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Nash equilibrium and its subgame perfection refinement are considered for the following games: Each of an infinite number of identical players selects a single action using his private information on the system's state; any symmetric strategy results in a discrete Markov chain among such states; the player's payoff is a function of the state, action, and common strategy selected by the other players. The distinction between equilibria which are subgame perfect and those which are not, is made apparent due to the possibility that some states may be transient. We illustrate the concept via queueing models in which the number of customers in the system constitutes the state space of a controlled Markov process.
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