Level Sets of the Value Function in Differential Games with Two Pursuers and One Evader. Interval Analysis Interpretation

An algorithm for numerical constructing level sets of the value function is shortly described for one class of linear differential games with fixed termination instant. Some model interception problems with one target and two interceptors are considered; all objects are weak maneuverable.     

多选择合作对策的最大限定核心

主要是对多选择合作对策中核心概念的扩展研究,称之为最大限定核心.首先,依据经典对策下核心的概念,针对多选择合作对策中参与者不参与和以最高水平参与联盟合作的情形,给出了多选择合作对策中最大限定核心的定义.然后,介绍了多选择对策中最大限定核心是非空的充要条件是该多选择对策是弱均衡对策.最后,构造了基于最大限定核心的简约对策,并应用1人合理性、弱个体合理性、一致性和逆一致性对其进行公理化.     

Level Sets of Classes of Mappings of Two-Step Carnot Groups in a Nonholonomic Interpretation

Siberian Mathematical Journal - We obtain the metric properties of level sets of certain sufficiently smooth mappings of two-step Carnot groups which are Hölder in the sub-Riemannian sense. In...     

凸对策核仁的非空性及合成凸对策核仁的单调性

本文给出了核仁与核及最小核心之间的关系 ,且证明了凸对策核仁的存在性和唯一性 ,证明了凸对策的合成对策仍是凸对策 .最后 ,我们讨论了合成凸对策的核仁不满足单调性 .     

The Well-Posedness for Multiobjective Generalized Games

In this paper, the new notions of the generalized Tykhonov well-posedness for multiobjective generalized games are investigated. By using the gap functions of the multiobjective generalized games, we establish the equivalent relationship between the generalized Tykhonov well-posedness of the multiobjective generalized games and that of the minimization problems. Some metric characterizations for the generalized Tykhonov well-posedness of the multiobjective generalized games are also presented.     

The Egalitarian Solution for Multichoice Games

In a multichoice game a coalition is characterized by the level at which each player is acting, and to each coalition a real number is assigned. A multichoice solution assigns, for each multichoice game, a numerical value to each possible activity level of each player, intended to measure the contribution of each such level to reaching the grand coalition in which each player is active at the maximal level. The paper focuses on the egalitarian multichoice solution, characterized by the properties of Efficiency, Zero Contribution, Additivity, Anonymity, and Level Symmetry. The egalitarian solution is also shown to satisfy the property of marginalism: it measures the effect of lowering, ceteris paribus, a certain activity level by one. The solution is compared to a multichoice solution studied in Klijn, Slikker, and Zarzuelo (1999). Finally, it is discussed how the formalism of this paper can be applied to the different framework of multi-attribute utilities.     

The Abstraction of Reality for Games and Simulations

This paper examines the way in which reality is abstracted in the preparation and design of a game or simulation model. Two modes and four dimensions of abstraction are identified. Of particular importance is the construal dimension, which depicts the subjective content of a model as perceived by a participant. It is argued that anything more than trivial abstraction in this dimension alters the meaning of models to such an extent that human players will not be able properly to understand them. This limits the types of games with human players that can validly be played for research or education to those with relatively specific rather than general results. The argument is developed in terms of a spectrum of result generality for game and simulation models.     

拟阵限制下合作对策解的传递性

Vincent Feltkamp研究了Shapley解和Banzhaf解的公理性．Bilbao等人又对拟阵限制下的Shapley解的性质进行了讨论．本文在此基础上主要研究了拟阵限制下的合作对策Shapley解，并利用传递性、交换性、概率有效性和P-哑元性等四条公理证明了拟阵限制下合作对策Shapley解的唯一性．进而证明了拟阵限制条件下简单对策Shapley解的唯一性．最后给出了拟阵限制下合作对策的Banzhaf解的唯一性定理．     

集合对策边缘解的公理化方法

本文将单调集合对策边缘解推广到一般集合对策上,利用三个公理,确定了集合对策边缘解的唯—性．在证明唯—性的过程中,引进了单调集合对策将集合对策进行分解．证明过程与Aarts等人的方法完全不一样,在某些地方吸收了Young的有关思想．     

树上最大支撑森林对策

本文在无向网络上定义了最大支撑森林对策,利用图论知识研究了树上最大支撑森林对策的核和核仁,并将所得结论推广到无关网络上.     

有限合作博弈的Shapley分配

以Myerson关于有限合作的图博弈模型为基础,结合经典合作博弈的相关结论,建立了有限合作博弈的Shapley分配,讨论了分配的相关性质.同时在支付函数满足链递增性的假设下,进一步研究了有限合作关系变化对收益分配的影响,给出了相关的研究结论.     

超级模数博弈的存在性

本文定义了一类在有序Banach空间上的超模博弈,并利用著名的Birkhoff不动点定理证明了有序Banach空间上超模博弈Nash均衡的存在性.     

Lattices of Games

We show that, for any set S of combinatorial games, the set of games all of whose immediate options belong to S forms a complete lattice. If every option of a game in S also lies in S, then this lattice is completely distributive.     

Polytope Games

Starting from the definition of a bimatrix game, we restrict the pair of strategy sets jointly, not independently. Thus, we have a set , which is the set of all feasible strategy pairs. We pose the question of whether a Nash equilibrium exists, in that no player can obtain a higher payoff by deviating. We answer this question affirmatively for a very general case, imposing a minimum of conditions on the restricted sets and the payoff. Next, we concentrate on a special class of restricted games, the polytope bimatrix game, where the restrictions are linear and the payoff functions are bilinear. Further, we show how the polytope bimatrix game is a generalization of the bimatrix game. We give an algorithm for solving such a polytope bimatrix game; finally, we discuss refinements to the equilibrium point concept where we generalize results from the theory of bimatrix games.     

模糊二人非合作对策的简单Berge均衡

研究模糊二人非合作对策的简单Berge均衡的存在性.基于Zimmermann处理模糊多目标线性规划的观点和Zhukovskii提出的简单Berge均衡概念,定义了模糊二人非合作对策的简单Berge均衡并借助于Ky Fan不等式证明其存在性.     

Games with permission structures: The conjunctive approach

This paper is devoted to the game theoretic analysis of decision situations, in which the players have veto power over the actions undertaken by certain other players. We give a full characterization of the dividends in these games with a permission structure. We find that the collection of these games forms a subspace of the vector space of all games with side payments on a specified player set.Two applications of these results are provided. The first one deals with the projection of additive games on a permission structure. It is shown that the Shapley value of these projected games can be interpreted as an index that measures the power of the players in the permission structure. The second application applies the derived results on games, where the organization structure can be analysed separately from the production capacities of the participating players.