Harrenstein, Paul; van der Hoek, Wiebe; Meyer, John-Jules; Witteveen, Cees A modal characterization of Nash equilibrium. (English) Zbl 1041.03016 Fundam. Inform. 57, No. 2-4, 281-321 (2003). The paper deals with a logical analysis of the game-theoretical concept of Nash equilibrium in the model of specific type of extensive games of perfect information, being defined as labeled graphs. It is shown that modal languages can be used for the description of the considered concepts. The main contribution of the paper is the proposition of a logic for a multi-modal language and the proof of its completeness with respect to a class of frames corresponding with a specific group of extensive games. It is also shown that the proposed multi-modal language is suitable for the characterization of Nash equilibria and that the described approach can be refined by means of Propositional Dynamic Logic. Reviewer: Milan Mareš (Praha) Cited in 1 ReviewCited in 18 Documents MSC: 03B45 Modal logic (including the logic of norms) 68T27 Logic in artificial intelligence 91A35 Decision theory for games 91B52 Special types of economic equilibria 03B70 Logic in computer science Keywords:modal logic; dynamic logic; game theory; Nash equilibrium; multi-agent system PDFBibTeX XMLCite \textit{P. Harrenstein} et al., Fundam. Inform. 57, No. 2--4, 281--321 (2003; Zbl 1041.03016)