Implementation of a Value for Generalized Characteristic Function Games

Generalized characteristic function games are a variation of characteristic function games, in which the value of a coalition depends not only on the identities of its members, but also on the order in which the coalition is formed. This class of games is a useful abstraction for a number of realistic settings and economic situations, such as modeling relationships in social networks. To date, two main extensions of the Shapley value have been proposed for generalized characteristic function games: the Nowak-Radzik value and the S´anchez-Berganti˜nos value. In this context, the present article studies generalized characteristic function games from the point of view of implementation and computation. Specifically, the article presents a non-cooperative mechanism that implements the Nowak-Radzik value in Subgame-Perfect Nash Equilibria in expectation.