the University of Tokyo. Special thanks are due to Hideshi Itoh for suggesting the application to contract theory during the seminar at Osaka University. The usual disclaimer applies. Abstract: In potential games, as considered by Monderer and Shapley (1996a), each player's gain from a deviation is equal to the gain in a potential function. We prove that a game has a potential function if and o...

The Shapley value for directed graph (digraph) games, TU games with limited cooperation introduced by an arbitrary digraph prescribing the dominance relation among the players, is introduced. It is defined as the average of marginal contribution vectors corresponding to all permutations that do not violate the subordination of players. We assume that in order to cooperate players may join only ...

The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely stu...

We propose a simple mechanism to determine how the surplus generated by cooperation is to be shared in zero-monotonic environments with transferable utility. The mechanism consists of a bidding stage followed by a proposal stage. We show that the subgame perfect equilibrium outcomes of this mechanism coincide with the vector of the Shapley value payoffs. We extend our results to implement the w...

We suggest a new one-parameter family of solidarity values for TU-games. The members of this class are distinguished by the type of player whose removal from a game does not a¤ect the remaining players payo¤s. While the Shapley value and the equal division value are the boundary members of this family, the solidarity value is its center. With exception of the Shapley value, all members of this ...

Our concern is the extension of the theory of the Shapley value to problems involving externalities. Using the standard axiom systems behind the Shapley value for an arbitrary exogenous coalition structure leads to the identification of bounds on players’ payoffs around an “externality-free” value. In endogenizing the coalition structure, we analyze a two-stage process of coalition formation in...

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it the ...

This paper presents a time-consistent dynamic Shapley value imputation for class of differential network games. A novel form measuring the worth coalitions – named as cooperative-trajectory characteristic function is developed imputation. This new functions evaluated along cooperative trajectory. It measures under process cooperation instead min-max confrontation or...