Vertical linear complementarity and discounted zero-sum stochastic games with ARAT structure

Abstract

In this paper we consider a two-person zero-sum discounted stochastic game with ARAT structure and formulate the problem of computing a pair of pure optimal stationary strategies and the corresponding value vector of such a game as a vertical linear complementarity problem. We show that Cottle-Dantzig's algorithm (a generalization of Lemke's algorithm) can solve this problem under a mild assumption.