Statics and dynamics of selfish interactions in distributed service systems

TL;DR

This paper analyzes the complex landscape of Nash equilibria in distributed service systems with congestion, revealing how selfish agent dynamics tend to favor high-utility equilibria despite the abundance of lower-utility ones.

Contribution

It introduces a cavity method-based technique to fully characterize Nash equilibria in congestion games and explores how initial conditions influence equilibrium selection.

Findings

Large variety of equilibria with different statistical properties.

Selfish dynamics tend to reach high-utility equilibria.

Lower-utility equilibria are exponentially more numerous but less likely to be reached.

Abstract

We study a class of games which model the competition among agents to access some service provided by distributed service units and which exhibit congestion and frustration phenomena when service units have limited capacity. We propose a technique, based on the cavity method of statistical physics, to characterize the full spectrum of Nash equilibria of the game. The analysis reveals a large variety of equilibria, with very different statistical properties. Natural selfish dynamics, such as best-response, usually tend to large-utility equilibria, even though those of smaller utility are exponentially more numerous. Interestingly, the latter actually can be reached by selecting the initial conditions of the best-response dynamics close to the saturation limit of the service unit capacities. We also study a more realistic stochastic variant of the game by means of a simple and effective approximation of the average over the random parameters, showing that the properties of the average-case Nash equilibria are qualitatively similar to the deterministic ones.