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

Hypercubes and compromise values for cooperative fuzzy games

90D12;03E72cooperative 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

Egalitarianism in convex fuzzy games

cooperative games;algorithm

A New Characterization of Convex Games

A cooperative game turns out to be convex if and only if all its marginal games are superadditive.characterization;convex games;marginal games;superadditive 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

How to Cope with Division Problems under Interval Uncertainty of Claims?

The paper deals with division situations where individual claims can vary within closed intervals.Uncertainty of claims is removed by compromising in a consistent way the upper and lower bounds of the claim intervals.Deterministic division problems with compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to e .cient and reasonable rules for division problems under interval uncertainty of claims.uncertainty;claims;division problems