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1.
In terms of the similarity of matrices, by combining the dual operator and the linear mapping with respect to Hamiache’s associated game on the game space, the Shapley value for TU-games is axiomatized as the unique value verifying dual similar associated consistency, continuity, and the inessential game property. 相似文献
2.
We propose a dynamic process leading to the Shapley value of TU games or any solution satisfying Inessential Game (IG) and Continuity (CONT), based on a modified version of Hamiache's notion of an associated game.
The authors are very grateful to William Thomson and two anonymous referees for valuable comments which much improve the paper.
They provide better statements and proofs of several major results than the original ones. 相似文献
3.
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
4.
《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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7.
Transversality of the Shapley value 总被引:1,自引:0,他引:1
A few applications of the Shapley value are described. The main choice criterion is to look at quite diversified fields, to
appreciate how wide is the terrain that has been explored and colonized using this and related tools.
The title is inspired by a tutorial that one of the authors planned to deliver at the 7th meeting on Game Theory and Practice
(Montreal, 2007), but was unable to do it for personal reasons. Thanks to Georges Zaccour whose invitation sparked the present
survey. 相似文献
8.
Néstor E. Aguilera Silvia C. Di Marco Mariana S. Escalante 《European Journal of Operational Research》2010
We address the problem of finding a suitable definition of a value similar to that of Shapley’s, when the games are defined on a subfamily of coalitions with no structure. We present two frameworks: one based on the familiar efficiency, linearity and null player axioms, and the other on linearity and the behavior on unanimity games. We give several properties and examples in each case, and give necessary and sufficient conditions on the family of coalitions for the approaches to coincide. 相似文献
9.
The main goal of this paper is to introduce the probability game. On one hand, we analyze the Shapley value by providing an axiomatic characterization. We propose the so-called independent fairness property, meaning that for any two players, the player with larger individual value gets a larger portion of the total benefit. On the other, we use the Shapley value for studying the profitability of merging two agents. 相似文献
10.
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
11.
Gérard Hamiache 《International Journal of Game Theory》2001,29(4):517-532
This paper presents two new axiomatizations of the Owen value for games with coalition structures. Two associated games are
defined and a consistency axiom is required. The construction of the associated games presupposes that coalitions behave in
an aggressive manner towards players who are not members of the same unions and in a friendly manner towards players that
do belong to their unions. The consistency axiom necessitates the definition of only one associated game which is not a reduced
game.
Received: February 1999/Revised version: January 2000 相似文献
12.
An axiomatization of the Shapley value using a fairness property 总被引:1,自引:0,他引:1
René van den Brink 《International Journal of Game Theory》2002,30(3):309-319
In this paper we provide an axiomatization of the Shapley value for TU-games using a fairness property. This property states that if to a game we add another game in which two players are symmetric then their payoffs change by the same amount. We show that the Shapley value is characterized by this fairness property,
efficiency and the null player property. These three axioms also characterize the Shapley value on the class of simple games.
Revised August 2001 相似文献
13.
Chih-Ru Hsiao 《Southeast Asian Bulletin of Mathematics》2003,26(3):413-420
We discover an interesting relationship between the Shapley value and the asymmetric Shapley value.AMS Subject Classification (2000): Primary 91A06, 91A12, 91B12, 91B74, Secondary 91A80 相似文献
14.
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
15.
16.
N. I. Naumova 《International Journal of Game Theory》2005,33(4):523-534
Let f be a single valued solution for cooperative TU games that satisfies inessential game property, efficiency, Hart Mas-Colell
consistency and for two person games is strictly monotonic and individually unbounded. Then there exists a family of strictly
increasing functions associated with players that completely determines f. For two person games, both players have equal differences between their functions at the solution point and at the values
of characteristic function of their singletons. This solution for two person games is uniquely extended to n person games due to consistency and efficiency. The extension uses the potential with respect to the family of functions
and generalizes potentials introduced by Hart and Mas Colell [6]. The weighted Shapley values, the proportional value described
by Ortmann [11], and new values generated by power functions are among these solutions.
The author is grateful to anonymous referee and Associate Editor for their comments and suggestions. 相似文献
17.
Dan Butnariu 《Fuzzy Sets and Systems》1980,4(1):63-72
The aim of the paper is to explain new concepts of solutions for n-persons fuzzy games. Precisely, it contains new definitions for ‘core’ and ‘Shapley value’ in the case of the n-persons fuzzy games. The basic mathematical results contained in the paper are these which assert the consistency of the ‘core’ and of the ‘Shapley value’. It is proved that the core (defined in the paper) is consistent for any n-persons fuzzy game and that the Shapley values exists and it is unique for any fuzzy game with proportional values. 相似文献
18.
Forming coalitions and the Shapley NTU value 总被引:1,自引:0,他引:1
A simple protocol for coalition formation is presented. First, an order of the players is randomly chosen. Then, a coalition grows by sequentially incorporating new members in this order. The protocol is studied in the context of non-transferable utility (NTU) games in characteristic function form. If (weighted) utility transfers are feasible when everybody cooperates, then the expected subgame perfect equilibrium payoff allocation anticipated before any implemented game is the Shapley NTU value. 相似文献
19.
It is proved that Youngs [4] axiomatization for the Shapley value by marginalism, efficiency, and symmetry is still valid for the Shapley value defined on the class of nonnegative constant-sum games with nonzero worth of grand coalition and on the entire class of constant-sum games as well.The research was supported by NWO (The Netherlands Organization for Scientific Research) grant NL-RF 047-008-010.I am thankful to Theo Driessen, Natalia Naumova and Elena Yanovskaya for interesting discussions and comments. The useful remarks of two anonymous referees are also appreciated. 相似文献
20.
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