  We investigate the behavior of equilibria in an $M/M/1$ feedback queue where
price and time sensitive customers are homogeneous with respect to service
valuation and cost per unit time of waiting. Upon arrival, customers can
observe the number of customers in the system and then decide to join or to
balk. Customers are served in order of arrival. After being served, each
customer either successfully completes the service and departs the system with
probability $q$, or the service fails and the customer immediately joins the
end of the queue to wait to be served again until she successfully completes
it.
  We analyse this decision problem as a noncooperative game among the
customers. We show that there exists a unique symmetric Nash equilibrium
threshold strategy. We then prove that the symmetric Nash equilibrium threshold
strategy is evolutionarily stable. Moreover, if we relax the strategy
restrictions by allowing customers to renege, in the new Nash equilibrium,
customers have a greater incentive to join. However, this does not necessarily
increase the equilibrium expected payoff, and for some parameter values, it
decreases it.
