IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v10y2019i1p11-d208066.html
   My bibliography  Save this article

Evolution of Cooperation with Peer Punishment under Prospect Theory

Author

Listed:
  • Satoshi Uchida

    (Research Center for Ethi-Culture Studies, RINRI Institute, Tokyo 102-0094, Japan)

  • Hitoshi Yamamoto

    (Faculty of Business Administration, Rissho University, Tokyo 141-8602, Japan)

  • Isamu Okada

    (Faculty of Business Administration, Soka University, Tokyo 192-8577, Japan)

  • Tatsuya Sasaki

    (F-Power Inc., Tokyo 106-6119, Japan
    Faculty of Mathematics, University of Vienna, 1090 Vienna, Austria)

Abstract

Social dilemmas are among the most puzzling issues in the biological and social sciences. Extensive theoretical efforts have been made in various realms such as economics, biology, mathematics, and even physics to figure out solution mechanisms to the dilemma in recent decades. Although punishment is thought to be a key mechanism, evolutionary game theory has revealed that the simplest form of punishment called peer punishment is useless to solve the dilemma, since peer punishment itself is costly. In the literature, more complex types of punishment, such as pool punishment or institutional punishment, have been exploited as effective mechanisms. So far, mechanisms that enable peer punishment to function as a solution to the social dilemma remain unclear. In this paper, we propose a theoretical way for peer punishment to work as a solution mechanism for the dilemma by incorporating prospect theory into evolutionary game theory. Prospect theory models human beings as agents that estimate small probabilities and loss of profit as greater than they actually are; thus, those agents feel that punishments are more frequent and harsher than they really are. We show that this kind of cognitive distortion makes players decide to cooperate to avoid being punished and that the cooperative state achieved by this mechanism is globally stable as well as evolutionarily stable in a wide range of parameter values.

Suggested Citation

  • Satoshi Uchida & Hitoshi Yamamoto & Isamu Okada & Tatsuya Sasaki, 2019. "Evolution of Cooperation with Peer Punishment under Prospect Theory," Games, MDPI, vol. 10(1), pages 1-13, February.
    • Handle: RePEc:gam:jgames:v:10:y:2019:i:1:p:11-:d:208066
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/10/1/11/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/10/1/11/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Axelrod, Robert, 1986. "An Evolutionary Approach to Norms," American Political Science Review, Cambridge University Press, vol. 80(4), pages 1095-1111, December.
    2. Amos Tversky & Daniel Kahneman, 1991. "Loss Aversion in Riskless Choice: A Reference-Dependent Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 1039-1061.
    3. Boyu Zhang & Cong Li & Hannelore Silva & Peter Bednarik & Karl Sigmund, 2014. "The evolution of sanctioning institutions: an experimental approach to the social contract," Experimental Economics, Springer;Economic Science Association, vol. 17(2), pages 285-303, June.
    4. Michael Kosfeld & Akira Okada & Arno Riedl, 2009. "Institution Formation in Public Goods Games," American Economic Review, American Economic Association, vol. 99(4), pages 1335-1355, September.
    5. Ernst Fehr & Simon Gächter, 2002. "Altruistic punishment in humans," Nature, Nature, vol. 415(6868), pages 137-140, January.
    6. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    7. Tatsuya Sasaki & Isamu Okada & Satoshi Uchida & Xiaojie Chen, 2015. "Commitment to Cooperation and Peer Punishment: Its Evolution," Games, MDPI, vol. 6(4), pages 1-14, November.
    8. Casari, Marco & Luini, Luigi, 2009. "Cooperation under alternative punishment institutions: An experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 273-282, August.
    9. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    10. Andreoni, James & Gee, Laura K., 2012. "Gun for hire: Delegated enforcement and peer punishment in public goods provision," Journal of Public Economics, Elsevier, vol. 96(11), pages 1036-1046.
    11. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    12. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    13. David G. Rand & Martin A. Nowak, 2011. "The evolution of antisocial punishment in optional public goods games," Nature Communications, Nature, vol. 2(1), pages 1-7, September.
    14. Nikiforakis, Nikos, 2008. "Punishment and counter-punishment in public good games: Can we really govern ourselves," Journal of Public Economics, Elsevier, vol. 92(1-2), pages 91-112, February.
    15. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    16. Isamu Okada & Hitoshi Yamamoto & Fujio Toriumi & Tatsuya Sasaki, 2015. "The Effect of Incentives and Meta-incentives on the Evolution of Cooperation," PLOS Computational Biology, Public Library of Science, vol. 11(5), pages 1-17, May.
    17. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    18. Karl Sigmund & Hannelore De Silva & Arne Traulsen & Christoph Hauert, 2010. "Social learning promotes institutions for governing the commons," Nature, Nature, vol. 466(7308), pages 861-863, August.
    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. Isamu Okada, 2020. "A Review of Theoretical Studies on Indirect Reciprocity," Games, MDPI, vol. 11(3), pages 1-17, July.
    2. Jieli Hu & Tieli Wang, 2023. "Strategies of Participants in the Carbon Trading Market—An Analysis Based on the Evolutionary Game," Sustainability, MDPI, vol. 15(14), pages 1-24, July.

    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. Satoshi Uchida & Tatsuya Sasaki & Hitoshi Yamamoto & Isamu Okada, 2024. "Evolution of “Pay-It-Forward” in the Presence of the Temptation to Free-Ride," Games, MDPI, vol. 15(3), pages 1-15, April.
    2. Tatsuya Sasaki & Isamu Okada & Satoshi Uchida & Xiaojie Chen, 2015. "Commitment to Cooperation and Peer Punishment: Its Evolution," Games, MDPI, vol. 6(4), pages 1-14, November.
    3. Christiane Reif & Dirk Rübbelke & Andreas Löschel, 2017. "Improving Voluntary Public Good Provision Through a Non-governmental, Endogenous Matching Mechanism: Experimental Evidence," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 67(3), pages 559-589, July.
    4. Boyu Zhang & Cong Li & Hannelore Silva & Peter Bednarik & Karl Sigmund, 2014. "The evolution of sanctioning institutions: an experimental approach to the social contract," Experimental Economics, Springer;Economic Science Association, vol. 17(2), pages 285-303, June.
    5. Cobo-Reyes, Ramón & Katz, Gabriel & Meraglia, Simone, 2019. "Endogenous sanctioning institutions and migration patterns: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 158(C), pages 575-606.
    6. Dirk Engelmann & Nikos Nikiforakis, 2015. "In the long-run we are all dead: on the benefits of peer punishment in rich environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(3), pages 561-577, October.
    7. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics.
    8. KAMEI Kenju, 2022. "Self-regulatory Resources and Institutional Formation: A first experimental test," Discussion papers 22084, Research Institute of Economy, Trade and Industry (RIETI).
    9. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    10. Eddie Dekel & Barton L. Lipman, 2010. "How (Not) to Do Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 257-282, September.
    11. Shaw, W. Douglass & Woodward, Richard T., 2008. "Why environmental and resource economists should care about non-expected utility models," Resource and Energy Economics, Elsevier, vol. 30(1), pages 66-89, January.
    12. Kenju Kamei & Smriti Sharma & Matthew J. Walker, 2023. "Collective Sanction Enforcement: New Experimental Evidence from Two Societies," Keio-IES Discussion Paper Series 2023-014, Institute for Economics Studies, Keio University.
    13. Kamei, Kenju, 2024. "Self-regulatory resources and institutional formation: An experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 222(C), pages 354-374.
    14. Haven, Emmanuel & Khrennikova, Polina, 2018. "A quantum-probabilistic paradigm: Non-consequential reasoning and state dependence in investment choice," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 186-197.
    15. Isamu Okada, 2020. "A Review of Theoretical Studies on Indirect Reciprocity," Games, MDPI, vol. 11(3), pages 1-17, July.
    16. Philipp Schreck & Dominik Aaken & Karl Homann, 2020. "“There’s Life in the Old Dog Yet”: The Homo economicus model and its value for behavioral ethics," Journal of Business Economics, Springer, vol. 90(3), pages 401-425, April.
    17. Yamamoto, Hitoshi & Okada, Isamu, 2016. "How to keep punishment to maintain cooperation: Introducing social vaccine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 526-536.
    18. Andreoni, James & Gee, Laura K., 2012. "Gun for hire: Delegated enforcement and peer punishment in public goods provision," Journal of Public Economics, Elsevier, vol. 96(11), pages 1036-1046.
    19. Enrico Diecidue & Peter Wakker & Marcel Zeelenberg, 2007. "Eliciting decision weights by adapting de Finetti’s betting-odds method to prospect theory," Journal of Risk and Uncertainty, Springer, vol. 34(3), pages 179-199, June.
    20. Basieva, Irina & Khrennikova, Polina & Pothos, Emmanuel M. & Asano, Masanari & Khrennikov, Andrei, 2018. "Quantum-like model of subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 150-162.

    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:gam:jgames:v:10:y:2019:i:1:p:11-:d:208066. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.