibrium is not a Nash Equilibrium and that it differs from the cyclical behavior predictedby another family of dynamics, such as replicator and logit, in a continuous action space.