363 research outputs found
Convex Fuzzy Games and Participation Monotonic Allocation Schemes
AMS classifications: 90D12; 03E72Convex games;Core;Decisionmaking;Fuzzy coalitions;Fuzzy games;Monotonic allocation schemes;Weber set
Convex fuzzy games and participation monotonic allocation schemes
90D12;03E72cooperative games
Cooperative Games with Overlapping Coalitions
In the usual models of cooperative game theory, the outcome of a coalition
formation process is either the grand coalition or a coalition structure that
consists of disjoint coalitions. However, in many domains where coalitions are
associated with tasks, an agent may be involved in executing more than one
task, and thus may distribute his resources among several coalitions. To tackle
such scenarios, we introduce a model for cooperative games with overlapping
coalitions--or overlapping coalition formation (OCF) games. We then explore the
issue of stability in this setting. In particular, we introduce a notion of the
core, which generalizes the corresponding notion in the traditional
(non-overlapping) scenario. Then, under some quite general conditions, we
characterize the elements of the core, and show that any element of the core
maximizes the social welfare. We also introduce a concept of balancedness for
overlapping coalitional games, and use it to characterize coalition structures
that can be extended to elements of the core. Finally, we generalize the notion
of convexity to our setting, and show that under some natural assumptions
convex games have a non-empty core. Moreover, we introduce two alternative
notions of stability in OCF that allow a wider range of deviations, and explore
the relationships among the corresponding definitions of the core, as well as
the classic (non-overlapping) core and the Aubin core. We illustrate the
general properties of the three cores, and also study them from a computational
perspective, thus obtaining additional insights into their fundamental
structure
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
Cooperative investment games or population games
The model of a cooperative fuzzy game is interpreted as both a population game and a cooperative investment game. Three types of core- like solutions induced by these interpretations are introduced and investigated. The interpretation of a game as a population game allows us to define sub-games. We show that, unlike the well-known Shapley- Shubik theorem on market games (Shapley-Shubik) there might be a population game such that each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a population game needs to be also homogeneous. We also discuss some special classes of population games such as convex games, exact games, homogeneousgames and additive games.investment game, population game, fuzzy game, core-like solution, market game
On Cores and Stable Sets for Fuzzy Games
AMS classifications: 90D12; 03E72;cooperative games;decision making;fuzzy games
Fuzzy coalitional structures (alternatives)
The uncertainty of expectations and vagueness of the interests belong to
natural components of cooperative situations, in general. Therefore, some
kind of formalization of uncertainty and vagueness should be included in
realistic models of cooperative behaviour. This paper attempts to contribute
to the endeavour of designing a universal model of vagueness in cooperative
situations. Namely, some initial auxiliary steps toward the development of
such a model are described. We use the concept of fuzzy coalitions suggested
in [1], discuss the concepts of superadditivity and convexity, and introduce a
concept of the coalitional structure of fuzzy coalitions.
The first version of this paper [10] was presented at the Czech-Japan
Seminar in Valtice 2003. It was obvious that the roots of some open questions
can be found in the concept of superadditivity (with consequences on some
other related concepts), which deserve more attention. This version of the
paper extends the previous one by discussion of alternative approaches to
this topic
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