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.     

Bargaining sets and the core in partitioning games

Partitioning games are useful on two counts: first, in modeling situations with restricted cooperative possibilities between the agents; second, as a general framework for many unrestricted cooperative games generated by combinatorial optimization problems.We show that the family of partitioning games defined on a fixed basic collection is closed under the strategic equivalence of games, and also for taking the monotonic cover of games. Based on these properties we establish the coincidence of the Mas-Colell, the classical, the semireactive, and the reactive bargaining setswith the core for interesting balanced subclasses of partitioning games, including assignment games, tree-restricted superadditive games, and simple network games. Prepared during the author’s Bolyai János Research Fellowship. Also supported by OTKA grant T46194.     

多目标的随机结盟对策的ZS-值

本文研究的是多目标随机结盟对策的问题，是将单目标的随机结盟对策的ZS-值拓展到多目标的随机结盟对策上，同时考虑了局中人对不同目标的偏好程度，从而，给出了多目标随机结盟对策的ZS-值的定义，并讨论了该值的性质及定理。     

Search and Ambush Games with Capacities

Search games with capacities are bipersonal zero-sum games where a player has to hide a number of objects or an amount of material in a fixed number of containers and his opponent attempts to locate them. In this article, we deal with games on a discrete structureless set and on a discrete set with linear order. In both cases, the capacities under consideration are continuous. Some of the games studied generalize previously studied games.     

On some families of cooperative fuzzy games

In a fuzzy cooperative game the players may choose to partially participate in a coalition. A fuzzy coalition consists of a group of participating players along with their participation level. The characteristic function of a fuzzy game specifies the worth of each such coalition. This paper introduces well-known properties of classical cooperative games to the theory of fuzzy games, and studies their interrelations. It deals with convex games, exact games, games with a large core, extendable games and games with a stable core.     

Folk theorems in multicriteria repeated N-person games

In this paper we consider the question of existence of a multicriteria-Nash equilibrium in multicriteria multistage N-person games. Besides, we present several forms of multicriteria-Nash equilibrium for repeated games both with infinitely and finitely many stages. The author thanks the Spanish Ministry of Science and Technology through grant number BFM01-2378.     

Qualitative analysis of secured outcome regions for two-target games

Qualitative (game of kind) outcomes of two-target games are analyzed in this paper, under both the zero-sum and nonzero-sum preference ordering of outcomes by the players. The outcome regions of each player are defined from a security standpoint. The secured draw and mutual-kill regions of a player depend explicitly on his preference ordering of outcomes and should be constructed separately for each player, especially in a nonzero-sum game. General guidelines are presented for identifying the secured outcome regions of players in a class of two-target games that satisfy an Isaacs-like condition, in terms of the qualitative solutions of the two underlying single-target pursuit-evasion games. A construction has been proposed for obtaining the qualitative solution of a large class of two-target games. Illustrative examples are included.This work was done while the first author was a Research Associate in the Department of Electrical Engineering at the Indian Institute of Science, Bangalore, and was financially supported by the Council of Scientific and Industrial Research, Delhi, India.     

双准均衡合作对策τ值的公理化

介绍了能准确刻画现实生活中每个参与者有三种选择的双合作对策,在此基础上研究了双合作对策的τ值,并对双准均衡合作对策的τ值进行了公理化,其中双合作对策的上向量、间隙函数、让步向量的构造是刻画其τ值的基础．     

On some geometry and equivalence classes of normal form games

Equivalence classes of normal form games are defined using the discontinuities of correspondences of standard equilibrium concepts like correlated, Nash, and robust equilibrium, or risk dominance and rationalizability. Resulting equivalence classes are fully characterized and compared across different equilibrium concepts for 2 ×  2 games; larger games are also studied. It is argued that the procedure leads to broad and game-theoretically meaningful distinctions of games as well as to alternative ways of representing, comparing and testing equilibrium concepts.     

Periodic stopping games

Stopping games (without simultaneous stopping) are sequential games in which at every stage one of the players is chosen, who decides whether to continue the interaction or stop it, whereby a terminal payoff vector is obtained. Periodic stopping games are stopping games in which both of the processes that define it, the payoff process as well as the process by which players are chosen, are periodic and do not depend on the past choices. We prove that every periodic stopping game without simultaneous stopping, has either periodic subgame perfect ϵ-equilibrium or a subgame perfect 0-equilibrium in pure strategies. This work is part of the master thesis of the author done under the supervision of Prof. Eilon Solan. I am thankful to Prof. Solan for his inspiring guidance. I also thank two anonymous referees of the International Journal of Game Theory for their comments.     

Convex multi-choice games: Characterizations and monotonic allocation schemes

This paper focuses on new characterizations of convex multi-choice games using the notions of exactness and superadditivity. Furthermore, level-increase monotonic allocation schemes (limas) on the class of convex multi-choice games are introduced and studied. It turns out that each element of the Weber set of such a game is extendable to a limas, and the (total) Shapley value for multi-choice games generates a limas for each convex multi-choice game.     

Minimarg and maximarg operators

Two operators on the set ofn-person cooperative games are introduced, the minimarg operator and the maximarg operator. These operators can be seen as dual to each other. Some nice properties of these operators are given, and classes of games for which these operators yield convex (respectively, concave) games are considered. It is shown that, if these operators are applied iteratively on a game, in the limit one will yield a convex game and the other a concave game, and these two games will be dual to each other. Furthermore, it is proved that the convex games are precisely the fixed points of the minimarg operator and that the concave games are precisely the fixed points of the maximarg operator.     

双准均衡合作对策\tau值的公理化

介绍了能准确刻画现实生活中每个参与者有三种选择的双合作对策,在此基础上研究了双合作对策的\tau值,并对双准均衡合作对策的\tau值进行了公理化,其中双合作对策的上向量、间隙函数、让步向量的构造是刻画其\tau值的基础.     

Solutions for some bargaining games under the Harsanyi-Selten solution theory,part II: Analysis of specific bargaining games

Part II of the paper (for Part I see Harsanyi (1982)) describes the actual solutions the Harsanyi-Selten solution theory provides for some important classes of bargaining games, such as unanimity games; trade between one seller and several potential buyers; and two-person bargaining games with incomplete information on one side or on both sides. It also discusses some concepts and theorems useful in computing the solution; and explains how our concept of risk dominance enables us to analyze game situations in terms of some intuitively very compelling probabilistic (subjective-probability) considerations disallowed by classical game theory.     

不确定性下强Berge均衡的存在性

在已知不确定参数变化的范围下,研究了非合作博弈与广义非合作博弈的强Berge均衡的存在性,基于强Berge均衡与不确定性下非合作博弈的强Nash均衡的概念,给出了不确定参数下非合作博弈与广义非合作博弈的强Berge均衡的定义,并利用Fan-Glicksberg不动点定理证明其存在性,最后用算例验证其可行性.     

Probabilities of Pure Nash Equilibria in Matrix Games when the Payoff Entries of One Player Are Randomly Selected

The Nash equilibrium in pure strategies represents an important solution concept in nonzero sum matrix games. Existence of Nash equilibria in games with known and with randomly selected payoff entries have been studied extensively. In many real games, however, a player may know his own payoff entries but not the payoff entries of the other player. In this paper, we consider nonzero sum matrix games where the payoff entries of one player are known, but the payoff entries of the other player are assumed to be randomly selected. We are interested in determining the probabilities of existence of pure Nash equilibria in such games. We characterize these probabilities by first determining the finite space of ordinal matrix games that corresponds to the infinite space of matrix games with random entries for only one player. We then partition this space into mutually exclusive spaces that correspond to games with no Nash equilibria and with r Nash equilibria. In order to effectively compute the sizes of these spaces, we introduce the concept of top-rated preferences minimal ordinal games. We then present a theorem which provides a mechanism for computing the number of games in each of these mutually exclusive spaces, which then can be used to determine the probabilities. Finally, we summarize the results by deriving the probabilities of existence of unique, nonunique, and no Nash equilibria, and we present an illustrative example.     

Limit Consistent Solutions in Noncooperative Games

Strong and limit consistency in finite noncooperative games are studied. A solution is called strongly consistent if it is both consistent and conversely consistent (Ref. 1). We provide sufficient conditions on one-person behavior such that a strongly consistent solution is nonempty. We introduce limit consistency for normal form games and extensive form games. Roughly, this means that the solution can be approximated by strongly consistent solutions. We then show that the perfect and proper equilibrium correspondences in normal form games, as well as the weakly perfect and sequential equilibrium correspondences for extensive form games, are limit consistent.     

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 .     

Cooperative equilibria in discounted stochastic sequential games

This paper addresses the problem of computation of cooperative equilibria in discounted stochastic sequential games. The proposed approach contains as a special case the method of Green and Porter (developed originally for repeated oligopoly games), but it is more general than the latter in the sense that it generates nontrivial equilibrium solutions for a much larger class of dynamic games. This fact is demonstrated on two examples, one concerned with duopolistic economics and the other with fishery management.