Stochastic approximation of symmetric Nash equilibria in queueing games

TL;DR

This paper introduces a new stochastic-approximation algorithm that efficiently computes symmetric Nash equilibria in complex queueing games, leveraging simulation and dynamic strategy updates to handle models where direct analysis is difficult.

Contribution

The paper presents a novel stochastic-approximation method for finding symmetric Nash equilibria in queueing games, applicable under mild assumptions and using a single simulation process.

Findings

Algorithm converges to equilibrium almost surely

Applicable to a broad class of queueing models

Provides a practical tool for equilibrium approximation

Abstract

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 on the utility function and on the regenerative structure of the queueing 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.