On Linear Congestion Games with Altruistic Social Context

TL;DR

This paper investigates the existence and efficiency of pure Nash equilibria in linear congestion games with altruistic social contexts, providing characterizations and bounds that extend prior results.

Contribution

It offers a broad characterization of social contexts ensuring equilibrium existence and tight bounds on their inefficiency, extending previous findings in the literature.

Findings

Pure Nash equilibria exist under specific social contexts.

Bounds on the price of anarchy and stability are established.

Some results improve or extend previous literature.

Abstract

We study the issues of existence and inefficiency of pure Nash equilibria in linear congestion games with altruistic social context, in the spirit of the model recently proposed by de Keijzer {\em et al.} \cite{DSAB13}. In such a framework, given a real matrix $\Gamma=(\gamma_{ij})$ specifying a particular social context, each player $i$ aims at optimizing a linear combination of the payoffs of all the players in the game, where, for each player $j$, the multiplicative coefficient is given by the value $\gamma_{ij}$. We give a broad characterization of the social contexts for which pure Nash equilibria are always guaranteed to exist and provide tight or almost tight bounds on their prices of anarchy and stability. In some of the considered cases, our achievements either improve or extend results previously known in the literature.