An Axiomatic Characterization of Weighted Congestion Games

Аннотация

In weighted congestion games, players’ weights and resource functions are predefined. This way, they can be applied for modeling traffic intensity, exploring market competition, and analyzing other problems with a congestion effect. In some normal-form games how ever, players’ weights and resource functions are not defined explicitly and players may be unaware of their existence. This article finds the necessary and sufficient conditions for representing a normal-form game as a weighted congestion game. Axioms are formulated that guarantee there exist positive weights of players and positive-definite resource functions. It is proved that a normal-form game satisfies the axioms of Positivity and the Independence of Irrelevant Choices (Konishi et al., 1997) if and only if it is a singleton weighted congestion game. This result indicates that the payoff functions of players in hedonic games are represented in the form of a weighted congestion game. It is demonstrated that a normal-form game satisfies the axioms of Non-Negativity, Transfer, Resource Marginal Contribution, and the Independence of Irrelevant Choices if and only if it is a full weighted congestion game with player-independent resource functions.