A Dynamic Model of Bertrand Competition for an Oligopolistic Market

Abstract

We study an infinitely-repeated Bertrand competition game among a fixed number of firms in a market of both stochastic entry and stochastic demand. A firm’s entry into market in the next period is possible by making a positioning investment with stochastic success rate. The market demand in the next period is also stochastic and will not be realized until the firm enters the market. A successful investment allows a firm to participate in the Bertrand competition and an unsuccessful investment prevents a firm from entering the market, for the next period. We characterize the symmetric Markov perfect Nash Equilibrium (SMPNE) of such a dynamic game, where a firm’s strategy consists of two components: positioning strategy and pricing strategy. In examples with 1, 2, and 3 firms, we show the stage game market outcome, present the dynamic process of market structure, solve for the steady state of the dynamic system, and discuss about the speed of convergence to the steady state. Our work contributes to the dynamic oligopoly literature by allowing for two dimensions of stochastic uncertainty in firms’ decision-making.