Heavy Traffic Approximation of Equilibria in Resource Sharing Games

TL;DR

This paper introduces a heavy traffic approximation for equilibria in resource sharing games, combining queueing and strategic behavior, and analyzes its efficiency and revenue implications.

Contribution

It proposes a novel heavy traffic equilibrium concept as an approximation of Nash equilibrium in resource sharing games with queueing.

Findings

Provides bounds for the price of anarchy in heavy traffic equilibrium

Analyzes efficiency and revenue in the proposed model

Introduces an asymptotic regime for complex queueing systems

Abstract

We consider a model of priced resource sharing that combines both queueing behavior and strategic behavior. We study a priority service model where a single server allocates its capacity to agents in proportion to their payment to the system, and users from different classes act to minimize the sum of their cost for processing delay and payment. As the exact processing time of this system is hard to compute, we introduce the notion of heavy traffic equilibrium as an approximation of the Nash equilibrium, derived by considering the asymptotic regime where the system load approaches capacity. We discuss efficiency and revenue, and in particular provide a bound for the price of anarchy of the heavy traffic equilibrium.