IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v321y2018icp641-653.html
   My bibliography  Save this article

The effect of the stake size on the evolution of fairness

Author

Listed:
  • Zhang, Yanling
  • Chen, Xiaojie
  • Liu, Aizhi
  • Sun, Changyin

Abstract

The stake-size effect on the evolution of fairness has attracted increasing attention from experiments for a long time, yet there has not been a clear and consistent conclusion. Budgetary restrictions make it necessary to construct theoretical models. Here, we investigate the stake-size effect, which has been neglected by almost all previous models, in an evolutionary model of the Ultimatum Game. Our study proceeds in group-structured populations of finite size. For the Moran process and the Wright-Fisher process, we calculate the precise expressions of the average offer and the average demand under weak selection. The increase of the stake size causes populations to be closer to the rational selfish strategy, and we analyze how three key parameters influence the approach speed. We divide all possible stakes according to the evolution of generosity and tolerance, and find that the majority of all possible stakes promote generosity and tolerance for small group numbers. The largest stake promotes tolerance to an extreme. The intermediate stake or the largest stake promotes generosity to an extreme, and we analyze the effect of three key parameters on it. Our results can be used to help design more reasonable and more efficient experiments under restricted budgets.

Suggested Citation

  • Zhang, Yanling & Chen, Xiaojie & Liu, Aizhi & Sun, Changyin, 2018. "The effect of the stake size on the evolution of fairness," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 641-653.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:641-653
    DOI: 10.1016/j.amc.2017.11.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317307920
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.11.013?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 search for a different version of it.

    References listed on IDEAS

    as
    1. repec:feb:framed:0088 is not listed on IDEAS
    2. Roth, Alvin E. & Vesna Prasnikar & Masahiro Okuno-Fujiwara & Shmuel Zamir, 1991. "Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An Experimental Study," American Economic Review, American Economic Association, vol. 81(5), pages 1068-1095, December.
    3. Ofra Amir & David G Rand & Ya'akov Kobi Gal, 2012. "Economic Games on the Internet: The Effect of $1 Stakes," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-4, February.
    4. 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.
    5. 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.
    6. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    7. John List & Todd Cherry, 2000. "Learning to Accept in Ultimatum Games: Evidence from an Experimental Design that Generates Low Offers," Experimental Economics, Springer;Economic Science Association, vol. 3(1), pages 11-29, June.
    8. Straub, Paul G. & Murnighan, J. Keith, 1995. "An experimental investigation of ultimatum games: information, fairness, expectations, and lowest acceptable offers," Journal of Economic Behavior & Organization, Elsevier, vol. 27(3), pages 345-364, August.
    9. Emin Karagözoğlu & Ümit Barış Urhan, 2017. "The Effect of Stake Size in Experimental Bargaining and Distribution Games: A Survey," Group Decision and Negotiation, Springer, vol. 26(2), pages 285-325, March.
    10. Cameron, Lisa A, 1999. "Raising the Stakes in the Ultimatum Game: Experimental Evidence from Indonesia," Economic Inquiry, Western Economic Association International, vol. 37(1), pages 47-59, January.
    11. Hoffman, Elizabeth & McCabe, Kevin A & Smith, Vernon L, 1996. "On Expectations and the Monetary Stakes in Ultimatum Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(3), pages 289-301.
    12. Tompkinson, Paul & Bethwaite, Judy, 1995. "The ultimatum game: raising the stakes," Journal of Economic Behavior & Organization, Elsevier, vol. 27(3), pages 439-451, August.
    13. Hessel Oosterbeek & Randolph Sloof & Gijs van de Kuilen, 2004. "Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis," Experimental Economics, Springer;Economic Science Association, vol. 7(2), pages 171-188, June.
    14. Thaler, Richard H, 1988. "The Ultimatum Game," Journal of Economic Perspectives, American Economic Association, vol. 2(4), pages 195-206, Fall.
    15. Carpenter, Jeffrey & Verhoogen, Eric & Burks, Stephen, 2005. "The effect of stakes in distribution experiments," Economics Letters, Elsevier, vol. 86(3), pages 393-398, March.
    16. Forsythe Robert & Horowitz Joel L. & Savin N. E. & Sefton Martin, 1994. "Fairness in Simple Bargaining Experiments," Games and Economic Behavior, Elsevier, vol. 6(3), pages 347-369, May.
    17. 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.
    18. Robert Slonim & Alvin E. Roth, 1998. "Learning in High Stakes Ultimatum Games: An Experiment in the Slovak Republic," Econometrica, Econometric Society, vol. 66(3), pages 569-596, May.
    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. Larney, Andrea & Rotella, Amanda & Barclay, Pat, 2019. "Stake size effects in ultimatum game and dictator game offers: A meta-analysis," Organizational Behavior and Human Decision Processes, Elsevier, vol. 151(C), pages 61-72.
    2. Emin Karagözoğlu & Ümit Barış Urhan, 2017. "The Effect of Stake Size in Experimental Bargaining and Distribution Games: A Survey," Group Decision and Negotiation, Springer, vol. 26(2), pages 285-325, March.
    3. Murnighan, J. Keith & Wang, Long, 2016. "The social world as an experimental game," Organizational Behavior and Human Decision Processes, Elsevier, vol. 136(C), pages 80-94.
    4. Julie Novakova & Jaroslav Flegr, 2013. "How Much Is Our Fairness Worth? The Effect of Raising Stakes on Offers by Proposers and Minimum Acceptable Offers in Dictator and Ultimatum Games," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-9, April.
    5. 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.
    6. Cochard, François & Le Gallo, Julie & Georgantzis, Nikolaos & Tisserand, Jean-Christian, 2021. "Social preferences across different populations: Meta-analyses on the ultimatum game and dictator game," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 90(C).
    7. Ofra Amir & David G Rand & Ya'akov Kobi Gal, 2012. "Economic Games on the Internet: The Effect of $1 Stakes," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-4, February.
    8. Irlenbusch, Bernd, 2004. "Relying on a man's word?: An experimental study on non-binding contracts," International Review of Law and Economics, Elsevier, vol. 24(3), pages 299-332, September.
    9. Charness, Gary & Gneezy, Uri & Kuhn, Michael A., 2013. "Experimental methods: Extra-laboratory experiments-extending the reach of experimental economics," Journal of Economic Behavior & Organization, Elsevier, vol. 91(C), pages 93-100.
    10. Hasan, Hamid & Ejaz, Nauman, 2013. "Testing for Differences across Genders: A Replication of Ultimatum Game at International Islamic University, Islamabad," MPRA Paper 44923, University Library of Munich, Germany.
    11. Gagen, Michael, 2013. "Isomorphic Strategy Spaces in Game Theory," MPRA Paper 46176, University Library of Munich, Germany.
    12. Gizatulina, Alia & Gorelkina, Olga, 2021. "Selling “Money” on eBay: A field study of surplus division," Journal of Economic Behavior & Organization, Elsevier, vol. 181(C), pages 19-38.
    13. Damon Tomlin, 2015. "Rational Constraints and the Evolution of Fairness in the Ultimatum Game," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-17, July.
    14. Eckel, Catherine & Gintis, Herbert, 2010. "Blaming the messenger: Notes on the current state of experimental economics," Journal of Economic Behavior & Organization, Elsevier, vol. 73(1), pages 109-119, January.
    15. Akdeniz, Aslıhan & van Veelen, Matthijs, 2023. "Evolution and the ultimatum game," Games and Economic Behavior, Elsevier, vol. 142(C), pages 570-612.
    16. Gautam Gupta, 2019. "Experiments in Economics: A Survey," Studies in Microeconomics, , vol. 7(1), pages 89-109, June.
    17. Hamid Hasan & Nauman Ejaz, 2018. "Testing for Differences Across Genders: Evidence from Ultimatum Game," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 57(3), pages 333-349.
    18. James C. Cox & Vjollca Sadiraj, 2018. "Incentives," Experimental Economics Center Working Paper Series 2018-01, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
    19. Matteo M. Galizzi & Daniel Navarro-Martinez, 2019. "On the External Validity of Social Preference Games: A Systematic Lab-Field Study," Management Science, INFORMS, vol. 65(3), pages 976-1002, March.
    20. 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.

    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:eee:apmaco:v:321:y:2018:i:c:p:641-653. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.