Dependencies Between Players in Boolean Games

Elise Bonzon, Marie-Christine Lagasquie-Schiex, Jérôme Lang

Abstract: Boolean games are a logical setting for representing static 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 them controls a set of propositional variables and has a specific goal expressed by a propositional formula. There is a lot of graphical structures hidden in a Boolean game: the satisfaction of each player’s goal depends on players whose actions have an influence on these goals. Even if these dependencies are not specific to Boolean games, in this particular setting they give a way of finding simple characterizations of Nash equilibria and computing them.