IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v145y2022icp1-21.html
   My bibliography  Save this article

Evolution of cooperation with respect to fixation probabilities in multi-player games with random payoffs

Author

Listed:
  • Kroumi, Dhaker
  • Martin, Éloi
  • Lessard, Sabin

Abstract

We study the effect of variability in payoffs on the evolution of cooperation (C) against defection (D) in multi-player games in a finite well-mixed population. We show that an increase in the covariance between any two payoffs to D, or a decrease in the covariance between any two payoffs to C, increases the probability of ultimate fixation of C when represented once, and decreases the corresponding fixation probability for D. This is also the case with an increase in the covariance between any payoff to C and any payoff to D if and only if the sum of the numbers of C-players in the group associated with these payoffs is large enough compared to the group size. In classical social dilemmas with random cost and benefit for cooperation, the evolution of C is more likely to occur if the variances of the cost and benefit, as well as the group size, are small, while the covariance between cost and benefit is large.

Suggested Citation

  • Kroumi, Dhaker & Martin, Éloi & Lessard, Sabin, 2022. "Evolution of cooperation with respect to fixation probabilities in multi-player games with random payoffs," Theoretical Population Biology, Elsevier, vol. 145(C), pages 1-21.
    • Handle: RePEc:eee:thpobi:v:145:y:2022:i:c:p:1-21
    DOI: 10.1016/j.tpb.2022.02.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580922000120
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2022.02.001?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. Li, Cong & Lessard, Sabin, 2020. "Randomized matrix games in a finite population: Effect of stochastic fluctuations in the payoffs on the evolution of cooperation," Theoretical Population Biology, Elsevier, vol. 134(C), pages 77-91.
    2. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    3. Dhaker Kroumi & Sabin Lessard, 2015. "Strong Migration Limit for Games in Structured Populations: Applications to Dominance Hierarchy and Set Structure," Games, MDPI, vol. 6(3), pages 1-29, September.
    4. Kroumi, Dhaker & Lessard, Sabin, 2015. "Evolution of cooperation in a multidimensional phenotype space," Theoretical Population Biology, Elsevier, vol. 102(C), pages 60-75.
    5. 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.
    6. Dhaker Kroumi & Éloi Martin & Cong Li & Sabin Lessard, 2021. "Effect of Variability in Payoffs on Conditions for the Evolution of Cooperation in a Small Population," Dynamic Games and Applications, Springer, vol. 11(4), pages 803-834, December.
    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. Brian McLoone & Wai-Tong Louis Fan & Adam Pham & Rory Smead & Laurence Loewe, 2018. "Stochasticity, Selection, and the Evolution of Cooperation in a Two-Level Moran Model of the Snowdrift Game," Complexity, Hindawi, vol. 2018, pages 1-14, February.
    2. Dai, Darong, 2012. "On the Existence of Pareto Optimal Endogenous Matching," MPRA Paper 43125, University Library of Munich, Germany.
    3. 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.
    4. Shun Kurokawa & Joe Yuichiro Wakano & Yasuo Ihara, 2018. "Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions," Games, MDPI, vol. 9(4), pages 1-24, December.
    5. Lessard, Sabin & Li, Cong & Zheng, Xiu-Deng & Tao, Yi, 2021. "Inclusive fitness and Hamilton’s rule in a stochastic environment," Theoretical Population Biology, Elsevier, vol. 142(C), pages 91-99.
    6. Zhang, Qinchunxue & Shu, Lan & Jiang, Bichuan, 2023. "Moran process in evolutionary game dynamics with interval payoffs and its application," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    7. Dai, Darong, 2012. "On the Existence and Stability of Pareto Optimal Endogenous Matching with Fairness," MPRA Paper 40560, University Library of Munich, Germany.
    8. Dhaker Kroumi & Éloi Martin & Cong Li & Sabin Lessard, 2021. "Effect of Variability in Payoffs on Conditions for the Evolution of Cooperation in a Small Population," Dynamic Games and Applications, Springer, vol. 11(4), pages 803-834, December.
    9. Gokhale, Chaitanya S. & Hauert, Christoph, 2016. "Eco-evolutionary dynamics of social dilemmas," Theoretical Population Biology, Elsevier, vol. 111(C), pages 28-42.
    10. Chen, Yunong & Belmonte, Andrew & Griffin, Christopher, 2021. "Imitation of success leads to cost of living mediated fairness in the Ultimatum Game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    11. Sergio Currarini & Carmen Marchiori & Alessandro Tavoni, 2016. "Network Economics and the Environment: Insights and Perspectives," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(1), pages 159-189, September.
    12. Siegfried Berninghaus & Hans Haller & Alexander Outkin, 2006. "Neural networks and contagion," Revue d'économie industrielle, De Boeck Université, vol. 0(2), pages 11-11.
    13. Christian Hilbe & Moshe Hoffman & Martin A. Nowak, 2015. "Cooperate without Looking in a Non-Repeated Game," Games, MDPI, vol. 6(4), pages 1-15, September.
    14. Takuya Sekiguchi, 2023. "Fixation Probabilities of Strategies for Trimatrix Games and Their Applications to Triadic Conflict," Dynamic Games and Applications, Springer, vol. 13(3), pages 1005-1033, September.
    15. Te Wu & Feng Fu & Long Wang, 2011. "Moving Away from Nasty Encounters Enhances Cooperation in Ecological Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 6(11), pages 1-7, November.
    16. Konrad, Kai A. & Morath, Florian, 2020. "The Volunteer’s Dilemma in Finite Populations," CEPR Discussion Papers 15536, C.E.P.R. Discussion Papers.
    17. Basov, S., 2001. "An Evolutionary Model of Reciprocity," Department of Economics - Working Papers Series 812, The University of Melbourne.
    18. M. Kleshnina & K. Kaveh & K. Chatterjee, 2020. "The role of behavioural plasticity in finite vs infinite populations," Papers 2009.13160, arXiv.org.
    19. Floriana Gargiulo & José J Ramasco, 2012. "Influence of Opinion Dynamics on the Evolution of Games," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-7, November.
    20. Jehiel, Philippe, 1998. "Learning to Play Limited Forecast Equilibria," Games and Economic Behavior, Elsevier, vol. 22(2), pages 274-298, February.

    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:thpobi:v:145:y:2022:i:c:p:1-21. 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/intelligence .

    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.