The Böhm–Bawerk horse market: a cooperative analysis

Single–valued solutions for the case of two-sided market games without product differentiation, also known as Böhm–Bawerk horse market games, are analyzed. The nucleolus is proved to coincide with the τ value, and is thus the midpoint of the core. The Shapley value is in the core only if the game is a square glove market, and in this case also coincides with the two aforementioned solutions.Institutional support from research grants BEC 2002-00642, FEDER and SGR2001-0029 is gratefully acknowledged     

Pricing Behaviors on Networks: Some General Results for Two-way Networks

In this paper, we study monopolistic pricing behaviors within a two-way network. In this symbiotic production system, independent decision centers carry out an activity which concurs to the production of different system goods. The players are assumed to know the whole network. Due to this rationality, they try to capture a share of the profit of the firms who sell the system goods to the consumers. These double marginalization behaviors are studied within very general networks. Conditions with ensure existence and uniqueness are discussed. We even provided a complete characterization of an equilibrium. Potential applications are also discussed     

Terror and Counterterror Operations: Differential Game with Cyclical Nash Solution

The purpose of this paper is to study efficient measures to combat terror. To choose efficient actions against terror organizations, the response of terrorists has to be taken into consideration. Thus, an appropriate framework to study the intertemporal strategic interactions of Western governments and terror organizations is dynamic game theory. Using the open-loop Nash solution concept, it turns out that the system may exhibit long-run persistent oscillations. However, transitory behavior is nonunique.     

Economical tight examples for the biased Erd?s-Selfridge theorem

A positional game is essentially a generalization of tic-tac-toe played on a hypergraph (V,F). A pivotal result in the study of positional games is the Erd?s-Selfridge theorem, which gives simple criteria for the existence of a Breaker's winning strategy on a hypergraph F. It has been shown that the Erd?s-Selfridge theorem can be tight and that numerous extremal systems exist for that theorem. We focus on a generalization of the Erd?s-Selfridge theorem proven by Beck for biased (p:q) games, which we call the (p:q)-Erd?s-Selfridge theorem. We show that for pn-uniform hypergraphs there is a unique extremal system for the (p:q)-Erd?s-Selfridge theorem (q?2) when Maker must win in exactly n turns (i.e., as quickly as possible).     

Computing the cores of strategic games with punishment–dominance relations

In this paper, we discuss the computational complexity of the strategic cores of a class of n-person games defined by Masuzawa (Int J Game Theory 32:479–483, 2003), which includes economic situations with monotone externality. We propose an algorithm for finding an α-core strategy of any game in this class which, counting the evaluation of a payoff for a strategy profile as one step, terminates after O(n ³· M) operations, where M is the maximum size of a strategy set of any of the n players. The idea underlying this method is based on the property of reduced games. This paper is based on a part of the doctoral dissertation of the author. The author thanks Mikio Nakayama, Masashi Umezawa, William Thomson, an associate editor, and the anonymous referee for their helpful comments, suggestions, and advice. Thanks are also due to Yukihiko Funaki for a comment that led the author to this subject. The author is responsible for errors and inadvertencies.     

Random marginal and random removal values

We propose two variations of the non-cooperative bargaining model for games in coalitional form, introduced by Hart and Mas-Colell (Econometrica 64:357–380, 1996a). These strategic games implement, in the limit, two new NTU-values: the random marginal and the random removal values. Their main characteristic is that they always select a unique payoff allocation in NTU-games. The random marginal value coincides with the Consistent NTU-value (Maschler and Owen in Int J Game Theory 18:389–407, 1989) for hyperplane games, and with the Shapley value for TU games (Shapley in In: Contributions to the theory of Games II. Princeton University Press, Princeton, pp 307–317, 1953). The random removal value coincides with the solidarity value (Nowak and Radzik in Int J Game Theory 23:43–48, 1994) in TU-games. In large games we show that, in the special class of market games, the random marginal value coincides with the Shapley NTU-value (Shapley in In: La Décision. Editions du CNRS, Paris, 1969), and that the random removal value coincides with the equal split value.      

博弈联盟模糊收益的分配

提出了联盟模糊收益合理分配的一种新方法.首先,在模糊收益α截集上定义了α合理分配集,分析了该分配集与模糊收益Shapley值的关系.接着,给出了模糊收益的α合理Shapley分配函数,对其性质进行了讨论.然后,构造了模糊合理Shapley分配,证明其连续性,得到了联盟模糊收益与模糊合理Shapley分配具有包含关系的结论.     

Potential,value, and coalition formation

In this paper, a simple probabilistic model of coalition formation provides a unified interpretation for several extensions of the Shapley value. Weighted Shapley values, semivalues, weak (weighted or not) semivalues, and the Shapley value itself appear as variations of this model. Moreover, some notions that have been introduced in the search of alternatives to Shapley’s seminal characterization, as ‘balanced contributions’ and the ‘potential’ are reinterpreted from this point of view. Natural relationships of these conditions with some mentioned families of ‘values’ are shown. These reinterpretations strongly suggest that these conditions are more naturally interpreted in terms of coalition formation than in terms of the classical notion of ‘value.’      

A potential approach for ordinal games

We introduce the class of ordinal games with a potential, which are characterized by the absence of weak improvement cycles, the same condition used by Voorneveld and Norde (1997) for ordinal potential games.     

Dimension of complete simple games with minimum

Weighted majority games have the property that players are totally ordered by the desirability relation (introduced by Isbell in [J.R. Isbell, A class of majority games, Quarterly Journal of Mathematics, 7 (1956) 183–187]) because weights induce it. Games for which this relation is total are called complete simple games. Taylor and Zwicker proved in [A.D. Taylor, W.S. Zwicker, Weighted voting, multicameral representation, and power, Games and Economic Behavior 5 (1993) 170–181] that every simple game (or monotonic finite hypergraph) can be represented by an intersection of weighted majority games and consider the dimension of a game as the needed minimum number of them to get it. They provide the existence of non-complete simple games of every dimension and left open the problem for complete simple games.