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J. M. Bilbao J. R. Fernández N. Jiménez J. J. López 《Annals of Operations Research》2008,158(1):99-115
The aim of the present paper is to study a one-point solution concept for bicooperative games. For these games introduced
by Bilbao (Cooperative Games on Combinatorial Structures, 2000) , we define a one-point solution called the Shapley value, since this value can be interpreted in a similar way to the classical
Shapley value for cooperative games. The main result of the paper is an axiomatic characterization of this value. 相似文献
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A mean value for games with communication structures 总被引:1,自引:0,他引:1
Gérard Hamiache 《International Journal of Game Theory》2004,32(4):533-544
The mean value is a new extension of the Shapley value for games with communication structure representable by a simple graph; only pairwise meetings can occur, although some of them might not be permitted. The new value is characterized by a set of axioms of which the one with the most far-reaching effect is an associated consistency property already used in various contexts. The mean value of an n-player unanimity game is the arithmetic average of the mean values of (n–1)-player unanimity games with connected support, which means games in which the deleted players are not articulation point of the considered graph.I wish to thank the anonymous referees for their helpful remarks. The usual disclaimer applies.Received: April 2002/Accepted: February 2004 相似文献
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Ehud Lehrer 《International Journal of Game Theory》2003,31(3):341-351
This paper deals with a temporal aspect of cooperative games. A solution of the game is reached through an allocation process.
At each stage of the allocation process of a cooperative game a budget of fixed size is distributed among the players. In
the first part of this paper we study a type of process that, at any stage, endows the budget to a player whose contribution
to the total welfare, according to some measurements, is maximal. It is shown that the empirical distribution of the budget
induced by each process of the family converges to a least square value of the game, one such value being the Shapley value.
Other allocation processes presented here converge to the core or to the least core.
Received: January 2001/Revised: July 2002
I am grateful to the Associate Editor and to the two anonymous referees of International Journal of Game Theory. This research was partially supported by the Israel Science Foundation, grant no. 178/99 相似文献
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In this paper we analyze cooperative games whose characteristic function takes values in a partially ordered linear space.
Thus, the classical solution concepts in cooperative game theory have to be revisited and redefined: the core concept, Shapley–Bondareva
theorem and the Shapley value are extended for this class of games. The classes of standard, vector-valued and stochastic
cooperative games among others are particular cases of this general theory.
The research of the authors is partially supported by Spanish DGICYT grant numbers MTM2004-0909, HA2003-0121, HI2003-0189,
MTM2007-67433-C02-01, P06-FQM-01366. 相似文献
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《Operations Research Letters》2020,48(1):55-60
In this note, we discuss two solutions for cooperative transferable utility games, namely the Shapley value and the Proper Shapley value. We characterize positive Proper Shapley values by affine invariance and by an axiom that requires proportional allocation of the surplus according to the individual singleton worths in generalized joint venture games. As a counterpart, we show that affine invariance and an axiom that requires equal allocation of the surplus in generalized joint venture games characterize the Shapley value. 相似文献
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Irinel Dragan 《TOP》2006,14(1):61-73
The main result proved in this paper is the fact that any Least Square Value is the Shapley value of a game obtained from
the given game by rescaling. An Average per capita formula for Least Square Values, similar to the formula for the Shapley
value (Dragan (1992)), will lead to this conclusion and allow a parallel computation for these values. The potential for the
Least Square Values, a potential basis relative to Least Square Values and an approach similar to the one used for the Shapley
value is allowing us to solve the Inverse problem for Least Square Values. 相似文献
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Gérard Hamiache 《International Journal of Game Theory》2001,30(2):279-289
In this work, a new axiomatization of the Shapley is presented. An associated game is constructed. We define a sequence of
games, when the term of order n, in this sequence, is the associated game of the term of order (n−1). We show that the sequence converges and that the limit game is inessential. The solution is obtained using the inessential
game axiom, the associated consistency axiom and the continuity axiom. As a by-product, we note that neither the additivity
nor the efficiency axioms are needed.
Accepted September 2001 相似文献
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Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows that the equivalence is not preserved since these solutions can all be different for cooperative games with random payoffs. Properties are studied and a characterization on a subclass of games is provided.2000 Mathematics Subject Classification Number: 91A12.The authors thank two anonymous referees and an associate editor for their helpful comments.This author acknowledges financial support from the Netherlands Organization for Scientific Research (NWO) through project 613-304-059.Received: October 2000 相似文献
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A multichoice game is a generalization of a cooperative TU game in which each player has several activity levels. We study the solution for these games proposed by Van Den Nouweland et al. (1995) [Van Den Nouweland, A., Potters, J., Tijs, S., Zarzuelo, J.M., 1995. Cores and related solution concepts for multi-choice games. ZOR-Mathematical Methods of Operations Research 41, 289–311]. We show that this solution applied to the discrete cost sharing model coincides with the Aumann-Shapley method proposed by Moulin (1995) [Moulin, H., 1995. On additive methods to share joint costs. The Japanese Economic Review 46, 303–332]. Also, we show that the Aumann-Shapley value for continuum games can be obtained as the limit of multichoice values for admissible convergence sequences of multichoice games. Finally, we characterize this solution by using the axioms of balanced contributions and efficiency. 相似文献
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This paper deals with cooperative games in which only certain coalitions are allowed to form. There have been previous models developed to confront the problem of unallowable coalitions. Games restricted by a communication graph were introduced by Myerson and Owen. In their model, the feasible coalitions are those that induce connected subgraphs. Another type of model is introduced in Gilles, Owen and van den Brink. In their model, the possibilities of coalition formation are determined by the positions of the players in a so-called permission structure. Faigle proposed another model for cooperative games defined on lattice structures. We introduce a combinatorial structure called augmenting system which is a generalization of the antimatroid structure and the system of connected subgraphs of a graph. In this framework, the Shapley value of games on augmenting systems is introduced and two axiomatizations of this value are showed. 相似文献
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The selectope for cooperative games 总被引:1,自引:0,他引:1
The selectope of a cooperative transferable utility game is the convex hull of the payoff vectors obtained by assigning the
Harsanyi dividends of the coalitions to members determined by so-called selectors. The selectope is studied from a set-theoretic
point of view, as superset of the core and of the Weber set; and from a value-theoretic point of view, as containing weighted
Shapley values, random order values, and sharing values.
Received May 1997/Revised version September 1999 相似文献
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A multi-choice game is a generalization of a cooperative game in which each player has several activity levels. We study
the extended Shapley value as proposed by Derks and Peters (1993). Van den Nouweland (1993) provided a characterization that
is an extension of Young's (1985) characterization of the Shapley value. Here we provide several other characterizations,
one of which is the analogue of Shapley's (1953) original characterization. The three other characterizations are inspired
by Myerson's (1980) characterization of the Shapley value using balanced contributions.
Received: November 1997/final version: February 1999 相似文献
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A nontransferable utility (NTU) game assigns a set of feasible pay-off vectors to each coalition. In this article, we study NTU games in situations in which there are restrictions on coalition formation. These restrictions will be modelled through interior structures, which extend some of the structures considered in the literature on transferable utility games for modelling restricted cooperation, such as permission structures or antimatroids. The Harsanyi value for NTU games is extended to the set of NTU games with interior structure. 相似文献
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Hamiache axiomatized the Shapley value as the unique solution verifying the inessential game property, continuity and associated consistency. Driessen extended Hamiache’s axiomatization to the enlarged class of efficient, symmetric, and linear values. In this paper, we introduce the notion of row (resp. column)-coalitional matrix in the framework of cooperative game theory. The Shapley value as well as the associated game are represented algebraically by their coalitional matrices called the Shapley standard matrix MSh and the associated transformation matrix Mλ, respectively. We develop a matrix approach for Hamiache’s axiomatization of the Shapley value. The associated consistency for the Shapley value is formulated as the matrix equality MSh = MSh · Mλ. The diagonalization procedure of Mλ and the inessential property for coalitional matrices are fundamental tools to prove the convergence of the sequence of repeated associated games as well as its limit game to be inessential. In addition, a similar matrix approach is applicable to study Driessen’s axiomatization of a certain class of linear values. In summary, it is illustrated that matrix analysis is a new and powerful technique for research in the field of cooperative game theory. 相似文献
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ZHANGSHENGKAI YANHUIZHEN ZHANGYADONG 《高校应用数学学报(英文版)》1997,12(2):205-214
In this paper we have studied n-person game problems of (0,1) normalization and composition. Also we have concerned multilinear extensions of composition games and especial games [5-7,9-14]. As we have studied Shapley value [1-4,15], we will give some proofs of the the orems. 相似文献