Extremal Markov Perfect Equilibria of Stochastic Games with Complementarities

Under natural assumptions, we show that the set of Stationary Markov Perfect Equilibria in pure strategies is non-empty for stochastic repeated games with complementarities. We characterize the set of extremal SMPE as unique fixed points of well-chosen contractions. Those extremal equilibria can be approximated exponentially fast, and uniform convergence obtains for any initial guess chosen on a relevant functional set. This characterization also allows to derive a standard result in Monotone Comparative Statics. We finally show how to extend our approach to some other classes of repeated stochastic games