Closed Non-atomic Resource Allocation Games

TL;DR

This paper analyzes how queue-based signaling of demand excess impacts efficiency in non-atomic congestion games, introducing a framework based on linear programming and studying equilibrium properties and inefficiency bounds.

Contribution

It formulates a class of congestion games with queue-based signaling using linear programs and characterizes equilibrium existence, properties, and inefficiency bounds.

Findings

Wardrop equilibria exist and are characterized by a potential function.

The price of anarchy is 2 for homogeneous players and infinite otherwise.

Queue delays significantly influence individual optimization and overall efficiency.

Abstract

How is efficiency affected when demand excesses over supply are signalled through waiting in queues? We consider a class of congestion games with a nonatomic set of players of a constant mass, based on a formulation of generic linear programs as sequential resource allocation games. Players continuously select activities such that they maximize linear objectives interpreted as time-average of activity rewards, while active resource constraints cause queueing. In turn, the resulting waiting delays enter in the optimization problem of each player. The existence of Wardrop-type equilibria and their properties are investivated by means of a potential function related to proportional fairness. The inefficiency of the equilibria relative to optimal resource allocation is characterized through the price of anarchy which is 2 if all players are of the same type ($\infty$ if not).