On Modal Logic Interpretations of Games
Paul Harrenstein, Wiebe van der Hoek, John-Jules Meyer, Cees Witteveen · 2002
Abstract. Multi-agent environments comprise decision makers whose deliberations involve reasoning about the expected behavior of other agents. Apposite concepts of rational choice have been studied and formalized in game theory and our particular interest is with their integration in a logical specification language for multiagent systems. This paper concerns the logical analysis of the gametheoretical notions of a (subgame perfect) Nash equilibrium and that of a (subgame perfect) best response strategy. Extensive forms of games are conceived of as Kripke frames and a version of Propositional Dynamic Logic is employed to describe them. We show how formula schemes of our language characterize those classes of frames in which the strategic choices of the agents can be said to be Nashoptimal. Our analysis focuses on extensive games of perfect information without repetition. 1