The Price of Anarchy in Large Games

TL;DR

This paper develops an analytical framework to bound the price of anarchy in large game-theoretic models, showing that in many cases, large games perform better than worst-case scenarios, especially in auctions and routing games.

Contribution

It introduces a general framework for analyzing the price of anarchy in large games and demonstrates its applicability across multiple models, revealing conditions for improved efficiency.

Findings

Large games often have better POA than worst-case instances.

Simple auctions can perform nearly optimally in realistic settings.

The framework applies to auctions and routing games, among others.

Abstract

Game-theoretic models relevant for computer science applications usually feature a large number of players. The goal of this paper is to develop an analytical framework for bounding the price of anarchy in such models. We demonstrate the wide applicability of our framework through instantiations for several well-studied models, including simultaneous single-item auctions, greedy combinatorial auctions, and routing games. In all cases, we identify conditions under which the POA of large games is much better than that of worst-case instances. Our results also give new senses in which simple auctions can perform almost as well as optimal ones in realistic settings.