Logic and Game Theory
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.
|Date of creation:||07 May 2013|
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- D. B. Bernheim, 2010.
"Rationalizable Strategic Behavior,"
Levine's Working Paper Archive
661465000000000381, David K. Levine.
- Bonanno, G., 1991.
"Players' Information in Extensive Games,"
393, California Davis - Institute of Governmental Affairs.
- Claudio Bravo-Ortega & Jose De Gregorio, .
"The Relative Richness of the Poor? Natural Resources, Human Capital and Economic Growth,"
Working Papers Central Bank of Chile
139, Central Bank of Chile.
- 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.
- 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.
- 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.
- Bonanno, G, 1992. "Set-Theoretic Equivalence of Extensive-Form Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 429-47.
- Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
- Oliver Board, 2002.
"Dynamic Interactive Epistemology,"
Economics Series Working Papers
125, University of Oxford, Department of Economics.
- 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.
- Giacomo Bonanno & Pierpaolo Battigalli, 2003. "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Working Papers 9814, University of California, Davis, Department of Economics.
- Pierpaolo Battigali & Giacomo Bonanno, . "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Department of Economics 98-14, California Davis - Department of Economics.
- Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2008.
"Admissibility in Games,"
Econometric Society, vol. 76(2), pages 307-352, 03.
- van Benthem, Johan, 2001. "Games in Dynamic-Epistemic Logic," Bulletin of Economic Research, Wiley Blackwell, vol. 53(4), pages 219-48, October.
- Bonanno, Giacomo, 2013.
"A dynamic epistemic characterization of backward induction without counterfactuals,"
Games and Economic Behavior,
Elsevier, vol. 78(C), pages 31-43.
- Giacomo Bonanno, 2012. "A dynamic epistemic characterization of backward induction without counterfactuals," Working Papers 122, University of California, Davis, Department of Economics.
- Quesada, Antonio, 2001. "On expressing maximum information in extensive games," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 161-167, September.
- 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..
- Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
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