A Link between Sequential Semi-anonymous Nonatomic Games and their Large Finite Counterparts

We show that equilibria of a sequential semi-anonymous nonatomic game (SSNG) can be adopted by players in corresponding large but finite dynamic games to achieve near-equilibrium payoffs. Such equilibria in the form of random state-to-action rules are parsimonious in form and easy to execute, as they are both oblivious of past history and blind to other players' present states. Our transient results can be extended to a stationary case, where the finite counterparts are special discounted stochastic games. The kind of equilibria we adopt for SSNG are similar to distributional equilibria that are well understood in literature, and they themselves are shown to exist.