  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.
