A Strategic Dynamic Programming Method for Studying Short-Memory Equilibria of Stochastic Games with Uncountable Number of States

Abstract

We study a class of infinite horizon stochastic games with uncountable number of states. We first characterize the set of all (nonstationary) short-term (Markovian) equilibrium values by developing a new (Abreu et al. in Econometrica 58(5):1041–1063, 1990)-type procedure operating in function spaces. This (among others) proves Markov perfect Nash equilibrium (MPNE) existence. Moreover, we present techniques of MPNE value set approximation by a sequence of sets of discretized functions iterated on our approximated APS-type operator. This method is new and has some advantages as compared to Judd et al. (Econometrica 71(4):1239–1254, 2003), Feng et al. (Int Econ Rev 55(1):83–110, 2014), or Sleet and Yeltekin (Dyn Games Appl doi: 10.1007/s13235-015-0139-1 , 2015). We show applications of our approach to hyperbolic discounting games and dynamic games with strategic complementarities.