ON ASYMPTOTIC VALUE FUNCTION FOR DYNAMIC GAMES WITH LONG- TIME-AVERAGE PAYOFF
The work is devoted to value functions of dynamic zero-sum games. The asymptotics of value functions is considered when each payoff averages over time by a given probability density (in particular for long- time-average payoff and discounted average payoff). For dynamics and families of probability densities, we found the conditions guaranteeing that the asymptotics, if present, is independent of the chosen family of probability densities.