Discounted stochastic games with strategic complementarities: theory and applications

Abstract

This paper considers a general class of discounted Markov stochastic games characterized by multidimensional state and action spaces with an order structure, and one-period reward functions and state transition law satisfying some complementarity and monotonicity conditions. Existence of pure-strategy Markov (Markov-stationary) equilibria for the finite (infinite) horizon game, with nondecreasing -and possibly discontinuous - strategies and value functions, is proved. The analysis is based on lattice programming, and not on concavity assumptions. Selected economic applications that fit the underlying framework are described: dynamic search with learning, long-run competition with learning-by-doing or network effects, and resource extraction.