A FINITE STEP ALGORITHM VIA A BIMATRIX GAME TO A SINGLE CONTROLLER NONZERO SUM STOCHASTIC GAME

Given a non-zero sum discounted stochastic game with finitely many sta tes and actions one can form a bimatrix game whose pure strategies are the pure stationary strategies of the players and whose penalty payof fs consist of the total discounted costs over all states at any pure s tationary pair, It is shown that any Nash equilibrium point of this bi matrix game can be used to find a Nash equilibrium point of the stocha stic game whenever the law of motion is controlled by one player. The theorem is extended to undiscounted stochastic games with irreducible transitions when the law of motion is controlled by one player. Exampl es are worked out to illustrate the algorithm proposed.