Social Context Games

We introduce social context games. A social context game is defined by an underlying game in strategic form, and a social context consisting of an undirected graph of neighborhood among players and aggregation functions. The players and strategies in a social context game are as in the underlying game, while the players' utilities in a social context game are computed from their payoffs in the underlying game based on the graph of neighborhood and the aggregation functions. Examples of social context games are ranking games and coalitional congestion games. In this paper we consider resource selection games as the underlying games, and four basic social contexts. An important property of resource selection games is the existence of pure strategy equilibrium. We study the existence of pure strategy Nash equilibrium in the corresponding social context games. We also show that the social context games possessing pure strategy Nash equilibria are not potential games, and therefore are distinguished from congestion games.