弱1—凸对策及其解的性质

本文提出了一类特殊的ｎ人合作对策模型─—弱１—凸对策，研究了弱１—凸对策的解的性质，并证明弱１—凸对策的解满足所有常见的公理化特征．     

Stability and Shapley value for an n-persons fuzzy game

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.     

多目标大博弈中弱Pareto-Berge均衡的存在性

研究了具有任意多个局中人的非合作多目标博弈(多目标大博弈).基于一般非合作博弈中的Berge均衡概念,定义多目标大博弈中的弱Pareto-Berge均衡.进一步推广了截口定理,得到新的截口定理,并且利用这个新的截口定理证明多目标大博弈中弱Pareto-Berge均衡的存在性.多目标大博弈中弱Pareto-Nash均衡的存在性结论可作为弱Pareto-Berge均衡存在性的特例给出.     

Highway games on weakly cyclic graphs

A highway problem is determined by a connected graph which provides all potential entry and exit vertices and all possible edges that can be constructed between vertices, a cost function on the edges of the graph and a set of players, each in need of constructing a connection between a specific entry and exit vertex. Mosquera (2007) introduce highway problems and the corresponding cooperative cost games called highway games to address the problem of fair allocation of the construction costs in case the underlying graph is a tree. In this paper, we study the concavity and the balancedness of highway games on weakly cyclic graphs. A graph G is called highway-game concave if for each highway problem in which G is the underlying graph the corresponding highway game is concave. We show that a graph is highway-game concave if and only if it is weakly triangular. Moreover, we prove that highway games on weakly cyclic graphs are balanced.     

Coalition formation in the triad when two are weak and one is strong

Eighteen groups of subjects each participated in five different computer-controlled superadditive 3-person characteristic function games with sidepayments, that modeled negotiable conflicts in which two of the players are weak and one is considerably stronger. Both the degree to which the strong player was powerful and the type of communication were experimentally manipulated. The 90 game outcomes rejected any solution concept that predicts a single payoff vector for a given coalition structure, but supported the recently developed single-parameter α-power model that allows range predictions. Both the degree of power and type of communication were found to affect game outcomes and to determine the predictive power of models that make point predictions in 3-person games.     

On the determinateness of semi-infinite bimatrix games

In this paper it is shown that every 2 × ∞ bimatrix game is weakly determined. For the proof of this fact we introduce ?-optimal andk-guaranteeing points for a convex set in IR ^m and a labeling technique which is typical for 2 × ∞ bimatrix games.     

Axiomatizations of the core on the universal domain and other natural domains

We prove that the core on the set of all transferable utility games with players contained in a universe of at least five members can be axiomatized by the zero inessential game property, covariance under strategic equivalence, anonymity, boundedness, the weak reduced game property, the converse reduced game property, and the reconfirmation property. These properties also characterize the core on certain subsets of games, e.g., on the set of totally balanced games, on the set of balanced games, and on the set of superadditive games. Suitable extensions of these properties yield an axiomatization of the core on sets of nontransferable utility games. Received September 1999/Final version December 2000     

On weakly correlated and correlated equilibria in discontinuous games

This paper treats of non-zero-sum discontinuous games with compact Hausdorff strategy spaces. It is assumed that the payoff function of each player in the game is bounded, Borel measurable and is upper semicontinuous on his strategy space, for all fixed actions of the remaining players. It is shown that for each ε>0, such games possess weakly correlated ε-epuilibria introduced by Moulin and Vial as extension of correlated equilibria in the sense of Aumann. An upper semicontinuous came having weakly correlated equilibria and no correlated equilibria is discussed in details.     

不同权力结构对制造商双渠道供应链的影响研究

在一个制造商和一个零售商组成的供应链中, 制造商拥有线下传统渠道及线上直销双渠道。首先根据消费者剩余理论, 构建了制造商双渠道需求函数;接着分别构建了两类Stackelberg博弈及Nash博弈三种权力结构下制造商和零售商的利润模型并对模型进行了求解;最后分析了三种不同权力结构对制造商双渠道供应链的影响。研究发现:制造商线上直销渠道价格不受三种博弈权力结构的影响;线下传统渠道零售价格、需求, 线上直销渠道需求及制造商双渠道供应链总利润不受两类Stackelberg博弈权力结构的影响;线下传统渠道零售价格及线上直销渠道需求在Nash博弈权力结构下最小, 而线下传统渠道需求及供应链总利润在Nash博弈权力结构下最大;制造商批发价格、利润及零售商利润对三种博弈权力结构较敏感, 随供应链成员自身博弈权力地位的下降而逐渐降低。     

Almost strict competitiveness in extensive games

We consider an extension of an almost strictly competitive game, introduced by Aumann (1961), inn-person extensive games by incorporating Selten's subgame perfection. We call it a subgame perfect weakly-almost (SPWA) strictly competitive game, in particular, an SPWA strictly competitive game in strategic form is simply called a WA strictly competitive game. We give some general results on the structure of this class of games. One result gives an easy way to verify almost strict competitiveness of a given extensive game. We show that a two-person weakly unilaterally competitive extensive game, introduced by Kats and Thisse (1992) for normal form games, is SPWA strictly competitive. We remark that some of our main results for SPWA strictly competitive games do not hold for the modification of almost strict competitiveness with trembling-hand perfection.The author is indebted to Mamoru Kaneko for valuable discussions, comments and criticism throughout the paper. He thanks N. Bose, M. Frascatore, R. Gilles, H. Haller, A. Kats, J. Kline and an anonymous referee for helpful comments on earlier drafts. The usual disclaimer applies.     

信息集广义多目标博弈弱Pareto-Nash平衡点的存在性和稳定性

首先把信息集的概念引入到多目标博弈, 建立了信息集广义多目标博弈模型, 并指出了信息集广义多目标博弈以广义多目标博弈、广义n人非合作博弈、一般n人非合作博弈为特例, 然后用Fan-Glicksberg不动点定理证明了信息集广义多目标博弈弱Pareto-Nash平衡点的存在性, 最后在本质解和强本质解的意义下, 分别研究了信息集广义多目标博弈弱Pareto-Nash平衡点的通有稳定性和强本质连通区的存在性.     

A multistage pursuit-evasion game that admits a gaussian random process as a maximin control policy

In this paper we consider the existence and structure of both minimax and maximin policies for the special class of LQG pursuit-evasion games which is characterized by (i) a blind evader; and (ii) a pursuer who can make use of noise corrupted state measurements. The particular class of games which we consider has been studied previously by other investigators who have shown that pure strategies exist for both players. The major contribution of our paper is the delineation of the existence and structure of a mixed strategy for the evader in this class of games. This new maximin strategy is defined by a gaussian measure, which can be determined explicitly by the method of least favorable prior distributions. We show that the validity of the pure solutions determined previously is limited by the duration of the game, due to the existence of a ‘pure solution conjugate point’; further, we prove that our new strategies are valid solutions which extend the possible duration of the game beyond the limit imposed by the pure solution conjugate point. We believe that our paper constitutes the first report on the existence of a mixed strategy for an LQG game, and the first report on the role conjugate points play in the transition between pure strategies and mixed strategies.     

Alfa-cut based linear programming methodology for constrained matrix games with payoffs of trapezoidal fuzzy numbers

The purpose of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of trapezoidal fuzzy numbers (TrFNs), which are a type of two-person non-cooperative games with payoffs expressed by TrFNs and players’ strategies being constrained. In this methodology, it is proven that any Alfa-constrained matrix game has an interval-type value and hereby any constrained matrix game with payoffs of TrFNs has a TrFN-type value. The auxiliary linear programming models are derived to compute the interval-type value of any Alfa-constrained matrix game and players’ optimal strategies. Thereby the TrFN-type value of any constrained matrix game with payoffs of TrFNs can be directly obtained through solving the derived four linear programming models with data taken from only 1-cut and 0-cut of TrFN-type payoffs. Validity and applicability of the models and method proposed in this paper are demonstrated with a numerical example of the market share game problem.     

Weak topology and infinite matrix games

This paper approaches infinite matrix games through the weak topology on the players' sets of strategies. A new class of semi-infinite and infinite matrix games is defined, and it is proved that these games always have a value and optimal strategies for each player. Using these games it is proved that some other important classes of infinite matrix game also have values. Received April 1996/Revised version June 1997/Final version September 1997     

Generic stability of Nash equilibria for noncooperative differential games

The stability of Nash equilibria against the perturbation of the right-hand side functions of state equations for noncooperative differential games is investigated. By employing the set-valued analysis theory, we show that the differential games whose equilibria are all stable form a dense residual set, and every differential game can be approximated arbitrarily by a sequence of stable differential games, that is, in the sense of Baire’s category most of the differential games are stable.     

Minimaxtheoreme und das Integraldarstellungsproblem

In the present paper conditions for the strict determinateness of two-person zero-sum games are considered. In order to get such minimax theorems we first study games with concave-convex pay-off function. If a game does not have this convexity property one usually passes to a mixed extension where both players are allowed to use probability measures (-additive randomizations) or, more generally, probability contents (finitely additive randomizations) as mixed strategies. By means of a very general minimax theorem for such finitely additive randomizations it can be shown that the problem of strict determinateness of -additive randomizations is equivalent to an integral representation problem. The latter is investigated in the last paragraph.

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Diese Arbeit enthält einen Teil der Ergebnisse der Habilitationsschrift des Verfassers.     

The semireactive bargaining set of a cooperative game

The semireactive bargaining set, a solution for cooperative games, is introduced. This solution is in general a subsolution of the bargaining set and a supersolution of the reactive bargaining set. However, on various classes of transferable utility games the semireactive and the reactive bargaining set coincide. The semireactive prebargaining set on TU games can be axiomatized by one-person rationality, the reduced game property, a weak version of the converse reduced game property with respect to subgrand coalitions, and subgrand stability. Furthermore, it is shown that there is a suitable weakening of subgrand stability, which allows to characterize the prebargaining set. Replacing the reduced game by the imputation saving reduced game and employing individual rationality as an additional axiom yields characterizations of both, the bargaining set and the semireactive bargaining set. Received September 2000/Revised version June 2001     

Scalarization Method in Multicriteria Games

Using a two-criteria two-person game as an example, the validity of the scalarization method applied for the parameterization of the set of game values and for estimating the players’ payoffs is investigated. It is shown that the use of linear scalarization by the players gives the results different from those obtained using Germeyer’s scalarization. Various formalizations of the concept of value of MC games are discussed.     

Totally monotonic games and flow games

Equivalences between totally balanced games and flow games, and between monotonic games and pseudoflow games are well-known. This paper shows that for every totally monotonic game there exists an equivalent flow game and that for every monotonic game, there exists an equivalent flow-based secondary market game.     

Sufficient conditions for unique stable sets in three agent pillage games

Pillage games (Jordan, 2006a) have two features that make them richer than cooperative games in either characteristic or partition function form: they allow power externalities between coalitions; they allow resources to contribute to coalitions’ power as well as to their utility. Extending von Neumann and Morgenstern’s analysis of three agent games in characteristic function form to anonymous pillage games, we characterise the core for any number of agents; for three agents, all anonymous pillage games with an empty core represent the same dominance relation. When a stable set exists, and the game also satisfies a continuity and a responsiveness axiom, it is unique and contains no more than 15 elements, a tight bound. By contrast, stable sets in three agent games in characteristic or partition function form may not be unique, and may contain continua. Finally, we provide an algorithm for computing the stable set, and can easily decide non-existence. Thus, in addition to offering attractive modelling possibilities, pillage games seem well behaved and analytically tractable, overcoming a difficulty that has long impeded use of cooperative game theory’s flexibility.