Stationary Markov Perfect Equilibria in Discounted Stochastic Games

TL;DR

This paper proves the existence of stationary Markov perfect equilibria in a broad class of stochastic games under a general transition condition, unifying and extending previous results with a new proof technique.

Contribution

It introduces a general condition called coarser transition kernels for equilibrium existence and provides a simple proof linking stochastic games to conditional expectations of correspondences.

Findings

Existence of equilibria under coarser transition kernels

Unification of various earlier existence results

Application to stochastic games with endogenous shocks and oligopoly models

Abstract

The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result covers various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with finite actions and state-independent transitions, and stochastic games with mixtures of constant transition kernels as special cases. A remarkably simple proof is provided via establishing a new connection between stochastic games and conditional expectations of correspondences. New applications of stochastic games are presented as illustrative examples, including stochastic games with endogenous shocks and a stochastic dynamic oligopoly model.