The Quality of Equilibria for Set Packing Games

TL;DR

This paper analyzes the efficiency of various equilibrium concepts in set packing games, showing that approximate equilibria are only moderately suboptimal and providing tight bounds on their price of anarchy.

Contribution

It introduces set packing games as a new framework and establishes tight bounds on the price of anarchy for multiple equilibrium concepts.

Findings

Approximate equilibria have moderate suboptimality.

Tight bounds are established for the price of anarchy.

Results apply to Nash, subgame perfect, and k-collusion equilibria.

Abstract

We introduce set packing games as an abstraction of situations in which $n$ selfish players select subsets of a finite set of indivisible items, and analyze the quality of several equilibria for this class of games. Assuming that players are able to approximately play equilibrium strategies, we show that the total quality of the resulting equilibrium solutions is only moderately suboptimal. Our results are tight bounds on the price of anarchy for three equilibrium concepts, namely Nash equilibria, subgame perfect equilibria, and an equilibrium concept that we refer to as $k$-collusion Nash equilibrium.