On non-equilibria threshold strategies in ticket queues

In many real life queueing systems, customer balk from the queue but the environment is aware of it only at their times to be served. Naturally, the balking is an outcome of the queue length, and the decision is based on a threshold. Yet, the inspected queue length contains customers who balked In this work, we consider a Markovian queue with infinite capacity with homogeneous customers with respect to their cost reward functions. We show that any threshold strategy is not a symmetric Nash equilibrium strategy. Furthermore, we show that for any threshold strategy adopted by all, the individual’s best response is a double threshold strategy. That is, join if and only if one of the following (i) the inspected queue length is smaller from one threshold, or (ii) the inspected queue length is larger than a second threshold. We discuss the validity of the result when the response time for an absence of customers is positive. We also show that in the case of a finite capacity queue a threshold strategy can be equilibrium, but this result depends on the model’s parameters (and the capacity).