IDEAS home Printed from https://ideas.repec.org/a/bpj/bejtec/v21y2021i2p525-556n9.html
   My bibliography  Save this article

Prudent Rationalizability in Generalized Extensive-form Games with Unawareness

Author

Listed:
  • Heifetz Aviad

    (The Economics and Management Department, The Open University of Israel, Ra'anana, Israel)

  • Meier Martin

    (Department of Economics, University of Bath, Bath, UK)

  • Schipper Burkhard C.

    (Department of Economics, University of California, Davis, USA)

Abstract

We define a cautious version of extensive-form rationalizability for generalized extensive-form games with unawareness that we call prudent rationalizability. It is an extensive-form analog of iterated admissibility. In each round of the procedure, for each tree and each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. We demonstrate the applicability of prudent rationalizability. In games of disclosure of verifiable information, we show that prudent rationalizability yields unraveling under full awareness but unraveling might fail under unawareness. We compare prudent rationalizability to extensive-form rationalizability. We show that prudent rationalizability may not refine extensive-form rationalizability strategies but conjecture that the paths induced by prudent rationalizable strategy profiles (weakly) refine the set of paths induced by extensive-form rationalizable strategies.

Suggested Citation

  • Heifetz Aviad & Meier Martin & Schipper Burkhard C., 2021. "Prudent Rationalizability in Generalized Extensive-form Games with Unawareness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 525-556, June.
  • Handle: RePEc:bpj:bejtec:v:21:y:2021:i:2:p:525-556:n:9
    DOI: 10.1515/bejte-2020-2013
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/bejte-2020-2013
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.1515/bejte-2020-2013?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. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    2. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
    3. Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, vol. 53(1), pages 15-42, October.
    4. Filiz-Ozbay, Emel, 2012. "Incorporating unawareness into contract theory," Games and Economic Behavior, Elsevier, vol. 76(1), pages 181-194.
    5. Simon Grant & John Quiggin, 2013. "Inductive reasoning about unawareness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 717-755, November.
    6. Grossman, Sanford J, 1981. "The Informational Role of Warranties and Private Disclosure about Product Quality," Journal of Law and Economics, University of Chicago Press, vol. 24(3), pages 461-483, December.
    7. Anonymous, 2014. "Introduction to the Issue," Journal of Wine Economics, Cambridge University Press, vol. 9(1), pages 1-2, May.
    8. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 219-249, June.
    9. 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..
    10. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    11. Schipper, Burkhard C. & Woo, Hee Yeul, 2019. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Quarterly Journal of Political Science, now publishers, vol. 14(1), pages 41-88, January.
    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. Paul Milgrom & John Roberts, 1986. "Relying on the Information of Interested Parties," RAND Journal of Economics, The RAND Corporation, vol. 17(1), pages 18-32, Spring.
    14. Stahl, Dale O., 1995. "Lexicographic rationalizability and iterated admissibility," Economics Letters, Elsevier, vol. 47(2), pages 155-159, February.
    15. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    16. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    17. , & ,, 2013. "The order independence of iterated dominance in extensive games," Theoretical Economics, Econometric Society, vol. 8(1), January.
    18. Anonymous, 2014. "Introduction to the Issue," Journal of Wine Economics, Cambridge University Press, vol. 9(2), pages 109-110, August.
    19. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    20. Perea, Andrés, 2018. "Why forward induction leads to the backward induction outcome: A new proof for Battigalli's theorem," Games and Economic Behavior, Elsevier, vol. 110(C), pages 120-138.
    21. Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
    22. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    23. Leandro Rêgo & Joseph Halpern, 2012. "Generalized solution concepts in games with possibly unaware players," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 131-155, February.
    24. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-649, May.
    25. Paul Milgrom, 2008. "What the Seller Won't Tell You: Persuasion and Disclosure in Markets," Journal of Economic Perspectives, American Economic Association, vol. 22(2), pages 115-131, Spring.
    26. Grossman, S J & Hart, O D, 1980. "Disclosure Laws and Takeover Bids," Journal of Finance, American Finance Association, vol. 35(2), pages 323-334, May.
    27. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 145, University of California, Davis, Department of Economics.
    28. Aviad Heifetz & Andrés Perea, 2015. "On the outcome equivalence of backward induction and extensive form rationalizability," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 37-59, February.
    29. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 153, University of California, Davis, Department of Economics.
    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. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    2. Auster, Sarah & Pavoni, Nicola, 2024. "Optimal delegation and information transmission under limited awareness," Theoretical Economics, Econometric Society, vol. 19(1), January.
    3. Gaia Belardinelli & Burkhard C. Schipper, 2023. "Implicit Knowledge in Unawareness Structures," Working Papers 360, University of California, Davis, Department of Economics.
    4. Martin Meier & Burkhard C. Schipper, 2022. "Conditional dominance in games with unawareness," Working Papers 351, University of California, Davis, Department of Economics.
    5. Li, Ying Xue & Schipper, Burkhard C., 2020. "Strategic reasoning in persuasion games: An experiment," Games and Economic Behavior, Elsevier, vol. 121(C), pages 329-367.
    6. Guarino, Pierfrancesco, 2020. "An epistemic analysis of dynamic games with unawareness," Games and Economic Behavior, Elsevier, vol. 120(C), pages 257-288.
    7. Burkhard C. Schipper & Hang Zhou, 2022. "Level-k Thinking in the Extensive Form," Working Papers 352, 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. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    2. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    3. Martin Meier & Burkhard C. Schipper, 2022. "Conditional dominance in games with unawareness," Working Papers 351, University of California, Davis, Department of Economics.
    4. Li, Ying Xue & Schipper, Burkhard C., 2020. "Strategic reasoning in persuasion games: An experiment," Games and Economic Behavior, Elsevier, vol. 121(C), pages 329-367.
    5. Perea, Andrés, 2022. "Common belief in rationality in games with unawareness," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 11-30.
    6. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    7. Burkhard Schipper & Hee Yeul Woo, 2014. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Working Papers 148, University of California, Davis, Department of Economics.
    8. Schipper, Burkhard C. & Woo, Hee Yeul, 2019. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Quarterly Journal of Political Science, now publishers, vol. 14(1), pages 41-88, January.
    9. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C, 2011. "Prudent rationalizability in generalized extensive-form games," MPRA Paper 30220, University Library of Munich, Germany.
    10. Burkhard Schipper, 2017. "Kuhn's Theorem for Extensive Games with Unawareness," Working Papers 176, University of California, Davis, Department of Economics.
    11. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    12. Burkhard Schipper, 2017. "Kuhn's Theorem for Extensive Games with Unawareness," Working Papers 204, University of California, Davis, Department of Economics.
    13. Burkhard Schipper & Hee Yeul Woo, 2012. "Political Awareness and Microtargeting of Voters in Electoral Competition," Working Papers 124, University of California, Davis, Department of Economics.
    14. Catonini, Emiliano, 2020. "On non-monotonic strategic reasoning," Games and Economic Behavior, Elsevier, vol. 120(C), pages 209-224.
    15. Arieli, Itai & Aumann, Robert J., 2015. "The logic of backward induction," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 443-464.
    16. Catonini, Emiliano, 2019. "Rationalizability and epistemic priority orderings," Games and Economic Behavior, Elsevier, vol. 114(C), pages 101-117.
    17. Manili, Julien, 2024. "Order independence for rationalizability," Games and Economic Behavior, Elsevier, vol. 143(C), pages 152-160.
    18. Burkhard Schipper & Hee Yeul Woo, 2012. "Political Awareness and Microtargeting of Voters in Electoral Competition," Working Papers 46, University of California, Davis, Department of Economics.
    19. Burkhard C. Schipper & Hang Zhou, 2022. "Level-k Thinking in the Extensive Form," Working Papers 352, University of California, Davis, Department of Economics.
    20. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.

    More about this item

    Keywords

    caution; extensive-form rationalizability; unawareness; disclosure; verifiable information; persuasion games; iterated admissibility; common strong cautious belief in rationality;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:bpj:bejtec:v:21:y:2021:i:2:p:525-556:n:9. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.