Stochastic Approximation of Symmetric Nash Equilibria in Queueing Games

Abstract

The common setting of a queueing-game model consists of a stochastic stream of customers arriving at a queueing system one by one, each customer strategically chooses an action that may depend on information they receive regarding the system state. The aggregate customer decision profile gives rise to a system steady state, and, provided customers arrive at said steady state, if their decision is utility maximizing (ex ante), then this aggregate decision profile constitutes a Nash equilibrium. However, expressing the steady-state distribution for a given decision profile is very often a difficult task, and in such a case, an attempt to find a Nash equilibrium via direct analysis is futile. In the article “Stochastic Approximation of Symmetric Nash Equilibria in Queueing Games,” Ravner and Snitkovsky suggest a novel stochastic algorithm that learns the Nash equilibrium in a class of queueing games, based on a single adaptive simulation. The method is robust and is easy to implement, offering a practical solution to queueing-game models that classical queueing-analytic methods prove inadequate.