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We investigate the behavior of equilibria in an $M/M/1$ feedback queue whereprice and time sensitive customers are homogeneous with respect to servicevaluation and cost per unit time of waiting. Upon arrival, customers canobserve the number of customers in the system and then decide to join or tobalk. Customers are served in order of arrival. After being served, eachcustomer either successfully completes the service and departs the system withprobability $q$, or the service fails and the customer immediately joins theend of the queue to wait to be served again until she successfully completesit.  We analyse this decision problem as a noncooperative game among thecustomers. We show that there exists a unique symmetric Nash equilibriumthreshold strategy. We then prove that the symmetric Nash equilibrium thresholdstrategy is evolutionarily stable. Moreover, if we relax the strategyrestrictions by allowing customers to renege, in the new Nash equilibrium,customers have a greater incentive to join. However, this does not necessarilyincrease the equilibrium expected payoff, and for some parameter values, itdecreases it.

Strategic Customer Behavior in an $M/M/1$ Feedback Queue