Nonlinear strategies in dynamic duopolistic competition with sticky prices

Abstract

We discuss nonlinear strategies in an infinite horizon duopoly game with sticky prices where firms maximize their discounted sum of profit. We construct a stationary feedback equilibrium without guessing value functions and feedback strategies that solve the Hamilton-Jacobi equation. For this purpose, we study the auxiliary equation that is derived from the Hamilton-Jacobi equation. We show that the domain of the state space plays an crucial role in characterizing feedback equilibria, and discuss several implications of this observation. In particular, we find that when the upper bound of the state space is not very high, previously unknown feedback equilibria emerge.