370 research outputs found
On Cores and Stable Sets for Fuzzy Games
AMS classifications: 90D12; 03E72;cooperative games;decision making;fuzzy 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
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 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
Fuzzy Clan Games and Bi-monotonic Allocation Rules
Clan game;Big boss game;Core;Decision making;Fuzzy coalition;Fuzzy game;Monotonic allocation rule
The Fuzzy Core and the (Π, β)- Balanced Core
This note provides a new proof of the non-emptiness of the fuzzy core in a pureexchange economy with finitely many agents. The proof is based on the concept of(Π, β)-balanced core for games without side payments due to Bonnisseau and Iehlé(2003).microeconomics ;
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