Games with Fuzzy Coalitions

Fairness and fuzzy coalitions

International Journal of Game Theory ◽

10.1007/s00182-021-00780-2 ◽

2021 ◽

Author(s):

Chiara Donnini ◽

Marialaura Pesce

Keyword(s):

New York ◽

Economic Theory ◽

Measure Space ◽

Exchange Economy ◽

Mathematical Methods ◽

Competitive Equilibria ◽

Fuzzy Coalitions ◽

Core Allocations

AbstractIn this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents’ measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation of individuals in coalitions, that induces an enlargement of the set of ordinary coalitions to the so-called fuzzy or generalized coalitions. We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.

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Risk-Bounded Formation of Fuzzy Coalitions Among Service Agents

Cooperative Information Agents X - Lecture Notes in Computer Science ◽

10.1007/11839354_24 ◽

2006 ◽

pp. 332-346 ◽

Cited By ~ 2

Author(s):

Bastian Blankenburg ◽

Minghua He ◽

Matthias Klusch ◽

Nicholas R. Jennings

Keyword(s):

Fuzzy Coalitions

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Forming Fuzzy Coalitions in Cooperative Superadditive Games

IEEE International Conference on e-Business Engineering (ICEBE'07) ◽

10.1109/icebe.2007.93 ◽

2007 ◽

Author(s):

Minghua He ◽

Xudong Luo ◽

Nicholas R. Jennings ◽

Michael Wooldridge

Keyword(s):

Fuzzy Coalitions

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ALTERNATIVE REPRESENTATION OF FUZZY COALITIONS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488509005917 ◽

2009 ◽

Vol 17 (03) ◽

pp. 345-364 ◽

Cited By ~ 1

Author(s):

MILAN MAREŠ ◽

MILAN VLACH

Keyword(s):

Cooperative Games ◽

Alternative Model ◽

Common Interest ◽

Compact Groups ◽

Alternative Representation ◽

Alternative Approach ◽

Individual Player ◽

Fuzzy Coalitions ◽

Fuzzy Subsets

The theory of cooperative games with vague cooperation is based on modelling fuzzy coalitions as fuzzy subsets of the set of all players who participate in the coalitions with some part of their "power". Here, we suggest an alternative approach assuming that coalitions are formed by relatively compact groups of individual players each of which represents a specific common interest. Each individual player may participate in several such groups and, as their member, in several coalitions. Our aim is to show that such an alternative model of fuzzy coalitions, in spite of its seemingly higher complexity, offers an interesting more sophisticated reflection of the structure of vague cooperation and of relations being in its background.

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