Price competition and probabilistic demand yield the Cournot outcome, the Bertrand outcome, and much more

In this paper we analyze a model of price competition in a market for a homogeneous product in which consumers express a probabilistic demand. A parameter, θ, describes the degree of precision with which consumers evaluate prices. We show that, according to the value of θ, the market can reach a very large set of symmetric equilibria. Both the Bertrand and the Cournot outcomes can emerge as equilibria of the game. In addition to these the price game can determine an equilibrium in which each firm charges the monopoly price without any cl. In the model a new entry can lead to both a decrease and an increase of the equilibrium price.