Altruism in atomic congestion games

Abstract

This paper studies the effects of introducing altruistic agents into atomic congestion games. Altruistic behavior is modeled by a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting social cost. Stable states are the Nash equilibria of these games, and we examine their existence and the convergence of sequential best-response dynamics. For symmetric singleton games with arbitrary delay functions we provide a polynomial time algorithm to decide existence for symmetric singleton games. Our algorithm can be extended to compute best and worst Nash equilibria if they exist. For more general congestion games existence becomes NP-hard to decide, even for symmetric network games with quadratic delay functions. Perhaps surprisingly, if all delay functions are linear, there exists a Nash equilibrium and any better-response dynamics converges. In addition, we consider a scenario in which a central altruistic institution can motivate agents to act altruistically. We provide constructive and hardness results for finding the minimum number of altruists to stabilize an optimal congestion profile and more general mechanisms to incentivize agents to adopt favorable behavior. © 2009 Springer Berlin Heidelberg.