Coalition Formation Resource Sharing Games in Networks

Abstract

Cooperative game theory deals with systems where players want to cooperate to improve their payoffs. But players may choose coalitions in a non-cooperative manner, leading to a coalition-formation game. We consider such a game with several players (willing to cooperate) and a possible adamant player (unwilling to cooperate) involved in resource-sharing. Here, the strategy of a player is the set of players with whom it wants to form a coalition. Given a strategy profile, an appropriate partition of coalitions is formed; players in each coalition maximize their collective utilities leading to a non-cooperative resource-sharing game among the coalitions, the (unique) utilities at the resulting equilibrium are shared via Shapley-value; these shares define the utilities of players for the given strategy profile in the coalition-formation game. We also consider the utilitarian solution to derive the price of anarchy.