Modeling Coalitional Power in Modal Logic

Abstract

Given a set of states, we introduce models which associate with every state a strategic game between a finite set of players which will result in a new state when played. The power of coalitions of agents in these games can be captured by the notion of alpha-effectivity, as studied in social choice theory: A coalition of players is alpha-effective for a set of states X if the coalition can guarantee an outcome in X. We propose a modal logic to formalize reasoining about alpha-efficiency, where <C>phi expresses that coalition C is alpha effective for phi.