共查询到20条相似文献,搜索用时 15 毫秒
1.
An alternative characterization of the weighted Banzhaf value 总被引:1,自引:0,他引:1
We provide a new characterization of the weighted Banzhaf value derived from some postulates in a recent paper by Radzik, Nowak and Driessen [7]. Our approach owes much to the work by Lehrer [4] on the classical Banzhaf value based on the idea of amalgamation of pairs of players and an induction construction of the value. Compared with the approach in [7] we consider two new postulates: a weighted version of Lehrer’s “2-efficiency axiom” [4] and a generalized “null player out” property studied in terms of symmetric games by Derks and Haller [2]. Received: December 1997/final version: October 1999 相似文献
2.
Luis M. Ruiz 《TOP》1999,7(1):163-168
In this note we show that the Banzhaf semivalue is consistent with respect to a suitable reduced game which keeps a clear
parallelism with that defined by Hart and Mas-Colell in (1989) to prove the consistency of the Shapley value. We also use
this reduced game property to characterize the Banzhaf semivalue. 相似文献
3.
本文结合文[1,2]中关于拟阵上静态结构和动态结构合作对策Shapley函数的描述,探讨了两类拟阵上的Banzhaf函数.通过给出相应的公理体系,论述了两类拟阵上Banzhaf函数的存在性和唯一性,拓展了拟阵上分配指标的研究范围.同时讨论了两类合作对策上Banzhaf函数的有关性质.最后通过算例来说明局中人在此类合作对策中的Banzhaf指标. 相似文献
4.
《Operations Research Letters》2022,50(2):190-194
The graph Banzhaf value was introduced and axiomatically characterized by Alonso-Meijide and Fiestras-Janeiro (2006). In this paper we propose the reduced game and consistency of the graph Banzhaf value for communication situations. By establishing the relationship between the Harsanyi dividends of a coalition in a communication situation and the reduced communication situation, we provide a new axiomatization of the graph Banzhaf value by means of the axioms of consistency and standardness. 相似文献
5.
Cooperative games on antimatroids are cooperative games in which coalition formation is restricted by a combinatorial structure which generalizes permission structures. These games group several well-known families of games which have important applications in economics and politics. The current paper establishes axioms that determine the restricted Banzhaf value for cooperative games on antimatroids. The set of given axioms generalizes the axiomatizations given for the Banzhaf permission values. We also give an axomatization of the restricted Banzhaf value for the smaller class of poset antimatroids. Finally, we apply the above results to auction situations. 相似文献
6.
7.
José M. Alonso-Meijide M. Gloria Fiestras-Janeiro 《Annals of Operations Research》2002,109(1-4):213-227
In this paper we introduce a new coalitional value in the context of TU games with an a priori system of unions, which it is called the symmetric coalitional Banzhaf value. This value satisfies the property of symmetry in the quotient game, the quotient game property, and it is a coalitional value of Banzhaf. Several characterizations are provided and two political examples illustrate the differences with respect to the Owen value and the Banzhaf–Owen value. 相似文献
8.
The coordination of strategies in a cooperative game, when some players decide to act together, is the basis of the partnership notion. Nevertheless, in some situations, it may be more convenient to form an effective coalition or alliance. In this work, we consider the Banzhaf semivalue and use it to discuss the convenience to form either partnerships or alliances, especially in simple games. Throughout the paper, some mathematical properties of the Banzhaf semivalue, in relation with the partnership formation, are derived. 相似文献
9.
We suggest new characterizations of the Banzhaf value without the symmetry axiom, which reveal that the characterizations by Lehrer (Int J Game Theory 17:89–99, 1988) and Nowak (Int J Game Theory 26:137–141, 1997) as well as most of the characterizations by Casajus (Theory Decis 71:365–372, 2011b) are redundant. Further, we explore symmetry implications of Lehrer’s 2-efficiency axiom. 相似文献
10.
The aim of this paper is to study a new class of cooperative games called interior operator games. These games are additive
games restricted by antimatroids. We consider several types of cooperative games as peer group games, big boss games, clan
games and information market games and show that all of them are interior operator games. Next, we analyze the properties
of these games and compute the Shapley, Banzhaf and Tijs values. 相似文献
11.
An axiomatic characterization of ‘a Banzhaf score’ notion is provided for a class of games called (j,k) simple games with a numeric measure associated to the output set, i.e., games with n players, j ordered qualitative alternatives in the input level and k possible ordered quantitative alternatives in the output. Three Banzhaf measures are also introduced which can be used to
determine a player's ‘a priori’ value in such a game. We illustrate by means of several real world examples how to compute
these measures.
Research partially supported by Grant BFM 2003-01314 of the Science and Technology Spanish Ministry and the European Regional
Development Fund. 相似文献
12.
Emilio Calvo Esther Gutiérrez Juan Carlos Santos 《International Journal of Game Theory》2000,29(2):177-188
We consider multichoice NTU games, i.e., cooperative NTU games in which players can participate in the game with several
levels of activity. For these games, we define and characterize axiomatically the multichoice consistent value, which is a generalization of the consistent NTU value for NTU games and of the multichoice value for multichoice TU games.
Moreover, we show that this value coincides with the consistent NTU value of a replicated NTU game and we provide a probabilistic
interpretation.
Received: May 1998/Final version: January 2000 相似文献
13.
针对联盟支付以判断值给出的n人合作对策问题,提出了一个基于1-9 判断标度的合作对策Multiplicative-Shapley 值求解公式. 首先给出了判断值平均支付函数的定义,研究了判断值的一致性及其调整方法. 其次通过定义相应的特征函数,给出了具有判断值支付的n人合作对策的优超、伪凸、伪核心、单位元等系列概念,并由此提出一个满足3条公理的Multiplicative-Shapley 值公式. 最后通过一个算例,验证了Multiplicative-Shapley 值公式的可行性和有效性. 相似文献
14.
This contribution is located in the common area of operational research and economics, with a close relation and joint future potential with optimization: game theory. We focus on collaborative game theory under uncertainty. This study is on a new class of cooperative games where the set of players is finite and the coalition values are interval grey numbers. An interesting solution concept, the grey Shapley value, is introduced and characterized with the properties of additivity, efficiency, symmetry and dummy player, which are straightforward generalizations of the corresponding properties in the classical cooperative game theory. The paper ends with a conclusion and an outlook to future studies. 相似文献
15.
Josep Freixas Dorota Marciniak Montserrat Pons 《European Journal of Operational Research》2012,216(2):367-375
In this paper, we characterize the games in which Johnston, Shapley-Shubik and Penrose-Banzhaf-Coleman indices are ordinally equivalent, meaning that they rank players in the same way. We prove that these three indices are ordinally equivalent in semicomplete simple games, which is a newly defined class that contains complete games and includes most of the real-world examples of binary voting systems. This result constitutes a twofold extension of Diffo Lambo and Moulen’s result (Diffo Lambo and Moulen, 2002) in the sense that ordinal equivalence emerges for three power indices (not just for the Shapley-Shubik and Penrose-Banzhaf-Coleman indices), and it holds for a class of games strictly larger than the class of complete games. 相似文献
16.
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
17.
In the present note, the axiomatic characterization of the value function of two-person, zero-sum games in normal form by Vilkas and Tijs is extended to the value function of discounted, two-person, zero-sum stochastic games. The characterizing axioms can be indicated by the following terms: objectivity, monotony, and sufficiency for both players; or sufficiency for one of the players and symmetry. Also, a characterization without using the monotony axiom is given. 相似文献
18.
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
19.
This paper studies a class of delivery problems associated with the Chinese postman problem and a corresponding class of delivery
games. A delivery problem in this class is determined by a connected graph, a cost function defined on its edges and a special
chosen vertex in that graph which will be referred to as the post office. It is assumed that the edges in the graph are owned
by different individuals and the delivery game is concerned with the allocation of the traveling costs incurred by the server,
who starts at the post office and is expected to traverse all edges in the graph before returning to the post office. A graph
G is called Chinese postman-submodular, or, for short, CP-submodular (CP-totally balanced, CP-balanced, respectively) if for
each delivery problem in which G is the underlying graph the associated delivery game is submodular (totally balanced, balanced, respectively).
For undirected graphs we prove that CP-submodular graphs and CP-totally balanced graphs are weakly cyclic graphs and conversely.
An undirected graph is shown to be CP-balanced if and only if it is a weakly Euler graph. For directed graphs, CP-submodular
graphs can be characterized by directed weakly cyclic graphs. Further, it is proven that any strongly connected directed graph
is CP-balanced. For mixed graphs it is shown that a graph is CP-submodular if and only if it is a mixed weakly cyclic graph.
Finally, we note that undirected, directed and mixed weakly cyclic graphs can be recognized in linear time.
Received May 20, 1997 / Revised version received August 18, 1998?Published online June 11, 1999 相似文献