Effectivity functions and efficient coalitions in Boolean games

International audienceBoolean games are a logical setting for representing strategic games in asuccinct way, taking advantage of the expressive power and conciseness of propositionallogic. A Boolean game consists of a set of players, each of which controls a setof 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 dichotomouspreferences, the following notion emerges naturally: a coalition in a Boolean game isefficient if it has the power to guarantee that all goals of the members of the coalitionare satisfied. We study the properties of efficient coalitions