IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v54y2025i1d10.1007_s00182-025-00942-6.html
   My bibliography  Save this article

The best experienced payoff dynamic in the ultimatum minigame

Author

Listed:
  • Ratul Lahkar

    (Ashoka University)

  • Amarjyoti Mahanta

    (IIT Guwahati)

Abstract

In the ultimatum minigame, proposers can offer either half the total prize or a minimal quantity (e.g., 1). Responders can accept or reject. At the subgame perfect equilibrium, proposers offer the minimal quantity and responders accept. We apply the best experienced payoff (BEP) dynamic to the large population version of this game. The BEP dynamic is generated when players try their strategies a certain number of times and choose the strategy that generates the highest average payoff. We establish conditions under which the subgame perfect equilibrium is stable or unstable. If it is unstable, another stable state can arise where a significant fraction of proposers make high offers.

Suggested Citation

  • Ratul Lahkar & Amarjyoti Mahanta, 2025. "The best experienced payoff dynamic in the ultimatum minigame," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(1), pages 1-30, June.
    • Handle: RePEc:spr:jogath:v:54:y:2025:i:1:d:10.1007_s00182-025-00942-6
    DOI: 10.1007/s00182-025-00942-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-025-00942-6
    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/s00182-025-00942-6?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Sethi, Rajiv, 2000. "Stability of Equilibria in Games with Procedurally Rational Players," Games and Economic Behavior, Elsevier, vol. 32(1), pages 85-104, July.
    2. Güth, Werner & Kocher, Martin G., 2014. "More than thirty years of ultimatum bargaining experiments: Motives, variations, and a survey of the recent literature," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 396-409.
    3. Bergstrom, Theodore C, 1995. "On the Evolution of Altruistic Ethical Rules for Siblings," American Economic Review, American Economic Association, vol. 85(1), pages 58-81, March.
    4. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    5. Arigapudi, Srinivas & Heller, Yuval & Milchtaich, Igal, 2021. "Instability of defection in the prisoner's dilemma under best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 197(C).
    6. Ingela Alger & Jörgen W. Weibull, 2013. "Homo Moralis—Preference Evolution Under Incomplete Information and Assortative Matching," Econometrica, Econometric Society, vol. 81(6), pages 2269-2302, November.
    7. Juan Camilo Cárdenas & César Mantilla & Rajiv Sethi, 2015. "Stable Sampling Equilibrium in Common Pool Resource Games," Games, MDPI, vol. 6(3), pages 1-19, August.
    8. Steffen Andersen & Seda Ertac & Uri Gneezy & Moshe Hoffman & John A. List, 2011. "Stakes Matter in Ultimatum Games," American Economic Review, American Economic Association, vol. 101(7), pages 3427-3439, December.
    9. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2020. "Stability for best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 185(C).
    10. David K. Levine, 1998. "Modeling Altruism and Spitefulness in Experiment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(3), pages 593-622, July.
    11. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
    12. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
    13. Srinivas Arigapudi & Yuval Heller & Igal Milchtaich, 2020. "Instability of Defection in the Prisoner's Dilemma Under Best Experienced Payoff Dynamics," Papers 2005.05779, arXiv.org, revised Jan 2021.
    14. Sethi, Rajiv, 2021. "Stable sampling in repeated games," Journal of Economic Theory, Elsevier, vol. 197(C).
    15. César Mantilla & Rajiv Sethi & Juan Camilo Cárdenas, 2020. "Efficiency and stability of sampling equilibrium in public goods games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(2), pages 355-370, April.
    16. repec:feb:framed:0088 is not listed on IDEAS
    17. Arigapudi, Srinivas & Lahkar, Ratul, 2024. "Emergence of trust in the trust game under best experienced payoff dynamics," Economics Letters, Elsevier, vol. 236(C).
    18. Sutter, Matthias & Kocher, Martin & Strau[ss], Sabine, 2003. "Bargaining under time pressure in an experimental ultimatum game," Economics Letters, Elsevier, vol. 81(3), pages 341-347, December.
    19. Sethi, Rajiv & Somanathan, E, 1996. "The Evolution of Social Norms in Common Property Resource Use," American Economic Review, American Economic Association, vol. 86(4), pages 766-788, September.
    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. Sethi, Rajiv, 2021. "Stable sampling in repeated games," Journal of Economic Theory, Elsevier, vol. 197(C).
    2. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2023. "Strategy sets closed under payoff sampling," Games and Economic Behavior, Elsevier, vol. 138(C), pages 126-142.
    3. Arigapudi, Srinivas & Heller, Yuval, 2025. "Stable mixing in Hawk–Dove Games under best experienced payoff dynamics," Games and Economic Behavior, Elsevier, vol. 151(C), pages 148-161.
    4. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2022. "Stability of strict equilibria in best experienced payoff dynamics: Simple formulas and applications," Journal of Economic Theory, Elsevier, vol. 206(C).
    5. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2023. "Heterogeneous Noise and Stable Miscoordination," Papers 2305.10301, arXiv.org, revised Jan 2025.
    6. Arigapudi, Srinivas & Heller, Yuval & Schreiber, Amnon, 2021. "Sampling Dynamics and Stable Mixing in Hawk–Dove Games," MPRA Paper 108819, University Library of Munich, Germany.
    7. Güth, Werner & Kocher, Martin G., 2014. "More than thirty years of ultimatum bargaining experiments: Motives, variations, and a survey of the recent literature," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 396-409.
    8. Sawa, Ryoji & Wu, Jiabin, 2023. "Statistical inference in evolutionary dynamics," Games and Economic Behavior, Elsevier, vol. 137(C), pages 294-316.
    9. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2021. "Sampling dynamics and stable mixing in hawk-dove games," Papers 2107.08423, arXiv.org, revised Jun 2022.
    10. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    11. Ryoji Sawa, 2022. "Statistical Inference in Evolutionary Dynamics," Working Papers e170, Tokyo Center for Economic Research.
    12. Arigapudi, Srinivas & Lahkar, Ratul, 2024. "Emergence of trust in the trust game under best experienced payoff dynamics," Economics Letters, Elsevier, vol. 236(C).
    13. Aina, Chiara & Battigalli, Pierpaolo & Gamba, Astrid, 2020. "Frustration and anger in the Ultimatum Game: An experiment," Games and Economic Behavior, Elsevier, vol. 122(C), pages 150-167.
    14. Berkemer, Rainer & Starke, Jens & Kawamoto, Atsushi, 2023. "Sampling dynamics applied to the traveler's dilemma reveals non-Nash behavior," Games and Economic Behavior, Elsevier, vol. 142(C), pages 339-356.
    15. Sethi, Rajiv & Somanathan, E., 2003. "Understanding reciprocity," Journal of Economic Behavior & Organization, Elsevier, vol. 50(1), pages 1-27, January.
    16. Arigapudi, Srinivas, 2024. "Evolutionary dynamics in bilingual games," Journal of Economic Dynamics and Control, Elsevier, vol. 165(C).
    17. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2025. "Uniqueness of Inflection Points in Binomial Exceedance Function Compositions," Papers 2507.22211, arXiv.org.
    18. Andrea Essl & Frauke von Bieberstein & Michael Kosfeld & Markus Kröll, 2018. "Sales Performance and Social Preferences," CESifo Working Paper Series 7030, CESifo.
    19. Casal, Sandro & Fallucchi, Francesco & Quercia, Simone, 2019. "The role of morals in three-player ultimatum games," Journal of Economic Psychology, Elsevier, vol. 70(C), pages 67-79.
    20. Bezin, Emeline & Ponthière, Gregory, 2019. "The tragedy of the commons and socialization: Theory and policy," Journal of Environmental Economics and Management, Elsevier, vol. 98(C).

    More about this item

    Keywords

    ;
    ;
    ;

    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:jogath:v:54:y:2025:i:1:d:10.1007_s00182-025-00942-6. 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.