Stability of the core mapping in games with a countable set of players

Greenberg (1990) and Ray (1989) showed that in coalitional games with a finite set of players the core consists of those and only those payoffs that cannot be dominated using payoffs in the core of a subgame. We extend the definition of the dominance relation to coalitional games with an infinite set of players and show that this result may not hold in games with a countable set of players (even in convex games). But if a coalitional game with a countable set of players satisfies a mild continuity property, its core consists of those and only those payoff vectors which cannot be dominated using payoffs in the core of a subgame.     

APPROXIMATION OF COMMON FIXED POINT OF FAMILIES OF NONLINEAR MAPPINGS WITH APPLICATIONS

It is our purpose in this paper to show that some results obtained in uniformly convex real Banach space with uniformly G?ateaux differentiable norm are extendable to more general reflexive and strictly convex real Banach space with uniformly G?ateaux differentiable norm. Demicompactness condition imposed in such results is dispensed with. Furthermore,Applications of our theorems to approximation of common fixed point of countable infinite family of continuous pseudocontractive mappings and approximation of common solution of countable infinite family of generalized mixed equilibrium problems are also discussed. Our theorems improve, generalize, unify and extend several recently announced results.     

The modified nucleolus: Properties and axiomatizations

A new solution concept for cooperative transferable utility games is introduced, which is strongly related to the nucleolus and therefore called modified nucleolus. It takes into account both the “power”, i.e. the worth, and the “blocking power” of a coalition, i.e. the amount which the coalition cannot be prevented from by the complement coalition. It can be shown that the modified nucleolus is reasonable, individually rational for weakly superadditive games, coincides with the prenucleolus for constant-sum games, and is contained in the core for convex games. Finally this paper proposes two axiomatizations of this solution concept on the set of games on an infinite universe of players which are similar to Sobolev's characterization of the prenucleolus.     

Total Reward Stochastic Games and Sensitive Average Reward Strategies

In this paper, total reward stochastic games are surveyed. Total reward games are motivated as a refinement of average reward games. The total reward is defined as the limiting average of the partial sums of the stream of payoffs. It is shown that total reward games with finite state space are strategically equivalent to a class of average reward games with an infinite countable state space. The role of stationary strategies in total reward games is investigated in detail. Further, it is outlined that, for total reward games with average reward value 0 and where additionally both players possess average reward optimal stationary strategies, it holds that the total reward value exists.     

On Nikaido-Isoda type theorems for discounted stochastic games

We present a class of countable state space stochastic games with discontinuous payoff functions satisfying some assumptions similar to the ones of Nikaido and Isoda for one-stage games. We prove that these games possess stationary equilibria. We show that after adding some concavity assumptions these equilibria are nonrandomized. Further, we present an example of input (or production) dynamic game satisfying the assumptions of our model. We give a closed-form solution for this game.     

The Shapley value and average convex games

In this paper we reformulate the necessary and sufficient conditions for the Shapley value to lie in the core of the game. Two new classes of games, which strictly include convex games, are introduced: average convex games and partially average convex games. Partially average convex games, which need not be superadditive, include average convex games. The Shapley value of a game for both classes is in the core. Some Cobb Douglas production games with increasing returns to scale turn out to be average convex games. The paper concludes with a comparison between the new classes of games introduced and some previous extensions of the convexity notion.The authors thank G. Owen, S. Tijs, and J. Ostroy and two anonymous referees of the International Journal of Game Theory for their comments and suggestions. The usual disclamer applies. We are grateful to the Universidad del Pais Vasco-EHU (grant UPV 209.321-H053/90) and the Ministry of Education and Science of Spain (CICYT grant PB900654) for providing reseach support.     

On the Laplacian spectrum of an infinite graph

In this paper, we introduce the notion of Laplacian spectrum of an infinite countable graph in a different way than in the papers by B. Mohar. We prove some basic properties of this type of spectrum. The approach used is in line with our approach to the limiting spectrum of an infinite graph. The technique of the Laplacian spectrum of finite graphs is essential in this approach.     

Filling certain cuts in discrete weakly o‐minimal structures

Discrete weakly o‐minimal structures, although not so stimulating as their dense counterparts, do exhibit a certain wealth of examples and pathologies. For instance they lack prime models and monotonicity for definable functions, and are not preserved by elementary equivalence. First we exhibit these features. Then we consider a countable theory of weakly o‐minimal structures with infinite definable discrete (convex) subsets and we study the Boolean algebra of definable sets of its countable models. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Playing with mixed strategies on infinite sets

We prove that the property of having a value and Vervoort's Strong Zero-One Law transfer from infinite perfect information games played with mixed strategies on finite sets to those on countable sets. Received April 2001/Final version June 2002     

Constructible Convex Sets

We investigate when closed convex sets can be written as countable intersections of closed half-spaces in Banach spaces. It is reasonable to consider this class to comprise the constructible convex sets since such sets are precisely those that can be defined by a countable number of linear inequalities, hence are accessible to techniques of semi-infinite convex programming. We also explore some model theoretic implications. Applications to set convergence are given as limiting examples.     

Zero-sum risk-sensitive stochastic games for continuous time Markov chains

We study infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled continuous time Markov chains on a countable state space. For the discounted-cost game, we prove the existence of value and saddle-point equilibrium in the class of Markov strategies under nominal conditions. For the ergodic-cost game, we prove the existence of values and saddle point equilibrium by studying the corresponding Hamilton-Jacobi-Isaacs equation under a certain Lyapunov condition.     

Hypercyclic operators on quasi-Mazur spaces

Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special locally convex spaces, for example, Köthe (LF)-sequence spaces and countable inductive limits of quasi-Mazur spaces, we investigate their hypercyclicity. As we see, bounded biorthogonal systems play an important role in the construction of Ansari. Moreover, we obtain characteristic conditions respectively for locally convex spaces having bounded sequences with dense linear spans and for locally convex spaces having bounded absorbing sets, which are useful in judging the existence of bounded biorthogonal systems.     

Averaged Subgradient Methods for Constrained Convex Optimization and Nash Equilibria Computation

We consider the problem of finding minima of convex functions under convex inequality constraints as well as the problem of finding Nash equilibria in n -person constant sum games. We prove that both problems can be solved by algorithms whose basic principles consist of representing the original problems as infinite systems of convex inequalities which, in turn, can be approached by outer projection techniques. Experiments showing how one of these algorithms behaves in test cases are presented and, in context, we describe a numerical method for computing subgradients of convex functions.     

Countable infinite existentially closed models of universally axiomatizable theories

In the present article, we obtain a new criterion for amodel of a universally axiomatizable theory to be existentially closed. The notion of a maximal existential type is used in the proof and for investigating properties of countable infinite existentially closed structures. The notions of a prime and a homogeneous model, which are classical for the general model theory, are introduced for such structures. We study universal theories with the joint embedding property admitting a single countable infinite existentially closed model. We also construct, for every natural n, an example of a complete inductive theory with a countable infinite family of countable infinite models such that n of them are existentially closed and exactly two are homogeneous.     

基于多维线性扩展的模糊联盟合作对策tau值性质与计算方法

研究模糊联盟合作对策tau值的计算方法及其性质. 利用多维线性扩展方法定义了模糊联盟合作对策的tau值, 证明了其存在性、唯一性等性质, 并推导出基于多维线性扩展凸模糊联盟合作对策tau值的计算公式. 研究结果发现, 基于多维线性扩展的模糊联盟合作对策tau值是对清晰联盟合作对策tau值的扩展, 而清晰联盟合作对策tau值仅是其特例. 特别地, 对于凸模糊联盟合作对策, 利用其tau值计算公式, 可进一步简化求解过程.     

On existence of cone-maximal points in real topological linear spaces

A sufficient condition for a convex coneC in a Hausdorff topological linear space is given in order to ensure the existence of cone-maximal points. The condition becomes a necessary one in a topological linear space with a countable local base, that is, if the space is pseudometrizable. The paper extends known results to infinite dimensions and we answer Corley’s question in the affirmative with the exception of a pathological case.     

无穷可数族非自射非扩张映象之公共不动点的带误差逼近问题

设E具Gateaux可微的严格凸的自反Banach空间,C是E的一非空闭凸子集.受姚永红等2007年文献[1]的启发.本文在此Banach空间框架下引进了一涉及无穷可数族非自射非扩张映象{T:C→E)<'∞><,t=1>的含误差的显式迭代算法,并且在非常少的限制条件下证明了该迭代序列的强收敛于无穷可数族非自射非扩张映象...     

Countable inductive limits of frechet algebras

We show that the Gelfand-Mazur theorem holds for countable inductive limits of Frechet algebras (we do not assume that the homomorphisms which define the inductive limit are continuous, or one-to-one). This question is motivated by the fact that the spectrum of some elements of such an algebra may be empty. We also discuss in detail a countable inductive limit of Frechet algebras of holomorphic functions, which provides an elementary, but seminal, counterexample to the biinvariant subspace problem for complete, reflexive, locally convex spaces.