Existence of a Pure Strategy Equilibrium in Markov Games with Strategic Complementarities for Finite Actions and States

Abstract

In this paper, we provide the sufficient conditions for a Markov perfect equilibrium in pure strategies to exist for a class of stochastic games with finite horizon, in which any stage game has strategic complementarities. In contrast to previous studies (e.g., Curtat (1996) and Amir (2002), we assume herein that the sets of actions and the set of states is finite and do not assume dominant diagonal conditions for payoffs and the transition probability, which yield the uniqueness of equilibria. The greatest equilibrium is monotonically increasing in the state. The main result is applied to a model of a Bertrand competition with investment.

Keywords: Stochastic Game, Markov Perfect Equilibrium, Supermodular Game, Strategic Complementarity, Pure Strategy Equilibrium

JEL Classification: C63, C72