Bounding the Inefficiency of Altruism Through Social Contribution Games

TL;DR

This paper introduces social contribution games (SCGs) as a framework to analyze altruistic behavior in games, providing a reduction technique to establish bounds on the robust price of anarchy for various well-known game classes.

Contribution

The paper presents a new class of games called SCGs and a reduction method to analyze altruistic extensions, extending bounds to several classic game types.

Findings

SCGs are altruism-independently smooth, maintaining the same robust price of anarchy.

The reduction technique applies to many well-known games like congestion and scheduling games.

Results extend to friendship models under certain conditions.

Abstract

We introduce a new class of games, called social contribution games (SCGs), where each player's individual cost is equal to the cost he induces on society because of his presence. Our results reveal that SCGs constitute useful abstractions of altruistic games when it comes to the analysis of the robust price of anarchy. We first show that SCGs are altruism-independently smooth, i.e., the robust price of anarchy of these games remains the same under arbitrary altruistic extensions. We then devise a general reduction technique that enables us to reduce the problem of establishing smoothness for an altruistic extension of a base game to a corresponding SCG. Our reduction applies whenever the base game relates to a canonical SCG by satisfying a simple social contribution boundedness property. As it turns out, several well-known games satisfy this property and are thus amenable to our reduction technique. Examples include min-sum scheduling games, congestion games, second price auctions and valid utility games. Using our technique, we derive mostly tight bounds on the robust price of anarchy of their altruistic extensions. For the majority of the mentioned game classes, the results extend to the more differentiated friendship setting. As we show, our reduction technique covers this model if the base game satisfies three additional natural properties.