Boolean Hedonic Games

TL;DR

This paper introduces a formal framework for analyzing hedonic games with dichotomous preferences, using propositional formulas to represent players' preferences and characterizing solution concepts.

Contribution

It develops a succinct propositional representation for dichotomous hedonic games and characterizes solution concepts within this formalism.

Findings

Propositional formulas effectively represent players' dichotomous preferences.

Characterization of solution concepts using propositional logic.

Framework simplifies analysis of hedonic games with dichotomous preferences.

Abstract

We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player's preference relation partitions the set of coalitions of which that player is a member into just two equivalence classes: satisfactory and unsatisfactory. A player is indifferent between satisfactory coalitions, and is indifferent between unsatisfactory coalitions, but strictly prefers any satisfactory coalition over any unsatisfactory coalition. We develop a succinct representation for such games, in which each player's preference relation is represented by a propositional formula. We show how solution concepts for hedonic games with dichotomous preferences are characterised by propositional formulas.