Boolean Games with Epistemic Goals

Thomas Ågotnes, Paul Harrenstein, Wiebe van der Hoek, Michael J. Wooldridge

Abstract: We introduce and formally study games in which the goals of players relate to the epistemic states of players in the game. For example, one player might have a goal that another player knows a certain proposition, while another player might have as a goal that a certain player does not know some proposition. The formal model we use to study epistemic games is a variation of the increasingly popular Boolean games model in which each player controls a number of Boolean variables, but has limited ability to see the truth values of the overall set of formulae that hold in the game. Each player in an epistemic Boolean game has a goal, defined as a formula of modal epistemic logic. Using such a language for goals allows us to explicitly and compactly represent desirable epistemic states. After motivating and formally defining epistemic Boolean games as a concise representation of epistemic Kripke structures, we investigate their complexity and study their properties.