Nonzero-sum stochastic differential games with additive structure and average payoffs

This paper deals with nonzero-sum stochastic differential games with an additive structure and long-run average payoffs. Our main objective is to give conditions for the existence of Nash equilibria in the set of relaxed stationary strategies. Such conditions also ensure the existence of a Nash equilibrium within the set of stationary Markov (deterministic) strategies, and that the values of the average payoffs for these equilibria coincide almost everywhere with respect to Lebesgue's measure. This fact generalizes the results in the controlled (single player game) case found by Raghavan [47] and Rosenblueth [48]. We use relaxation theory and standard dynamic programming techniques to achieve our goals. We illustrate our results with an example motivated by a manufacturing system.