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1.
The simplified modified nucleolus of a cooperative TU-game 总被引:1,自引:0,他引:1
Svetlana Tarashnina 《TOP》2011,19(1):150-166
In the present paper, we introduce a new solution concept for TU-games, the simplified modified nucleolus or the SM-nucleolus. It is based on the idea of the modified nucleolus (the modiclus) and takes into account both the constructive
power and the blocking power of a coalition. The SM-nucleolus inherits this convenient property from the modified nucleolus, but it avoids its high computational complexity.
We prove that the SM-nucleolus of an arbitrary n-person TU-game coincides with the prenucleolus of a certain n-person constant-sum game, which is constructed as the average of the game and its dual. Some properties of the new solution
are discussed. We show that the SM-nucleolus coincides with the Shapley value for three-person games. However, this does not hold for general n-person cooperative TU-games. To confirm this fact, a counter example is presented in the paper. On top of this, we give several
examples that illustrate similarities and differences between the SM-nucleolus and well-known solution concepts for TU-games. Finally, the SM-nucleolus is applied to the weighted voting games. 相似文献
2.
Yu-Hsien Liao 《Fuzzy Optimization and Decision Making》2016,15(2):129-138
In the framework of fuzzy transferable-utility games, we propose alternative reduced games by considering the players and their activity levels simultaneously. Further, we characterize the consistent value by means of related consistency and different properties. 相似文献
3.
This short note proves that the least square nucleolus (Ruiz et al. (1996)) and the lexicographical solution (Sakawa and Nishizaki (1994)) select the same imputation in each game with nonempty imputation set. As a consequence the
least square nucleolus is a general nucleolus (Maschler et al. (1992)).
Received: December 1998/Revised version: July 1999 相似文献
4.
This note extends the solution concept of the core for cooperative games to multi-choice games. We propose an extension of
the theorem of Bondareva (Problemy Kybernetiki 10:119–139, 1963) and Shapley (Nav Res Logist Q 14:453–460, 1967) to multi-choice games. Also, we introduce a notion of reduced games for multi-choice games and provide an axiomatization
of the core on multi-choice games by means of corresponding notion of consistency and its converse. 相似文献
5.
Vito Fragnelli Fioravante Patrone 《Journal of Mathematical Analysis and Applications》2006,314(2):412-422
The lexicographic order is not representable by a real-valued function, contrary to many other orders or preorders. So, standard tools and results for well-posed minimum problems cannot be used. We prove that under suitable hypotheses it is however possible to guarantee the well-posedness of a lexicographic minimum over a compact or convex set. This result allows us to prove that some game theoretical solution concepts, based on lexicographic order are well-posed: in particular, this is true for the nucleolus. 相似文献
6.
Marcin Malawski 《International Journal of Game Theory》2002,31(1):47-67
The Banzhaf value is the only value satisfying the equal treatment, dummy player and marginal contributions conditions and
neutrality of some linear operators on the spaces of games. Under some of these neutrality assumptions, equal treatment can
be replaced by even weaker conditions. For linear values having the dummy player property, equal treatment is equivalent to
symmetry. All these properties together imply the marginal contributions condition, but in some Banzhaf value axiomatizations
marginal contributions cannot be a substitute for linearity.
Received: December 1997/Revised version: May 2001 相似文献
7.
In this paper we exhibit axiomatizations for the theories of existentially closed posets and existentially closed semilattices.
We do this by considering an infinite axiomatization which characterizes these structures in terms of embeddings of finite
substructures, an axiomatization which exists for any locally finite universal class with a finite language and with the joint
embedding and amalgamation properties. We then find particular finite subsets of these axioms which suffice to axiomatize
both classes.
Research supported by an NSERC Postdoctoral Fellowship.
Research supported by NSERC Grant No. A7256. 相似文献
8.
Yu-Hsien Liao 《Fuzzy Optimization and Decision Making》2017,16(3):257-268
By applying the supreme-utilities under fuzzy behavior, we propose a new solution on fuzzy games. In order to present the rationality for this solution, we adopt an extended reduction to provide related axiomatizations and dynamics process. Based on different viewpoint, we also define excess function to introduce alternative formulation and related dynamic process for this solution respectively. 相似文献
9.
This article describes the per capita nucleolus for bankruptcy games as a bankruptcy rule. This rule, called the clights rule, is based on the well-known constrained equal awards principle and it takes into account a vector of clights, a new term which is a blend of claims and rights. These clights only depend on the vector of claims while the height of the estate determines whether the clights should be interpreted as modified claims or as rights. It is shown that both the clights rule and the Aumann–Maschler rule can be captured within the family of so-called claim-and-right rules. 相似文献
10.
Fan Yang 《Annals of Pure and Applied Logic》2019,170(9):1128-1149
In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in [22] and [11]. We prove a characterization theorem for negatable formulas in independence logic and negatable sentences in dependence logic, and identify an interesting class of formulas that are negatable in independence logic. Dependence and independence atoms, first-order formulas belong to this class. We also demonstrate our extended system of independence logic by giving explicit derivations for Armstrong's Axioms and the Geiger-Paz-Pearl axioms of dependence and independence atoms. 相似文献
11.
Trees with revenues are a generalization of standard trees. In a tree with revenues, players have to pay for their connections to the root, but a player can also earn some revenue from being connected to the root. In this paper, we present an algorithm for calculating the nucleolus. 相似文献
12.
The general nucleolus and the reduced game property 总被引:1,自引:0,他引:1
Professor M. Maschler J. A. M. Potters S. H. Tijs 《International Journal of Game Theory》1992,21(1):85-106
The nucleolus of a TU game is a solution concept whose main attraction is that it always resides in any nonempty -core. In this paper we generalize the nucleolus to an arbitrary pair (,F), where is a topological space andF is a finite set of real continuous functions whose domain is . For such pairs we also introduce the least core concept. We then characterize the nucleolus forclasses of such pairs by means of a set of axioms, one of which requires that it resides in the least core. It turns out that different classes require different axiomatic characterizations.One of the classes consists of TU-games in which several coalitions may be nonpermissible and, moreover, the space of imputations is required to be a certain generalized core. We call these gamestruncated games. For the class of truncated games, one of the axioms is a new kind ofreduced game property, in which consistency is achieved even if some coalitions leave the game, being promised the nucleolus payoffs. Finally, we extend Kohlberg's characterization of the nucleolus to the class of truncated games. 相似文献
13.
Roberto Serrano 《International Journal of Game Theory》1993,22(4):345-357
I present a non-cooperative bargaining game, in which responders may exit at any time and have endogenous outside options. When the order of proposers corresponds to the power that players have in the underlying coalitional function, the unique Markov perfect equilibrium outcome of the game is the prenucleolus. The result holds for 3-player superadditive games. An example shows that it cannot be extented to the same class of games forn players. The mechanism is inspired by the consistency property of the prenucleolus.I am grateful to Vijay Krishna, Andreu Mas-Colell, Eric Maskin, Amy Salsbury, and an anonymous referee for helpful comments and suggestions. 相似文献
14.
Z. Galil 《International Journal of Game Theory》1974,3(3):129-140
In this paper, we considern-person weighted majority games with major and minor players. We prove under certain conditions that if the minor players split into equal “mini-minor” players the nucleolus' components which correspond to the major players do not change. 相似文献
15.
This paper is devoted to the study of solutions for multi-choice games which admit a potential, such as the potential associated
with the extended Shapley value proposed by Hsiao and Raghavan (Int J Game Theory 21:301–302, 1992; Games Econ Behav 5:240–256,
1993). Several axiomatizations of the family of all solutions that admit a potential are offered and, as a main result, it
is shown that each of these solutions can be obtained by applying the extended Shapley value to an appropriately modified
game. In the framework of multi-choice games, we also provide an extension of the reduced game introduced by Hart and Mas-Colell
(Econometrica 57:589–614, 1989). Different from the works of Hsiao and Raghavan (1992, 1993), we provide two types of axiomatizations,
one is the analogue of Myerson’s (Int J Game Theory 9:169–182, 1980) axiomatization of the Shapley value based on the property
of balanced contributions. The other axiomatization is obtained by means of the property of consistency. 相似文献
16.
The process of computing the nucleolus of arbitrary transferable utility games is notoriously hard. A number of papers have appeared in which the nucleolus is computed by an algorithm in which either one or a huge number of huge linear programs have to be solved. We show that on the class of veto-rich games, the nucleolus is the unique kernel element. Veto-rich games are games in which one of the players is needed by coalitions in order to obtain a non-zero payoff. We then provide a fast algorithm which does not use linear programming techniques to compute the nucleolus of these games. Furthermore, we provide a few examples of economic situations which belong to the class of veto-rich games and which are treated in the literature. 相似文献
17.
This paper provides an axiomatic framework to compare the D-core (the set of undominated imputations) and the core of a cooperative
game with transferable utility. Theorem 1 states that the D-core is the only solution satisfying projection consistency, reasonableness
(from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity.
Moreover, these axioms also characterize the core on the domain of convex games, totally balanced games, balanced games, and
superadditive games.
相似文献
18.
Mathematical Programming - The maximum number of edge-disjoint spanning trees in a network has been used as a measure of the strength of a network. It gives the number of disjoint ways that the... 相似文献
19.
Nimrod Megiddo 《Israel Journal of Mathematics》1971,9(2):210-221
The kernel and the nucleolus of a product of two simple games are given in terms of the kernels and the nucleoluses of the
component games. 相似文献
20.
A certain trade of the information about a technological innovation between the initial owner of the information andn identical producers is studied by means of a cooperative game theoretic approach. The information trading situation is modelled as a cooperative (n+1)-person game with side payments. The symmetrical strong -cores (including the core), the nucleolus and the kernel of the cooperative game model are determined. Interpretations of these game theoretic solutions and their implications for the information trading problem are given. 相似文献