The dynamic instability of dispersed price equilibria

We examine whether price dispersion is an equilibrium phenomenon or a cyclical phenomenon. We develop a finite strategy model of price dispersion based on the infinite strategy model of Burdett and Judd (1983). Adopting an evolutionary standpoint, we examine the stability of dispersed price equilibrium under perturbed best response dynamics. We conclude that when both sellers and consumers participate actively in the market, all dispersed price equilibria are unstable leading us to interpret price dispersion as a cyclical process. For a particular case of the model, we prove the existence of a limit cycle.