Additive Stable Solutions on Perfect Cones of Cooperative Games

Closed kernel systems of the coalition matrix turn out to correspond to cones of games on which the core correspondence is additive and on which the related canonical barycentric solution is additive, stable and continuous. Different perfect cones corresponding to closed kernel systems are described.cooperative games;core;barycenter of the core;perfect cone of games

Cases in Cooperation and Cutting the Cake

Cooperative game;sharing problem

Cooperative Games arising from Information Sharing Situations

Relations are established between information sharing (IS) situations and IS-games on one hand and information collecting (IC) situations and IC-games on the other hand. It is shown that IC-games can be obtained as convex combinations of so-called local games. Properties are described which IC-games possess if all related local games have the respective properties. Special attention is paid to the classes of convex IC-games and of k-concave IC-games. This last class turns out to consist of total big boss games. For the class of total big boss games a new solution concept is introduced: bi-monotonic allocation schemes.cooperative games;information;big boss games;bi-monotonic allocation scheme

Tree-connected Peer Group Situations and Peer Group Games

A class of cooperative games is introduced which arises from situations in which a set of agents is hierarchically structured and where potential individual economic abilities interfere with the behavioristic rules induced by the organization structure.These games form a cone generated by a specific class of unanimity games, namely those based on coalitions called peer groups. Different economic situations like auctions, communication situations, sequencing situations and flow situations are related to peer group games.For peer group games classical solution concepts have nice properties.auctions;cooperative games;peer groups

Strongly Essential Coalitions and the Nucleolus of Peer Group Games

Most of the known efficient algorithms designed to compute the nucleolus for special classes of balanced games are based on two facts: (i) in any balanced game, the coalitions which actually determine the nucleolus are essential; and (ii) all essential coalitions in any of the games in the class belong to a prespeci ed collection of size polynomial in the number of players.We consider a subclass of essential coalitions, called strongly essential coalitions, and show that in any game, the collection of strongly essential coalitions contains all the coalitions which actually determine the core, and in case the core is not empty, the nucleolus and the kernelcore.As an application, we consider peer group games, and show that they admit at most 2n - 1 strongly essential coalitions, whereas the number of essential coalitions could be as much as 2n-1. We propose an algorithm that computes the nucleolus of an n-player peer group game in O(n2) time directly from the data of the underlying peer group situation.game theory;algorithm;cooperative games;kernel estimation;peer games

Egalitarianism in Convex Fuzzy Games

In this paper the egalitarian solution for convex cooperative fuzzy games is introduced.The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game.This adjusted algorithm is also a finite algorithm, because the convexity of a fuzzy game implies in each step the existence of a maximal element which corresponds to a crisp coalition.For arbitrary fuzzy games the equal division core is introduced.It turns out that both the equal division core and the egalitariansolution of a convex fuzzy game coincide with the corresponding equal division core and the constrained egalitarian solution, respectively, of the related crisp game.game theory

Hypercubes and Compromise Values for Cooperative Fuzzy Games

AMS classification: 90D12; 03E72;cooperative games;Compromise values;Core;Fuzzy coalitions;Fuzzy games;Hypercubes;Path solutions;Weber set

Cones of Games arising from Market Entry Problems

Market entry situations are modelled, where an entrepreneur has to decide for a collection of markets which market to enter and which not. The entrepreneur can improve his prior information by making use of a group of informants, each of them knowing the situation in one or more markets. For such a market entry situation a related cooperative game is introduced, which can be helpful in dealing with the question of how to share the reward of cooperation. The games arising turn out to be elements of the cone of information market games which were introduced for another economic context. This implies that the cooperative solutions of these games have interesting properties. Extra attention is paid to the subcone of information market games arising from market entry situations where for each market only one informant knows the state of the market.cooperative games;information market entry;information market games

Convex Games versus Clan Games

In this paper we provide characterizations of convex games and total clan games by using properties of their corresponding marginal games.We show that a "dualize and restrict" procedure transforms total clan games with zero worth for the clan into monotonic convex games.Furthermore, each monotonic convex game generates a total clan game with zero worth for the clan by a "dualize and extend" procedure.These procedures are also useful for relating core elements and elements of the Weber set of the corresponding games.convex games;core;dual games;marginal games;total clan games;Weber set