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Reasoning about strategies and rational play in dynamic games

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  • Giacomo Bonanno

    (Department of Economics, University of California Davis)

Abstract

We discuss the issues that arise in modeling the notion of common belief of rationality in epistemic models of dynamic games, in particular at the level of interpretation of strategies. A strategy in a dynamic game is defined as a function that associates with every information set a choice at that information set. Implicit in this definition is a set of counterfactual statements concerning what a player would do at information sets that are not reached, or a belief revision policy concerning behavior at information sets that are ruled out by the initial beliefs. We discuss the role of both objective and subjective counterfactuals in attempting to flesh out the interpretation of strategies in epistemic models of dynamic games.

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Bibliographic Info

Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 149.

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Length: 37
Date of creation: 12 Mar 2014
Date of revision:
Handle: RePEc:cda:wpaper:14-9

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Keywords: Extensive-form game; strategy; counterfactual; belief revision; Kripke frame; modal logic;

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  1. Oliver Board, 2002. "Dynamic Interactive Epistemology," Economics Series Working Papers 125, University of Oxford, Department of Economics.
  2. Pierpaolo Battigalli & Alfredo Di Tillio & Dov Samet, 2011. "Strategies and interactive beliefs in dynamic games," Working Papers 375, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  3. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
  4. Joseph Y. Halpern, 1999. "Hypothetical knowledge and counterfactual reasoning," International Journal of Game Theory, Springer, vol. 28(3), pages 315-330.
  5. 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.
  6. Clausing, Thorsten, 2004. "Belief Revision In Games Of Perfect Information," Economics and Philosophy, Cambridge University Press, vol. 20(01), pages 89-115, April.
  7. Bonanno, Giacomo & Nehring, Klaus, 1998. "Assessing the truth axiom under incomplete information," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 3-29, July.
  8. Joseph Y. Halpern, 2000. "Substantive Rationality and Backward Induction," Game Theory and Information 0004008, EconWPA.
  9. Stalnaker, Robert, 1999. "Extensive and strategic forms: Games and models for games," Research in Economics, Elsevier, vol. 53(3), pages 293-319, September.
  10. Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer, vol. 35(4), pages 465-492, April.
  11. Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, EconWPA, revised 17 Aug 1994.
  12. Oliver Board, 2006. "The Equivalence of Bayes and Causal Rationality in Games," Theory and Decision, Springer, vol. 61(1), pages 1-19, 08.
  13. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  14. Feinberg, Yossi, 2005. "Subjective reasoning--dynamic games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 54-93, July.
  15. Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
  16. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  17. Tyran, Jean-Robert, 2003. "Behavioral Game Theory. Experiments in Strategic Interaction: Colin F. Camerer, Princeton University Press, Princeton, New Jersey, 2003, p. 550, Price $65.00/[UK pound]42.95, ISBN 0-691-09039-4," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 32(6), pages 717-720, December.
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