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A modal characterization of Nash equilibrium. (English) Zbl 1041.03016

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.

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
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