Social context congestion games

We consider the social context games introduced by Ashlagi et al. (2008), where we are given a classical game, an undirected social context graph expressing collaboration among the players and an aggregation function. The players and strategies are as in the underlying game, while the players’ costs are computed from their immediate costs, that is the original payoffs in the underlying game, according to the neighborhood in the social context graph and the aggregation function. More precisely, the perceived cost incurred by a player is the result of the aggregation function applied to the immediate costs of her neighbors and of the player herself. We investigate social context games in which the underlying games are linear congestion games and Shapley cost sharing games, while the aggregation functions are min, max and sum. In each of the six arising cases, we first completely characterize the class of the social context graph topologies guaranteeing the existence of pure Nash equilibria. We then provide optimal or asymptotically optimal bounds on the price of anarchy of 22 out of the 24 cases obtained by considering four social cost functions, namely, max and sum of the players’ immediate and perceived costs. Finally, we extend some of our results to multicast games, a relevant subclass of the Shapley cost sharing ones.