Stability in price competition revisited

We consider consumers with the same reservation price, who desire to buy at most one unit of a good. Firms compete only in prices, but there are other features firms cannot control that would eventually lead an agent to buy in one firm or another. We introduce such uncertainty in a model of a price competition game with incomplete information. This competition takes place under stability and we provide equilibrium existence results. We analyze different specifications of residual demands which yield further interpretations that deepen the phenomenon of price dispersion, Bertrand’s paradox and market power.