20 Modal logic for games and information

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Game-theoretic ideas have long played an influential rule in analyzing various branches of logic. This chapter focuses on using modal logics to describe and reason about games. It also investigates the uses of modal logic. Some structure on the various strands of research, to create an organization, which highlights the essential lines of research are focused. The chapter also discusses modeling imperfect information and multi-agent information update through dynamic epistemic logics; reasoning about game structure through operations for combining games; and logics of collective action and the power of coalitions of agents over time. Game trees can be viewed as Kripke models, where the possible moves are modeled by an accessibility relation and additional information about payoffs and turn taking are encoded by propositional atoms. Structural equivalence notions such as bisimulation turn into game equivalence notions, and extensions of the modal language, which can capture game-theoretic solution concepts such as the subgame-perfect equilibrium are investigated.

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