Social Context Congestion Games

The widespread of decentralized and autonomous computational systems, such as highly distributed networks, has rapidly increased the interest of computer scientists for existence and efficiency of equilib-ria solutions in presence of selfish non-cooperative users. Nevertheless, there are scenarios of practical application (i.e., social networks) in which it can be observed a certain degree of cooperation among users who are related by some kind of knowledge relationships. In such environments, in fact, it may be the case that the happiness of a player does not depend only on her experienced utility, but it is rather somehow related to the one of her " friends ". As a consequence, considerable research effort is being devoted to the determination and investigation of suitable frameworks able to combine in a realistic way game theoretical concepts with social network aspects. Such a task is usually accomplished by coupling a standard non-cooperative game with a social graph expressing some kind of relationship among the players involved in the game. Social graphs, termed as social knowledge graphs, were first used in [2–4,6] in order to model the lack of complete information among players. In particular, each player in the game is represented as a node in the graph and it is assumed that there exists an edge between node v i and node v j if and only if player i knows player j's adopted strategy. Another model, exploiting social graphs in a different and perhaps more powerful way, is that of social context games introduced in [1]. These kinds of games constitute an interesting extension able to capture important concepts related to social aspects in non-cooperative games, like, for instance, collaboration, coordination and collusion among subsets of players. Consider a strategic game SG defined by a given set of players, strategies and payoff functions which we assume, without loss of generality, to be costs for the players and which are called immediate costs. Given a social graph G, termed here as social context graph, the neighborhood of node v i in G defines the set of players interacting with player i. The particular type of interaction is then characterized by an aggregation function f which maps tuples of real values into real values. A social context game, defined by the triple (SG, G, f), is a game in which players play as in SG and the cost experienced by player i, called perceived cost, is obtained …