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Effectivity functions and efficient coalitions in Boolean games

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Abstract

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.

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Authors and Affiliations

  1. Université Paris Descartes, LIPADE, 75270, Paris Cédex 06, France

    Elise Bonzon

  2. Université de Toulouse, UPS, IRIT, 31062, Toulouse Cédex 9, France

    Marie-Christine Lagasquie-Schiex

  3. Université Paris Dauphine, LAMSADE, 75775, Paris Cédex 16, France

    Jérôme Lang

Authors
  1. Elise Bonzon
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  2. Marie-Christine Lagasquie-Schiex
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  3. Jérôme Lang
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Correspondence to Elise Bonzon.

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Bonzon, E., Lagasquie-Schiex, MC. & Lang, J. Effectivity functions and efficient coalitions in Boolean games. Synthese 187 (Suppl 1), 73–103 (2012). https://doi.org/10.1007/s11229-012-0130-y

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  • DOI: https://doi.org/10.1007/s11229-012-0130-y

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