Two hardness results for core stability in hedonic coalition formation games

We establish NP-completeness of two problems on core stable coalitions in hedonic games. In the first problem every player has only two acceptable coalitions in his preference list, and in the second problem the preference structures arise from the distances in an underlying metric space.     

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     

On the bargaining set, kernel and core of superadditive games

We prove that for superadditive games a necessary and sufficient condition for the bargaining set to coincide with the core is that the monotonic cover of the excess game induced by a payoff be balanced for each imputation in the bargaining set. We present some new results obtained by verifying this condition for specific classes of games. For N-zero-monotonic games we show that the same condition required at each kernel element is also necessary and sufficient for the kernel to be contained in the core. We also give examples showing that to maintain these characterizations, the respective assumptions on the games cannot be lifted. Received: March 1998/Revised version: December 1998     

Bargaining with commitments

We study a simple bargaining mechanism in which, given an order of players, the first n–1 players sequentially announce their reservation price. Once these prices are given, the last player may choose a coalition to cooperate with, and pay each member of this coalition his reservation price. The only expected final equilibrium payoff is a new solution concept, the selective value, which can be defined by means of marginal contributions vectors of a reduced game. The selective value coincides with the Shapley value for convex games. Moreover, for 3-player games the vectors of marginal contributions determine the core when it is nonempty.A previous version of this paper has benefited from helpful comments from Gustavo Bergantiños. Numerous suggestions of two anonymous referees, the Associate Editor, and William Thomson, Editor, have led to significant improvements of the final version. Financial support by the Spanish Ministerio de Ciencia y Tecnología and FEDER through grant BEC2002-04102-C02-01 and Xunta de Galicia through grant PGIDIT03PXIC30002PN is gratefully acknowledged.     

The bargaining set of four-person balanced games

It is well known that in three-person transferable-utility cooperative games the bargaining set ℳⁱ ₁ and the core coincide for any coalition structure, provided the latter solution is not empty. In contrast, five-person totally-balanced games are discussed in the literature in which the bargaining set ℳⁱ ₁ (for the grand coalition) is larger then the core. This paper answers the equivalence question in the remaining four-person case. We prove that in any four-person game and for arbitrary coalition structure, whenever the core is not empty, it coincides with the bargaining set ℳⁱ ₁. Our discussion employs a generalization of balancedness to games with coalition structures. Received: August 2001/Revised version: April 2002     

The modeling of coalition for environmental protection within co-utility framework

The game theoretic modelling of coalition for environmental protection within the framework of a new concept of co-utility is discussed. The co-utility concept contains mainly two elements. Firstly, agents can increase their payoffs by collaborating with each-other. Secondly, the outcome of collaboration is robust towards internal and external disturbances. The advantages of using of co-utility are two-fold. Primarily, the co-utility concept is broad and can serve as an umbrella concept in all applications where agents have a space for simultaneous improvement of payoffs. Secondly the co-utility concept can be associated with different stability concept such as myopic or farsighted stability. The myopic and farsighted co-utile sets are defined and their element-co-utile outcomes are found.     

考虑损失厌恶行为与谈判破裂的Rubinstein谈判博弈研究

本文考虑具有损失厌恶行为与破裂风险的Rubinstein谈判博弈。首先构建子博弈完美均衡,并证明子博弈完美均衡的存在性及唯一性。然后分析子博弈完美均衡的性质,结果表明:参与人受益于对手的损失厌恶行为,而因自身具有损失厌恶行为遭受损失;谈判破裂概率对均衡结果的影响取决于贴现因子与参与人的损失厌恶系数;当谈判破裂的概率趋于零时,极限均衡结果收敛于经典的Rubinstein谈判博弈结果。最后建立了与非对称Nash谈判解的关系,其中参与人的议价能力与自身的损失厌恶水平呈负相关性,与对手的损失厌恶水平呈正相关性;参与人的议价能力依赖于谈判破裂概率与出价时间间隔的比值。     

一类竞价程序的激励相容性

本中我们研究了一类竞价程序博弈，其中参与人具有私人信息，提出了使这类竞价程序合理有效的一些条件，证明了两个不相容定理。     

Stability in coalition formation games

In the context of coalition formation games a player evaluates a partition on the basis of the set she belongs to. For this evaluation to be possible, players are supposed to have preferences over sets to which they could belong. In this paper, we suggest two extensions of preferences over individuals to preferences over sets. For the first one, derived from the most preferred member of a set, it is shown that a strict core partition always exists if the original preferences are strict and a simple algorithm for the computation of one strict core partition is derived. This algorithm turns out to be strategy proof. The second extension, based on the least preferred member of a set, produces solutions very similar to those for the stable roommates problem. Received August 1998/Final version June 20, 2000     

An axiomatization of probabilistic Owen value for games with coalition structure

In the framework of games with coalition structure, we introduce probabilistic Owen value which is an extension of the Owen value and probabilistic Shapley value by considering the situation that not all priori unions are able to cooperate with others. Then we use five axioms of probabilistic efficiency, symmetric within coalitions, symmetric across coalitions applying to unanimity games, strong monotone property and linearity to axiomatize the value.     

基于VC谈判力的内生投资模型

近来,对风险投资的研究大都是从信息不对称、控制权的私有收益的角度出发,并且把首次投资水平看成是外生决定的变量.把其内生化并从谈判力的视角出发建立了一个两期信号博弈模型.通过模型分析,①得到了影响首次投资水平的关键因素:投资双方的谈判力、双方信息不对称以及事后不确定性程度;②对相关因素进行了量化分析,并讨论了投资双方谈判力的分配问题.     

A coalition formation value for games in partition function form

The coalition formation problem in an economy with externalities can be adequately modeled by using games in partition function form (PFF games), proposed by Thrall and Lucas. If we suppose that forming the grand coalition generates the largest total surplus, a central question is how to allocate the worth of the grand coalition to each player, i.e., how to find an adequate solution concept, taking into account the whole process of coalition formation. We propose in this paper the original concepts of scenario-value, process-value and coalition formation value, which represent the average contribution of players in a scenario (a particular sequence of coalitions within a given coalition formation process), in a process (a sequence of partitions of the society), and in the whole (all processes being taken into account), respectively. We give also two axiomatizations of our coalition formation value.     

ON ASPIRATION SOLUTIONS IN PREDICTING COALITION FORMATION IN COOPERATIVE GAMES

This paper consists of two parts. The first part introduces the strict aspiration as a new aspiration solution concept, which is proved to be existent for any cooperative game. The second part deals with the unsolved problem put forward by Bennett [1] by showing that there is at least one payoff which is balanced, partnered and equal gains aspiration. The proof is algebraic and constructive, thus providing an algorithm for finding such aspirations.     

Local set theory

In 1945, Eilenberg and MacLane introduced the new mathematical notion of category. Unfortunately, from the very beginning, category theory did not fit into the framework of either Zermelo—Fraenkel set theory or even von Neumann—Bernays—Gödel set-class theory. For this reason, in 1959, MacLane posed the general problem of constructing a new, more flexible, axiomatic set theory which would be an adequate logical basis for the whole of naïve category theory. In this paper, we give axiomatic foundations for local set theory. This theory might be one of the possible solutions of the MacLane problem.Translated from Matematicheskie Zametki, vol. 77, no. 2, 2005, pp. 194–212.Original Russian Text Copyright © 2005 by V. K. Zakharov.This revised version was published online in April 2005 with a corrected issue number.     

三方相互威慑讨价还价模型

研究了三方相互威慑讨价还价问题,从合作博弈的角度建立了三方相互威慑讨价还价模型.并且通过对均衡存在性和冲突可能性的分析,给出了三方相互威慑问题冲突发生的条件以及存在均衡状态时的均衡解.最后通过实验验证了本文分析的正确性.     

A general procedure to compute mixed modified semivalues for cooperative games with structure of coalition blocks

Semivalues are solution concepts for cooperative games that assign to each player a weighted sum of his/her marginal contributions to the coalitions, where the weights only depend on the coalition size. The Shapley value and the Banzhaf value are semivalues. Mixed modified semivalues are solutions for cooperative games when we consider a priori coalition blocks in the player set. For all these solutions, a computational procedure is offered in this paper.     

Partnership formation and binomial semivalues

Partnership formation in cooperative games is studied, and binomial semivalues are used to measure the effects of such a type of coalition arising from an agreement between (a group of) players. The joint effect on the set of involved players is also compared with that of the alternative alliance formation. The simple game case is especially considered, and the application to a real life example illustrates the use of coalitional values closely related to the binomial semivalues when dealing with partnership formation and coalitional bargaining simultaneously.     

Stationary perfect equilibria of an n-person noncooperative bargaining game and cooperative solution concepts

This paper characterizes the stationary (subgame) perfect equilibria of an n-person noncooperative bargaining model with characteristic functions, and provides strategic foundations of some cooperative solution concepts such as the core, the bargaining set and the kernel. The contribution of this paper is twofold. First, we show that a linear programming formulation successfully characterizes the stationary (subgame) perfect equilibria of our bargaining game. We suggest a linear programming formulation as an algorithm for the stationary (subgame) perfect equilibria of a class of n-person noncooperative games. Second, utilizing the linear programming formulation, we show that stationary (subgame) perfect equilibria of n-person noncooperative games provide strategic foundations for the bargaining set and the kernel.     

Optimal coalition formation and surplus distribution: Two sides of one coin

A fuzzy coalitional game represents a situation in which players can vary the intensity at which they participate in the coalitions accessible to them, as opposed to the treatment as a binary choice in the non-fuzzy (crisp) game. Building on the property - not made use of so far in the literature of fuzzy games - that a fuzzy game can be represented as a convex program, this paper shows that the optimum of such a program determines the optimal coalitions as well as the optimal rewards for the players, two sides of one coin. Furthermore, this program is seen to provide a unifying framework for representing the core, the least core, and the (fuzzy) nucleolus, among others. Next, we derive conditions for uniqueness of core rewards and to deal with non-uniqueness we introduce a family of parametric perturbations of the convex program that encompasses a large number of well-known concepts for selection from the core, including the Dutta-Ray solution (Dutta and Ray, 1989), the equal sacrifice solution (Yu, 1973), the equal division solution (Selten, 1972) and the tau-value (Tijs, 1981). We also generalize the concept of the Grand Coalition of contracting players by allowing for multiple technologies, and we specify the conditions for this allocation to be unique and Egalitarian. Finally, we show that our formulation offers a natural extension to existing models of production economies with threats and division rules for common surplus.