The present paper studies a new potential function of a cooperative game with a coalition structure. When define a marginal contribution of each player, a notion of a coalition formation by Hart and Kurz (1983) is considered. Our potential is a real-valued function in contrast to Winter (1992)’s one which is vector-valued function whose dimension is the number of elements in the coalition struc...

In a Shapley-Shubik assignment problem with a supermodular output matrix, we consider games in which each firm makes a take-it-orleave-it salary offer to one applicant, and a match is made only when the offer is accepted by her. We consider both one-shot and multistage games. In either game, we show that there can be many equilibrium salary vectors which are higher or lower than the minimum com...

The present paper introduces bicooperative games and develops some general values on the vector space of these games. First, we define biprobabilistic values for bicooperative games and observe in detail the axioms that characterize such values. Following the work of Weber [R.J. Weber, Probabilistic values for games, in: A.E. Roth (Ed.), The Shapley Value: Essays in Honor of Lloyd S. Shapley Ca...

We consider the problem of how to determine a fair source coding rate allocation method for the lossless data compression problem in multiterminal networks, e.g, the wireless sensor network where there are a large number of sources to be encoded. We model this problem by a game-theoretic approach and present a decomposition method for obtaining the Shapley value, a fair source coding rate vecto...

The evolutionary stability is a fundamental issue in single-criterion games. This paper considers the evolutionary stability in multicriteria games. Since a payoff is given by a vector, we provide several concepts which are equivalent in single-criterion games and investigate their hierarchical structure. On the other hand, Shapley has introduced concepts called a strong and a weak equilibrium....

In spite of increased attention on explainable machine learning models, explaining multi-output predictions has not yet been extensively addressed. Methods that use Shapley values to attribute feature contributions the decision making are one most popular approaches explain local individual and global predictions. By considering each output separately in tasks, these methods fail provide comple...

The asymptotic value, introduced by Kannai in 1966, is an asymptotic approach to the notion of the Shapley value for games with infinitely many players. A vector measure game is a game v where the worth v S of a coalition S is a function f of S where is a vector measure. Special classes of vector measure games are the weighted majority games and the two-house weighted majority games, where a tw...

We introduce a new axiom, the balanced contributions property for equal contributors. This axiom is defined by restricting the requirement of the balanced contributions property (Myerson (1980)) to two players whose contributions to the grand coalition are the same. We prove that this axiom, together with efficiency and weak covariance, characterizes a new class of solutions, the r-egalitarian ...

The principle of weak monotonicity for cooperative games states that if a game changes so that the worth of the grand coalition and some player’s marginal contribution to all coalitions increase or stay the same, then this player’s payoff should not decrease. We investigate the class of values that satisfy effi ciency, symmetry, and weak monotonicity. It turns out that this class coincides with...

This paper characterizes the aspects of exchangeability in the Shapley value. We show that, in the Shapley value, each player’s prospects of joining a t-player game as the last member of the game is a moment sequence of the uniform distribution. We prove that, with finite exchangeability, the Shapley value is the only value in which the probability assignment is a unique mixture of independent ...