A game theoretic model for two types of customers competing for service

Two types of customers arrive at a single server station and demand service. If a customer finds the server busy upon arrival (or retrial) he immediately departs and conducts a retrial after an exponential period of time and persists this way until he gets served. Both types of customers face linear costs for waiting and conducting retrials and wish to find optimal retrial rates which will minimize these costs. This problem is analysed as a two-person nonzero sum game. Both noncooperative strategies are studied.