Linear Complementarity and the Irreducible Polystochastic Game with the Average Cost Criterion When One Player Controls Transitions
We consider the polystochastic game in which the transition probabilities depend on the actions of a single player and the criterion is the limiting average of the expected costs for each player. Using linear complementarity theory, we present a computational scheme for computing a set of stationary equilibrium strategies and the corresponding costs for this game with the additional assumption that under any choice of stationary strategies for the players the resulting one step transition probability matrix is irreducible. This work extends our previous work on the computation of a set of stationary equilibrium strategies and the corresponding costs for a polystochastic game in which the transition probabilities depend on the actions of a single player and the criterion is the total discounted expected cost for each player.
KeywordsNash Equilibrium Linear Complementarity Problem Stationary Strategy Stochastic Game Basic Feasible Solution
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