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Logic and Game Theory

Listed author(s):
  • Giacomo Bonanno
  • Cédric Dégremont

    (Department of Economics, University of California Davis)

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.

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Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 135.

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Length: 31
Date of creation: 07 May 2013
Handle: RePEc:cda:wpaper:13-5
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  1. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
  2. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  3. Bonanno, G., 1991. "Players' Information in Extensive Games," Papers 393, California Davis - Institute of Governmental Affairs.
  4. Bonanno, Giacomo, 2013. "A dynamic epistemic characterization of backward induction without counterfactuals," Games and Economic Behavior, Elsevier, vol. 78(C), pages 31-43.
  5. Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.
  6. van Benthem, Johan, 2001. "Games in Dynamic-Epistemic Logic," Bulletin of Economic Research, Wiley Blackwell, vol. 53(4), pages 219-248, October.
  7. Bonanno, G, 1992. "Set-Theoretic Equivalence of Extensive-Form Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 429-447.
  8. Bravo-Ortega, Claudio & de Gregorio, Jose, 2005. "The relative richness of the poor? natural resources, human capital, and economic growth," Policy Research Working Paper Series 3484, The World Bank.
  9. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Synchronic information, knowledge and common knowledge in extensive games," Research in Economics, Elsevier, vol. 53(1), pages 77-99, March.
  10. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212 World Scientific Publishing Co. Pte. Ltd..
  11. Elmes Susan & Reny Philip J., 1994. "On the Strategic Equivalence of Extensive Form Games," Journal of Economic Theory, Elsevier, vol. 62(1), pages 1-23, February.
  12. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160 World Scientific Publishing Co. Pte. Ltd..
  13. Quesada, Antonio, 2001. "On expressing maximum information in extensive games," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 161-167, September.
  14. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
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