A dynamic epistemic characterization of backward induction without counterfactuals
We propose a dynamic framework where the rationality of a playerʼs choice is judged on the basis of the actual beliefs that he has at the time he makes that choice. The set of “possible worlds” is given by state-instant pairs (ω,t), where each state specifies the entire play of the game. At every (ω,t) the beliefs of the active player provide an answer to the question “what will happen if I take action a?”, for every available action a. A player is rational at (ω,t) if either he is not active or the action he takes is optimal given his beliefs. We characterize backward induction in terms of the following event: the first mover (i) is rational and has correct beliefs, (ii) believes that the active player at date 1 is rational and has correct beliefs, (iii) believes that the active player at date 1 believes that the active player at date 2 is rational and has correct beliefs, etc.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Elchanan Ben-Porath, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," Review of Economic Studies, Oxford University Press, vol. 64(1), pages 23-46.
- 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.
- Pierpaolo Battigali & Giacomo Bonanno, "undated". "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Department of Economics 98-14, California Davis - Department of Economics.
- 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.
- Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
- Itzhak Gilboa, 1993. "Can Free Choice Be Known?," Discussion Papers 1055, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
- Balkenborg, Dieter & Winter, Eyal, 1997. "A necessary and sufficient epistemic condition for playing backward induction," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 325-345, April.
- Balkenborg, Dieter & Eyal Winter, 1995. "A Necessary and Sufficient Epistemic Condition for Playing Backward Induction," Discussion Paper Serie B 331, University of Bonn, Germany.
- Thorsten Clausing, 2003. "Doxastic Conditions for Backward Induction," Theory and Decision, Springer, vol. 54(4), pages 315-336, June.
- Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
- Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, EconWPA, revised 17 Aug 1994.
- Perea,AndrÃ©s, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396, September.
- Halpern, Joseph Y., 2001. "Substantive Rationality and Backward Induction," Games and Economic Behavior, Elsevier, vol. 37(2), pages 425-435, November.
- Joseph Y. Halpern, 2000. "Substantive Rationality and Backward Induction," Game Theory and Information 0004008, EconWPA.
- Feinberg, Yossi, 2005. "Subjective reasoning--dynamic games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 54-93, July.
- Antonio Quesada, 2003. "From Common Knowledge of Rationality to Backward Induction," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 127-137.
- Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
- Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
- Clausing, Thorsten, 2004. "Belief Revision In Games Of Perfect Information," Economics and Philosophy, Cambridge University Press, vol. 20(01), pages 89-115, April.
- Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 465-492, April.
- 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.
- Perea,AndrÃ©s, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915, September.
- Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19. Full references (including those not matched with items on IDEAS)