Elementary Subpaths in Discounted Stochastic Games

This paper examines the subgame-perfect equilibria in discounted stochastic games with finite state and action spaces. The fixed-point characterization of equilibria is generalized to unobservable mixed strategies. It is also shown that the pure-strategy equilibria consist of elementary subpaths, which are repeating fragments that give the acceptable action plans in the game. The developed methodology offers a novel way of computing and analyzing equilibrium strategies that need not be stationary nor Markovian.