Nash Equilibrium and Subgame Perfection in Observable Queues

A subgame perfection refinement of Nash equilibrium is suggested for games of the following type: each of an infinite number of identical players selects an action using his private information on the system's state; any symmetric strategy results in a discrete Markov chain over such states; the player's payoff is a function of the state, the selected action, and the 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 are transient. We illustrate the concept by considering several queueing models in which the number of customers in the system constitutes the state of the system.