IDEAS home Printed from https://ideas.repec.org/p/sad/ypaper/10.html
   My bibliography  Save this paper

Perfect Bayesian Equilibrium in Kuhn Poker

Author

Listed:
  • Martín Iñaki Loriente

    (Department of Economics, Universidad de San Andrés)

  • Juan Cruz Diez

    (Department of Economics, Universidad de San Andrés)

Abstract

In 1950, Harold W. Kuhn introduced a simplified version of poker referred to as Kuhn Poker and solved it using the notion of Nash Equilibrium. His pioneering work inspired subsequent scholars who applied similar methodologies to other poker versions. In contrast we adopt a different procedure by employing Harsanyi’s approach to reach a Perfect Bayesian Equilibrium (PBE), a concept that emerged two decades after Kuhn’s original solutions. While computational techniques have greatly advanced the analysis of various poker variations, achieving a PBE remains elusive. Some studies suffer from methodological flaws, as they overlook the importance of incorporating beliefs into their analysis. In our research, we also conducted a rationality study and found that relaxing the sophistication of a player leads to a shift in optimal strategies towards more exploitative ones.

Suggested Citation

  • Martín Iñaki Loriente & Juan Cruz Diez, 2023. "Perfect Bayesian Equilibrium in Kuhn Poker," Young Researchers Working Papers 10, Universidad de San Andres, Departamento de Economia, revised Oct 2023.
    • Handle: RePEc:sad:ypaper:10
    as

    Download full text from publisher

    File URL: https://webacademicos.udesa.edu.ar/pub/econ/ydoc10.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    2. David H. Reiley & Michael B. Urbancic & Mark Walker, 2008. "Stripped-Down Poker: A Classroom Game with Signaling and Bluffing," The Journal of Economic Education, Taylor & Francis Journals, vol. 39(4), pages 323-341, September.
    3. Carpenter, Jeffrey & Graham, Michael & Wolf, Jesse, 2013. "Cognitive ability and strategic sophistication," Games and Economic Behavior, Elsevier, vol. 80(C), pages 115-130.
    4. Eduardo Fé & David Gill & Victoria Prowse, 2022. "Cognitive Skills, Strategic Sophistication, and Life Outcomes," Journal of Political Economy, University of Chicago Press, vol. 130(10), pages 2643-2704.
    5. Feng, Jun & Qin, Xiangdong & Wang, Xiaoyuan, 2021. "A Bayesian cognitive hierarchy model with fixed reasoning levels," Journal of Economic Behavior & Organization, Elsevier, vol. 192(C), pages 704-723.
    6. 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.
    7. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
    Full references (including those not matched with items on IDEAS)

    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. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
    2. Olivier Coibion & Yuriy Gorodnichenko & Saten Kumar & Jane Ryngaert, 2021. "Do You Know that I Know that You Know…? Higher-Order Beliefs in Survey Data," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(3), pages 1387-1446.
    3. Benjamin Patrick Evans & Mikhail Prokopenko, 2021. "Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making," Papers 2106.15844, arXiv.org, revised Mar 2023.
    4. Bayer, Ralph C. & Renou, Ludovic, 2016. "Logical omniscience at the laboratory," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 41-49.
    5. Joshua Zonca & Giorgio Coricelli & Luca Polonio, 2020. "Gaze patterns disclose the link between cognitive reflection and sophistication in strategic interaction," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 15(2), pages 230-245, March.
    6. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    7. Andreas Hula & P Read Montague & Peter Dayan, 2015. "Monte Carlo Planning Method Estimates Planning Horizons during Interactive Social Exchange," PLOS Computational Biology, Public Library of Science, vol. 11(6), pages 1-38, June.
    8. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    9. Itzhak Rasooly, 2022. "Going...going...wrong: a test of the level-k (and cognitive hierarchy) models of bidding behaviour," Economics Series Working Papers 959, University of Oxford, Department of Economics.
    10. Hanjoon Michael Jung, 2020. "Perfect regular equilibrium," International Journal of Economic Theory, The International Society for Economic Theory, vol. 16(4), pages 380-398, December.
    11. Despoina Alempaki & Andrew M. Colman & Felix Kölle & Graham Loomes & Briony D. Pulford, 2022. "Investigating the failure to best respond in experimental games," Experimental Economics, Springer;Economic Science Association, vol. 25(2), pages 656-679, April.
    12. Carlos Alós-Ferrer & Johannes Buckenmaier, 2021. "Cognitive sophistication and deliberation times," Experimental Economics, Springer;Economic Science Association, vol. 24(2), pages 558-592, June.
    13. Melkonian, Tigran A., 1998. "Two essays on reputation effects in economic models," ISU General Staff Papers 1998010108000012873, Iowa State University, Department of Economics.
    14. Itzhak Rasooly, 2021. "Going... going... wrong: a test of the level-k (and cognitive hierarchy) models of bidding behaviour," Papers 2111.05686, arXiv.org.
    15. Mark Schneider, 2018. "A Dual System Model of Risk and Time Preferences," Working Papers 18-18, Chapman University, Economic Science Institute.
    16. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    17. Duffy, Sean & Smith, John, 2014. "Cognitive load in the multi-player prisoner's dilemma game: Are there brains in games?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 51(C), pages 47-56.
    18. Chen, Chia-Ching & Chiu, I-Ming & Smith, John & Yamada, Tetsuji, 2013. "Too smart to be selfish? Measures of cognitive ability, social preferences, and consistency," Journal of Economic Behavior & Organization, Elsevier, vol. 90(C), pages 112-122.
    19. repec:cup:judgdm:v:15:y:2020:i:2:p:230-245 is not listed on IDEAS
    20. Cooper, Kristen & Schneider, Henry & Waldman, Michael, 2021. "Limited rationality and the strategic environment: Further evidence from a pricing game," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 90(C).
    21. Caballero, William N. & Lunday, Brian J. & Deckro, Richard F. & Pachter, Meir N., 2020. "Informing national security policy by modeling adversarial inducement and its governance," Socio-Economic Planning Sciences, Elsevier, vol. 69(C).

    More about this item

    Keywords

    Bayesian; Exploitative; GTO; KuhnPoker; PBE; Poker; Rationality;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:sad:ypaper: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: Maria Amelia Gibbons (email available below). General contact details of provider: https://edirc.repec.org/data/desanar.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.