Logic and Game Theory
[chapter]
Giacomo Bonanno, Cédric Dégremont
2014
Outstanding Contributions to Logic
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... bedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Johan van Benthem has highlighted in his work that many questions arising in the analysis of strategic interaction call for logical and computational analysis. These questions lead to both formal and conceptually illuminating answers, in that they contribute to clarifying some of the underlying assumptions behind certain aspects of game-theoretical reasoning. We focus on the insights of a part of the literature at the interface of game theory and mathematical logic that gravitates around van Benthem's work. We discuss the formal questions raised by the perspective consisting in taking games as models for formal languages, in particular modal languages, and how eliminative reasoning processes and solution algorithms can be analyzed logically as epistemic dynamics and discuss the role played by beliefs in game-theoretical analysis and how they should be modeled from a logical point of view. We give many pointers to the literature throughout the paper. Abstract Johan van Benthem has highlighted in his work that many questions arising in the analysis of strategic interaction call for logical and computational analysis. These questions lead to both formal and conceptually illuminating answers, in that they contribute to clarifying some of the underlying assumptions behind certain aspects of game-theoretical reasoning. We focus on the insights of a part of the literature at the interface of game theory and mathematical logic that gravitates around van Benthem's work. We discuss the formal questions raised by the perspective consisting in taking games as models for formal languages, in particular modal languages, and how eliminative reasoning processes and solution algorithms can be analyzed logically as epistemic dynamics and discuss the role played by beliefs in game-theoretical analysis and how they should be modeled from a logical point of view. We give many pointers to the literature throughout the paper. 1 2 Giacomo Bonanno and Cédric Dégremont These contributions have both a formal and conceptual aspect. They are formal in that they show how models of strategic interaction and game-theoretical concepts can be embedded in a broader formal context and analyzed from the perspective and with the tools of mathematical logic. They are also conceptual in that they contribute to clarifying some of the underlying assumptions behind certain aspects of gametheoretical reasoning. The late Michael Bacharach was one of the first to appreciate the usefulness of logic in reasoning about games: "Game theory is full of deep puzzles, and there is often disagreement about proposed solutions to them. The puzzlement and disagreement are neither empirical nor mathematical but, rather, concern the meanings of fundamental concepts ('solution', 'rational','complete information') and the soundness of certain arguments (that solutions must be Nash equilibria, that rational players defect in Prisoner's Dilemmas, that players should consider what would happen in eventualities which they regard as impossible). Logic appears to be an appropriate tool for game theory both because these conceptual obscurities involve notions such as reasoning, knowledge and counterfactuality which are part of the stock-in-trade of logic, and because it is a prime function of logic to establish the validity or invalidity of disputed arguments" ((Bacharach, 1994) , p. 21).
doi:10.1007/978-3-319-06025-5_15
fatcat:rad2pvvxindxvf7ytwfwektf7y