The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result includes various earlier existence results on correlated equilibria, noisy stochastic games, 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 . The minimality of our condition is demonstrated from a technical point of view. Our result also sheds some light on a recent example about the nonexistence of stationary equilibrium . New applications of stochastic games are presented as illustrative examples, including stochastic games with endogenous shocks and a stochastic dynamic oligopoly model.
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.
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includes
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stochastic games with finite actions and state-independent transitions, and
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. The minimality of our condition is demonstrated from a technical point of view. Our result also sheds some light on a recent example about the nonexistence of stationary equilibrium