Extremal choice equilibrium with applications to large games, stochastic games, & endogenous institutions

We prove existence and purification results for strategic environments possessing a product structure that includes classes of large games, stochastic games, and models of endogenous institutions. Applied to large games, the results yield existence of pure-strategy equilibria allowing for infinite-dimensional externalities. Applied to stochastic games, the results yield existence of stationary Markov perfect equilibria with extremal payoffs, which in turn yields existence of pure strategy stationary Markov perfect equilibria for games with sequential moves. Applied to the model of institutions, we obtain equilibrium existence with general group decision correspondences.