ECAI-2002 Conference Paper

[full paper]

On Modal Logic Interpretations of Games

Paul Harrenstein, Wiebe van der Hoek, John Jules Meyer, Cees Witteveen

Multi-agent environments comprise decision makers whose deliberations involve reasoning about the expected behaviour 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 multi-agent systems. This paper concerns the logical analysis of the game-theoretical 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 Nash-optimal. Our analysis focusses on extensive games of perfect information without repetition.

Keywords: Multi-Agent Systems, Game Theory, Dynamic Logic, Decision Theory

Citation: Paul Harrenstein, Wiebe van der Hoek, John Jules Meyer, Cees Witteveen: On Modal Logic Interpretations of Games. In F. van Harmelen (ed.): ECAI2002, Proceedings of the 15th European Conference on Artificial Intelligence, IOS Press, Amsterdam, 2002, pp.28-32.