Effectivity functions and efficient coalitions in Boolean games

Boolean games are a logical setting for representing strategic games in a succinct way, taking advantage of the expressive power and conciseness of propositional logic. A Boolean game consists of a set of players, each of which controls a set of propositional variables and has a specific goal expres...

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Bibliographic Details
Published in:Synthese (Dordrecht) 2012-08, Vol.187 (Suppl 1), p.73-103
Main Authors: Bonzon, Elise, Lagasquie-Schiex, Marie-Christine, Lang, Jérôme
Format: Article
Language:English
Subjects:
Boolean data
Cost efficiency
Cost functions
Education
Efficient strategies
Epistemology
Epistemology. Philosophy of science. Theory of knowledge
Game theory
Kidneys
Logic
Mathematical functions
Metaphysics
Philosophy
Philosophy of Language
Philosophy of Science
Urelements
Utility functions
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Summary:Boolean games are a logical setting for representing strategic games in a succinct way, taking advantage of the expressive power and conciseness of propositional logic. A Boolean game consists of a set of players, each of which controls a set of propositional variables and has a specific goal expressed by a propositional formula. We show here that Boolean games are a very simple setting, yet sophisticated enough, for analysing the formation of coalitions. Due to the fact that players have dichotomous preferences, the following notion emerges naturally: a coalition in a Boolean game is efficient if it has the power to guarantee that all goals of the members of the coalition are satisfied. We study the properties of efficient coalitions.
ISSN:0039-7857
1573-0964
DOI:10.1007/s11229-012-0130-y