Abstract. We characterize perfect public equilibrium payoffs in dynamic stochastic games. We consider the case where the length of the period shrinks, but players' rate of time discounting and the transition rate between states remain fixed. The set of equilibrium payoffs may be smaller than the set of payoffs generated by strategies that give each player at least his minmax payoff after every history. There may exist equilibrium payoffs that cannot be achieved with Markov strategies that are individually rational in every state. Our setting differs significantly from the case considered in previous literature (Dutta (1995), Fudenberg and Yamamoto (2011) and Hörner, Sugaya, Takahashi, and Vieille (2011)), where players become very patient (so that players discount vanishingly little the expected time until the next state transition). In particular, the set of equilibrium payoffs typically depends on the initial state.