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

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 o ptimal stationary strategies and the corresponding value vector of such a g ame as a vertical linear complementarily problem. We show that Cottle-Dantz ig's algorithm (a generalization of Lemke's algorithm) can solve this probl em under a mild assumption.