the shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. certainly, the shapley value can be used in interesting sharing cost/reward problems in the operations research area such as connection, routing, scheduling, production and inventory situations. in this paper, we focus on the shapl...

The present paper studies non-cooperative bargaining models implementing a cooperative solution proposed by Kamijo(2005). The basic idea was inspired by the bidding approach of Perez-Castrillo and Wettstein(2001). They show that this mechanism achieves the Shapley value payoff vector in equilibrium. The solution concept considered in this paper is a generalized Shapley value applied to TU(trans...

This paper studies coalition formation, payoff division and expected payoffs in a ”divide the dollar by majority rule” game with random proposers. A power index is called self-confirming if it can be obtained as an equilibrium of the game using the index itself as probability vector. Unlike the Shapley value and other commonly used power indices, the nucleolus has this property. The proof uses ...

In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoff...

The Semivalues were introduced axiomatically by Dubey et al [7], as weighted values of cooperative games. For transferable utility games (TU games), they obtained a formula for computing the Semivalue associated with a given weight vector. Among the Semivalues are the well known Shapley value, Banzhaf value, and many other values, for different weight vectors. Let G be the space of cooperative ...

Different axiomatic systems for the Shapley value can be found in the literature. For games with a coalition structure, the Shapley value also has been axiomatized in several ways. In this paper, we discuss a generalization of the Shapley value to the class of partition function form games. The concepts and axioms, related to the Shapley value, have been extended and a characterization for the ...

This paper concerns the analysis of the Shapley value in matching games. Matching games constitute a fundamental class of cooperative games which help understand and model auctions and assignments. In a matching game, the value of a coalition of vertices is the weight of the maximum size matching in the subgraph induced by the coalition. The Shapley value is one of the most important solution c...

We provide new axiomatic characterizations of the proportional Shapley value, a weighted value with the worths of the singletons as weights. This value satisfies anonymity and therefore symmetry just as the Shapley value and has characterizations which are proportional counterparts to the famous characterizations of the Shapley value in Shapley (1953b), Myerson (1980) and Young (1985a). If the ...

The concept of Shapley values was first introduced into the game theory by Shapley [1953] in the framework of transferable payoffs, playing an important role in the game theory. According to a standard textbook on game theory it is interpreted as in what follows. “Suppose that all the players are arranged in some order, all orders being equally likely. Then player i’s Shapley value is the expec...