IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v68y2019i3d10.1007_s00199-018-1142-8.html
   My bibliography  Save this article

Interactive epistemology in simple dynamic games with a continuum of strategies

Author

Listed:
  • Pierpaolo Battigalli

    (Bocconi University)

  • Pietro Tebaldi

    (University of Chicago)

Abstract

We extend the epistemic analysis of dynamic games of Battigalli and Siniscalchi (J Econ Theory 88:188–230, 1999, J Econ Theory 106:356–391, 2002, Res Econ 61:165–184, 2007) from finite dynamic games to all simple games, that is, finite and infinite-horizon multistage games with finite action sets at nonterminal stages and compact action sets at terminal stages. We prove a generalization of Lubin’s (Proc Am Math Soc 43:118–122, 1974) extension result to deal with conditional probability systems and strong belief. With this, we can provide a short proof of the following result: in every simple dynamic game, strong rationalizability characterizes the behavioral implications of rationality and common strong belief in rationality.

Suggested Citation

  • Pierpaolo Battigalli & Pietro Tebaldi, 2019. "Interactive epistemology in simple dynamic games with a continuum of strategies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 737-763, October.
    • Handle: RePEc:spr:joecth:v:68:y:2019:i:3:d:10.1007_s00199-018-1142-8
    DOI: 10.1007/s00199-018-1142-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-018-1142-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-018-1142-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
    2. H. Peyton Young & Shmuel Zamir (ed.), 2015. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 4, number 4.
    3. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, vol. 61(4), pages 165-184, December.
    4. Schmidt, Klaus M, 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Econometrica, Econometric Society, vol. 61(2), pages 325-351, March.
    5. Giuseppe Attanasi & Pierpaolo Battigalli & Elena Manzoni & Rosemarie Nagel, 2013. "Disclosure of Belief-Dependent Preferences in a Trust Game," Working Papers 506, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    6. Drew Fudenberg & David K. Levine, 2008. "Reputation And Equilibrium Selection In Games With A Patient Player," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 7, pages 123-142, World Scientific Publishing Co. Pte. Ltd..
    7. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    8. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    9. Sergiu Hart & Ilan Kremer & Motty Perry, 2017. "Evidence Games: Truth and Commitment," American Economic Review, American Economic Association, vol. 107(3), pages 690-713, March.
    10. Battigalli, Pierpaolo & Dufwenberg, Martin, 2009. "Dynamic psychological games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 1-35, January.
    11. Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 377-399, April.
    12. Pierpaolo Battigalli, 2006. "Rationalization In Signaling Games: Theory And Applications," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 67-93.
    13. Harrington, Joseph E., 2017. "A theory of collusion with partial mutual understanding," Research in Economics, Elsevier, vol. 71(1), pages 140-158.
    14. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    15. 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.
    16. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    17. Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
    18. Arieli, Itai, 2010. "Rationalizability in continuous games," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 912-924, September.
    19. Battigalli Pierpaolo & Prestipino Andrea, 2013. "Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 1-53, May.
    20. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    21. , & ,, 2012. "Forward induction reasoning revisited," Theoretical Economics, Econometric Society, vol. 7(1), January.
    22. Battigalli, Pierpaolo & Charness, Gary & Dufwenberg, Martin, 2013. "Deception: The role of guilt," Journal of Economic Behavior & Organization, Elsevier, vol. 93(C), pages 227-232.
    23. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    24. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    25. Catonini, Emiliano, 2019. "Rationalizability and epistemic priority orderings," Games and Economic Behavior, Elsevier, vol. 114(C), pages 101-117.
    26. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    27. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, vol. 148(2), pages 424-447.
    28. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    29. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    30. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
    31. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    32. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    33. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
    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. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    2. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    3. Battigalli, Pierpaolo & Corrao, Roberto & Sanna, Federico, 2020. "Epistemic game theory without types structures: An application to psychological games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 28-57.
    4. Pierpaolo Battigalli & Martin Dufwenberg, 2022. "Belief-Dependent Motivations and Psychological Game Theory," Journal of Economic Literature, American Economic Association, vol. 60(3), pages 833-882, September.
    5. Shi-Woei Lin & Januardi Januardi, 2023. "Two-period pricing and utilization decisions in a dual-channel service-only supply chain," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(2), pages 605-635, June.
    6. Pierpaolo Battigalli & Martin Dufwenberg, 2019. "Psychological Game Theory," Working Papers 646, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    7. Shi‐Woei Lin & Januardi, 2023. "Two‐stage pricing of perishable food supply chain with quality‐keeping and waste reduction efforts," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(3), pages 1749-1766, April.

    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. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    3. Guarino, Pierfrancesco, 2020. "An epistemic analysis of dynamic games with unawareness," Games and Economic Behavior, Elsevier, vol. 120(C), pages 257-288.
    4. Catonini, Emiliano, 2020. "On non-monotonic strategic reasoning," Games and Economic Behavior, Elsevier, vol. 120(C), pages 209-224.
    5. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    6. Zuazo-Garin, Peio, 2017. "Uncertain information structures and backward induction," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 135-151.
    7. Burkhard C. Schipper & Hang Zhou, 2022. "Level-k Thinking in the Extensive Form," Working Papers 352, University of California, Davis, Department of Economics.
    8. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, vol. 61(4), pages 165-184, December.
    9. Ziegler, Gabriel, 2022. "Informational robustness of common belief in rationality," Games and Economic Behavior, Elsevier, vol. 132(C), pages 592-597.
    10. Catonini, Emiliano, 2019. "Rationalizability and epistemic priority orderings," Games and Economic Behavior, Elsevier, vol. 114(C), pages 101-117.
    11. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    12. Amanda Friedenberg & H. Jerome Keisler, 2021. "Iterated dominance revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 377-421, September.
    13. Cappelletti Giuseppe, 2010. "A Note on Rationalizability and Restrictions on Beliefs," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-13, September.
    14. Perea, Andrés, 2017. "Forward induction reasoning and correct beliefs," Journal of Economic Theory, Elsevier, vol. 169(C), pages 489-516.
    15. Giuseppe Attanasi & Pierpaolo Battigalli & Elena Manzoni, 2016. "Incomplete-Information Models of Guilt Aversion in the Trust Game," Management Science, INFORMS, vol. 62(3), pages 648-667, March.
    16. Ziegler, Gabriel & Zuazo-Garin, Peio, 2020. "Strategic cautiousness as an expression of robustness to ambiguity," Games and Economic Behavior, Elsevier, vol. 119(C), pages 197-215.
    17. Shimoji, Makoto & Schweinzer, Paul, 2015. "Implementation without incentive compatibility: Two stories with partially informed planners," Games and Economic Behavior, Elsevier, vol. 91(C), pages 258-267.
    18. Battigalli, Pierpaolo & Corrao, Roberto & Dufwenberg, Martin, 2019. "Incorporating belief-dependent motivation in games," Journal of Economic Behavior & Organization, Elsevier, vol. 167(C), pages 185-218.
    19. Battigalli, P. & Catonini, E. & Manili, J., 2023. "Belief change, rationality, and strategic reasoning in sequential games," Games and Economic Behavior, Elsevier, vol. 142(C), pages 527-551.
    20. Battigalli, Pierpaolo & Corrao, Roberto & Sanna, Federico, 2020. "Epistemic game theory without types structures: An application to psychological games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 28-57.

    More about this item

    Keywords

    Epistemic game theory; Simple infinite dynamic game; Strong belief; Strong rationalizability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:spr:joecth:v:68:y:2019:i:3:d:10.1007_s00199-018-1142-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.