[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/cda/wpaper/10.html
   My bibliography  Save this paper

A dynamic epistemic characterization of backward induction without counterfactuals

Author

Listed:
  • Giacomo Bonanno

    (Department of Economics, University of California Davis)

Abstract
The analysis of rational play in dynamic games is usually done within a static framework that specifies a player's initial beliefs as well as his disposition to revise those beliefs conditional on hypothetical states of information. We suggest a simpler approach, where the rationality of a player's choice is judged on the basis of the actual beliefs that the player has at the time he has to make that choice. We propose a dynamic framework where the set of "possible worlds" is given by state-instant pairs (w,t). Each state w specifies the entire play of the game and, for every instant t, (w,t) specifies the history that is reached at that instant (in state w). A player is said to be active at (w,t) if the history reached in state w at date t is a decision history of his. At every state-instant pair (w,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 said to be rational at (w,t) if either he is not active there or the action he ends up taking at state w is "optimal" given his beliefs at (w,t). We provide a characterization of 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. Thus our epistemic characterization does not rely on dispositional belief revision or on (objective or subjective) counterfactuals.

Suggested Citation

  • Giacomo Bonanno, 2012. "A dynamic epistemic characterization of backward induction without counterfactuals," Working Papers 10, University of California, Davis, Department of Economics.
    • Handle: RePEc:cda:wpaper:10
    as

    Download full text from publisher

    File URL: https://repec.dss.ucdavis.edu/files/D1xbR5jboe81bfxNF5BsQdb1/12-2.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Elchanan Ben-Porath, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(1), pages 23-46.
    2. 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.
    3. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(2), pages 133-163, October.
    4. Itzhak Gilboa, 1993. "Can Free Choice Be Known?," Discussion Papers 1055, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
    6. 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.
    7. Thorsten Clausing, 2003. "Doxastic Conditions for Backward Induction," Theory and Decision, Springer, vol. 54(4), pages 315-336, June.
    8. Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
    9. 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.
    10. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396, September.
    11. Halpern, Joseph Y., 2001. "Substantive Rationality and Backward Induction," Games and Economic Behavior, Elsevier, vol. 37(2), pages 425-435, November.
    12. Bicchieri, Cristina & Jeffrey, Richard & Skyrms, Brian (ed.), 1999. "The Logic of Strategy," OUP Catalogue, Oxford University Press, number 9780195117158.
    13. Feinberg, Yossi, 2005. "Subjective reasoning--dynamic games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 54-93, July.
    14. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    15. Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
    16. Clausing, Thorsten, 2004. "Belief Revision In Games Of Perfect Information," Economics and Philosophy, Cambridge University Press, vol. 20(1), pages 89-115, April.
    17. 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.
    18. 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.
    19. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915, September.
    20. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Giacomo Bonanno, 2022. "Rational Play in Extensive-Form Games," Games, MDPI, vol. 13(6), pages 1-20, October.
    2. Giacomo Bonanno, 2012. "Epistemic foundations of game theory," Working Papers 70, University of California, Davis, Department of Economics.
    3. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    4. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 9, University of California, Davis, Department of Economics.
    5. Zuazo-Garin, Peio, 2017. "Uncertain information structures and backward induction," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 135-151.
    6. Mehmet S. Ismail, 2023. "Human and Machine Intelligence in n-Person Games with Partial Knowledge: Theory and Computation," Papers 2302.13937, arXiv.org, revised Feb 2024.
    7. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 24, University of California, Davis, Department of Economics.
    8. Giacomo Bonanno, 2013. "An epistemic characterization of generalized backward induction," Working Papers 132, University of California, Davis, Department of Economics.
    9. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
    10. Giacomo Bonanno, 2018. "Behavior and deliberation in perfect-information games: Nash equilibrium and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 1001-1032, September.
    11. Bonanno, Giacomo, 2014. "A doxastic behavioral characterization of generalized backward induction," Games and Economic Behavior, Elsevier, vol. 88(C), pages 221-241.
    12. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 134, University of California, Davis, Department of Economics.
    13. Giacomo Bonanno, 2013. "An epistemic characterization of generalized backward induction," Working Papers 60, University of California, Davis, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Giacomo Bonanno, 2018. "Behavior and deliberation in perfect-information games: Nash equilibrium and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 1001-1032, September.
    2. Graciela Kuechle, 2009. "What Happened To The Three‐Legged Centipede Game?," Journal of Economic Surveys, Wiley Blackwell, vol. 23(3), pages 562-585, July.
    3. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
    4. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 9, University of California, Davis, Department of Economics.
    5. Bonanno, Giacomo, 2013. "A dynamic epistemic characterization of backward induction without counterfactuals," Games and Economic Behavior, Elsevier, vol. 78(C), pages 31-43.
    6. Perea ý Monsuwé, A., 2006. "Epistemic foundations for backward induction: an overview," Research Memorandum 036, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    7. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    8. Bonanno, Giacomo, 2014. "A doxastic behavioral characterization of generalized backward induction," Games and Economic Behavior, Elsevier, vol. 88(C), pages 221-241.
    9. Giacomo Bonanno, 2021. "Rational play in games: A behavioral approach," Working Papers 344, University of California, Davis, Department of Economics.
    10. Perea, Andrés, 2008. "Minimal belief revision leads to backward induction," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 1-26, July.
    11. Giacomo Bonanno, 2012. "Epistemic foundations of game theory," Working Papers 70, University of California, Davis, Department of Economics.
    12. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
    13. Giacomo Bonanno, 2013. "An epistemic characterization of generalized backward induction," Working Papers 60, University of California, Davis, Department of Economics.
    14. Giacomo Bonanno, 2022. "Rational Play in Extensive-Form Games," Games, MDPI, vol. 13(6), pages 1-20, October.
    15. Giacomo Bonanno, 2013. "An epistemic characterization of generalized backward induction," Working Papers 132, University of California, Davis, Department of Economics.
    16. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    17. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
    18. Perea Andrés, 2003. "Rationalizability and Minimal Complexity in Dynamic Games," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    19. Giacomo Bonanno, 2008. "Non-cooperative game theory," Working Papers 86, University of California, Davis, Department of Economics.
    20. Feinberg, Yossi, 2005. "Subjective reasoning--dynamic games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 54-93, July.

    More about this item

    Keywords

    Perfect-information game; backward induction; dynamic interactive beliefs; rationality; Kripke frame;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cda:wpaper:10. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Letters and Science IT Services Unit (email available below). General contact details of provider: https://edirc.repec.org/data/educdus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.