The robust price of anarchy of altruistic games

We study the inefficiency of equilibria for several classes of games when players are (partially) altruistic. We model altruistic behavior by assuming that player i's perceived cost is a convex combination of 1-α _i times his direct cost and α_i times the social cost. Tuning the parameters α _i allows smooth interpolation between purely selfish and purely altruistic behavior. Within this framework, we study altruistic extensions of cost-sharing games, utility games, and linear congestion games. Our main contribution is an adaptation of Roughgarden's smoothness notion to altruistic extensions of games. We show that this extension captures the essential properties to determine the robust price of anarchy of these games, and use it to derive mostly tight bounds.