A constructive study of Markov equilibria in stochastic games with strategic complementarities

Abstract

We study a class of infinite horizon, discounted stochastic games with strategic complementarities. In our class of games, we prove the existence of a stationary Markov Nash equilibrium, as well as provide methods for constructing this least and greatest equilibrium via a simple successive approximation schemes. We also provide results on computable equilibrium comparative statics relative to ordered perturbations of the space of games. Under stronger assumptions, we prove the stationary Markov Nash equilibrium values form a complete lattice, with least and greatest equilibrium value functions being the uniform limit of approximations starting from pointwise lower and upper bounds.