Nonzero-sum stochastic games with unbounded costs: Discounted and average cost cases

The paper treats non-cooperative stochastic games with countable state space and with finitely many players each having finitely many moves available in a given state. As a function of the current state and move vector, each player incurs a nonnegative cost. Assumptions are given for the expected discounted cost game to have a Nash equilibrium randomized stationary strategy. These conditions hold for bounded costs, thereby generalizing Parthasarathy and Federgruen. Assumptions are given for the long-run average expected cost game to have a Nash equilibrium randomized stationary strategy, under which each palyer has constant average cost. A flow control example illustrates the results. This paper complements the treatment of the zero-sum case in Sennott.