  We suggest a novel stochastic approximation algorithm to compute a Symmetric
Nash Equilibrium strategy in a general queueing game with a finite action
space. The algorithm involves a single simulation of the queueing process with
dynamic updating of the strategy at regeneration times. Under mild assumptions
regarding the regenerative structure of the process the algorithm converges to
a symmetric equilibrium strategy almost surely. This yields a powerful tool
that can be used to approximate equilibrium strategies in a broad range of
strategic queueing models in which direct analysis is impracticable.
