IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0180754.html
   My bibliography  Save this article

From rationality to cooperativeness: The totally mixed Nash equilibrium in Markov strategies in the iterated Prisoner’s Dilemma

Author

Listed:
  • Ivan S Menshikov
  • Alexsandr V Shklover
  • Tatiana S Babkina
  • Mikhail G Myagkov

Abstract

In this research, the social behavior of the participants in a Prisoner's Dilemma laboratory game is explained on the basis of the quantal response equilibrium concept and the representation of the game in Markov strategies. In previous research, we demonstrated that social interaction during the experiment has a positive influence on cooperation, trust, and gratefulness. This research shows that the quantal response equilibrium concept agrees only with the results of experiments on cooperation in Prisoner’s Dilemma prior to social interaction. However, quantal response equilibrium does not explain of participants’ behavior after social interaction. As an alternative theoretical approach, an examination was conducted of iterated Prisoner's Dilemma game in Markov strategies. We built a totally mixed Nash equilibrium in this game; the equilibrium agrees with the results of the experiments both before and after social interaction.

Suggested Citation

  • Ivan S Menshikov & Alexsandr V Shklover & Tatiana S Babkina & Mikhail G Myagkov, 2017. "From rationality to cooperativeness: The totally mixed Nash equilibrium in Markov strategies in the iterated Prisoner’s Dilemma," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-17, November.
    • Handle: RePEc:plo:pone00:0180754
    DOI: 10.1371/journal.pone.0180754
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0180754
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0180754&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0180754?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
    ---><---

    References listed on IDEAS

    as
    1. McKelvey, Richard D. & Palfrey, Thomas R. & Weber, Roberto A., 2000. "The effects of payoff magnitude and heterogeneity on behavior in 2 x 2 games with unique mixed strategy equilibria," Journal of Economic Behavior & Organization, Elsevier, vol. 42(4), pages 523-548, August.
    2. Selten, Reinhard & Stoecker, Rolf, 1986. "End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 47-70, March.
    3. Cheng-Yi Xia & Xiao-Kun Meng & Zhen Wang, 2015. "Heterogeneous Coupling between Interdependent Lattices Promotes the Cooperation in the Prisoner’s Dilemma Game," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-13, June.
    4. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    5. Jacob Goeree & Charles Holt & Thomas Palfrey, 2005. "Regular Quantal Response Equilibrium," Experimental Economics, Springer;Economic Science Association, vol. 8(4), pages 347-367, December.
    6. Tumennasan, Norovsambuu, 2013. "To err is human: Implementation in quantal response equilibria," Games and Economic Behavior, Elsevier, vol. 77(1), pages 138-152.
    7. Syngjoo Choi & Douglas Gale & Shachar Kariv, 2012. "Social learning in networks: a Quantal Response Equilibrium analysis of experimental data," Review of Economic Design, Springer;Society for Economic Design, vol. 16(2), pages 135-157, September.
    8. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    9. Goeree, Jacob K. & Holt, Charles A. & Palfrey, Thomas R., 2002. "Quantal Response Equilibrium and Overbidding in Private-Value Auctions," Journal of Economic Theory, Elsevier, vol. 104(1), pages 247-272, May.
    10. Abagail McWilliams & Donald S. Siegel & Patrick M. Wright, 2006. "Corporate Social Responsibility: Strategic Implications," Journal of Management Studies, Wiley Blackwell, vol. 43(1), pages 1-18, January.
    11. Babkina, Tatiana & Myagkov, Mikhail & Lukinova, Evgeniya & Peshkovskaya, Anastasiya & Menshikova, Olga & Berkman, Elliot T., 2016. "Choice of the Group Increases Intra-Cooperation," MPRA Paper 77758, University Library of Munich, Germany.
    12. Richard McKelvey & Thomas Palfrey, 2015. "Erratum to: Quantal response equilibria for extensive form games," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 762-763, December.
    13. Roberts, Robin W., 1992. "Determinants of corporate social responsibility disclosure: An application of stakeholder theory," Accounting, Organizations and Society, Elsevier, vol. 17(6), pages 595-612, August.
    14. Goeree, Jacob K. & Holt, Charles A., 2000. "Asymmetric inequality aversion and noisy behavior in alternating-offer bargaining games," European Economic Review, Elsevier, vol. 44(4-6), pages 1079-1089, May.
    15. Englmaier, Florian & Wambach, Achim, 2010. "Optimal incentive contracts under inequity aversion," Games and Economic Behavior, Elsevier, vol. 69(2), pages 312-328, July.
    16. Alvin E. Roth, 1977. "Individual Rationality and Nash's Solution to the Bargaining Problem," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 64-65, February.
    17. Karandikar, Rajeeva & Mookherjee, Dilip & Ray, Debraj & Vega-Redondo, Fernando, 1998. "Evolving Aspirations and Cooperation," Journal of Economic Theory, Elsevier, vol. 80(2), pages 292-331, June.
    18. Elliot T Berkman & Evgeniya Lukinova & Ivan Menshikov & Mikhail Myagkov, 2015. "Sociality as a Natural Mechanism of Public Goods Provision," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-18, March.
    19. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 9-41, June.
    20. Zhi-Qin Ma & Cheng-Yi Xia & Shi-Wen Sun & Li Wang & Huai-Bin Wang & Juan Wang, 2011. "Heterogeneous Link Weight Promotes The Cooperation In Spatial Prisoner'S Dilemma," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(11), pages 1257-1268.
    21. Qian Zhuang & Zengru Di & Jinshan Wu, 2014. "Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-16, August.
    22. Yali Dong & Cong Li & Yi Tao & Boyu Zhang, 2015. "Evolution of Conformity in Social Dilemmas," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-12, September.
    23. Anastasia G Peshkovskaya & Tatiana S Babkina & Mikhail G Myagkov & Ivan A Kulikov & Ksenia V Ekshova & Kyle Harriff, 2017. "The socialization effect on decision making in the Prisoner's Dilemma game: An eye-tracking study," PLOS ONE, Public Library of Science, vol. 12(4), pages 1-15, April.
    24. Boyu Zhang, 2013. "Social Learning in the Ultimatum Game," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-6, September.
    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. Tatiana Kozitsina & Alexander Chaban & Evgeniya Lukinova & Mikhail Myagkov, 2020. "The effect of monetary incentives on sociality induced cooperation," Papers 2011.07597, arXiv.org.

    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. Zhang, Boyu & Hofbauer, Josef, 2016. "Quantal response methods for equilibrium selection in 2×2 coordination games," Games and Economic Behavior, Elsevier, vol. 97(C), pages 19-31.
    2. Philip A. Haile & Ali Hortaçsu & Grigory Kosenok, 2008. "On the Empirical Content of Quantal Response Equilibrium," American Economic Review, American Economic Association, vol. 98(1), pages 180-200, March.
    3. Zhang, Boyu, 2016. "Quantal response methods for equilibrium selection in normal form games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 113-123.
    4. Alcocer, Christian Diego & Jeitschko, Thomas D. & Shupp, Robert, 2020. "Naive and sophisticated mixing: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 170(C), pages 157-173.
    5. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2002. "The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies," Southern Economic Journal, John Wiley & Sons, vol. 69(1), pages 21-47, July.
    6. He, Simin & Wu, Jiabin, 2020. "Compromise and coordination: An experimental study," Games and Economic Behavior, Elsevier, vol. 119(C), pages 216-233.
    7. Kendall, Ryan, 2021. "Sequential competitions with a middle-mover advantage," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 91(C).
    8. Stefan Kohler & European University Institute, 2006. "Inequality Aversion and Stochastic Decision-making: Experimental Evidence from Zimbabwean Villages after Land Reform," Economics Series Working Papers GPRG-WPS-061, University of Oxford, Department of Economics.
    9. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    10. 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.
    11. Yi, Kang-Oh, 2005. "Quantal-response equilibrium models of the ultimatum bargaining game," Games and Economic Behavior, Elsevier, vol. 51(2), pages 324-348, May.
    12. Edward Cartwright & Anna Stepanova, 2017. "Efficiency in a forced contribution threshold public good game," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1163-1191, November.
    13. Xiaochuan Huang & Takehito Masuda & Yoshitaka Okano & Tatsuyoshi Saijo, 2014. "Cooperation among behaviorally heterogeneous players in social dilemma with stay or leave decisions," Working Papers SDES-2014-7, Kochi University of Technology, School of Economics and Management, revised Feb 2015.
    14. Ralph-C Bayer & Changxia Ke, 2010. "Rockets and Feathers in the Laboratory," School of Economics and Public Policy Working Papers 2010-20, University of Adelaide, School of Economics and Public Policy.
    15. Christoph Kuzmics & Daniel Rodenburger, 2020. "A case of evolutionarily stable attainable equilibrium in the laboratory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 685-721, October.
    16. Eva I. Hoppe & Patrick W. Schmitz, 2013. "Contracting under Incomplete Information and Social Preferences: An Experimental Study," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(4), pages 1516-1544.
    17. Andrew M. Davis & Elena Katok & Anthony M. Kwasnica, 2014. "Should Sellers Prefer Auctions? A Laboratory Comparison of Auctions and Sequential Mechanisms," Management Science, INFORMS, vol. 60(4), pages 990-1008, April.
    18. Breitmoser, Yves & Schweighofer-Kodritsch, Sebastian, 2019. "Obviousness Around the Clock," Rationality and Competition Discussion Paper Series 151, CRC TRR 190 Rationality and Competition.
    19. Herrera, Helios & Llorente-Saguer, Aniol & McMurray, Joseph C., 2019. "Information aggregation and turnout in proportional representation: A laboratory experiment," Journal of Public Economics, Elsevier, vol. 179(C).
    20. Breitmoser, Yves & Tan, Jonathan H.W. & Zizzo, Daniel John, 2014. "On the beliefs off the path: Equilibrium refinement due to quantal response and level-k," Games and Economic Behavior, Elsevier, vol. 86(C), pages 102-125.

    More about this item

    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:plo:pone00:0180754. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.