IDEAS home Printed from https://ideas.repec.org/p/tse/iastwp/32651.html
   My bibliography  Save this paper

Group size effects in social evolution

Author

Listed:
  • Nöldeke, Georg
  • Peña, Jorge

Abstract

How the size of social groups affects the evolution of cooperative behaviors is a classic question in evolutionary biology. Here we investigate group size effects in evolutionary games in which individuals choose whether to cooperate or defect. We find that increasing the group size decreases the proportion of cooperators at both stable and unstable rest points of the replicator dynamics. This implies that larger group sizes can have negative effects (by reducing the amount of cooperation at stable polymorphisms) and positive effects (by enlarging the basin of attraction of more cooperative outcomes) on the evolution of cooperation. These two effects can be simultaneously present in games whose evolutionary dynamics features both stable and unstable rest points, such as public goods games with participation thresholds. Our theory recovers and generalizes previous results and is applicable to a broad variety of social interactions that have been studied in the literature.

Suggested Citation

  • Nöldeke, Georg & Peña, Jorge, 2018. "Group size effects in social evolution," IAST Working Papers 18-75, Institute for Advanced Study in Toulouse (IAST).
    • Handle: RePEc:tse:iastwp:32651
    as

    Download full text from publisher

    File URL: http://iast.fr/pub/32651
    Download Restriction: no
    File URL: https://www.iast.fr/sites/default/files/IAST/wp/wp_iast75.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Palfrey, Thomas R. & Rosenthal, Howard, 1984. "Participation and the provision of discrete public goods: a strategic analysis," Journal of Public Economics, Elsevier, vol. 24(2), pages 171-193, July.
    2. Chaitanya Gokhale & Arne Traulsen, 2014. "Evolutionary Multiplayer Games," Dynamic Games and Applications, Springer, vol. 4(4), pages 468-488, December.
    3. De Jaegher, Kris, 2017. "Harsh environments and the evolution of multi-player cooperation," Theoretical Population Biology, Elsevier, vol. 113(C), pages 1-12.
    4. Dixit, Avinash & Olson, Mancur, 2000. "Does voluntary participation undermine the Coase Theorem?," Journal of Public Economics, Elsevier, vol. 76(3), pages 309-335, June.
    5. Cheikbossian, Guillaume & Fayat, Romain, 2018. "Group size, collective action and complementarities in efforts," Economics Letters, Elsevier, vol. 168(C), pages 77-81.
    6. Guillaume Cheikbossian & Romain Fayat, 2018. "Group size, collective action and complementarities in efforts," Post-Print hal-01945433, HAL.
    7. R. Mark Isaac & James M. Walker, 1988. "Group Size Effects in Public Goods Provision: The Voluntary Contributions Mechanism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(1), pages 179-199.
    8. Andreas Diekmann, 1985. "Volunteer's Dilemma," Journal of Conflict Resolution, Peace Science Society (International), vol. 29(4), pages 605-610, December.
    9. Goeree, Jacob K. & Holt, Charles A., 2005. "An Explanation of Anomalous Behavior in Models of Political Participation," American Political Science Review, Cambridge University Press, vol. 99(2), pages 201-213, May.
    10. Van Cleve, Jeremy & Lehmann, Laurent, 2013. "Stochastic stability and the evolution of coordination in spatially structured populations," Theoretical Population Biology, Elsevier, vol. 89(C), pages 75-87.
    11. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
    12. Marco Archetti, 2018. "How to Analyze Models of Nonlinear Public Goods," Games, MDPI, vol. 9(2), pages 1-15, April.
    13. Jeroen Weesie & Axel Franzen, 1998. "Cost Sharing in a Volunteer's Dilemma," Journal of Conflict Resolution, Peace Science Society (International), vol. 42(5), pages 600-618, October.
    14. Paul B. Rainey & Katrina Rainey, 2003. "Evolution of cooperation and conflict in experimental bacterial populations," Nature, Nature, vol. 425(6953), pages 72-74, September.
    15. Esteban, Joan & Ray, Debraj, 2001. "Collective Action and the Group Size Paradox," American Political Science Review, Cambridge University Press, vol. 95(3), pages 663-672, September.
    16. Van Cleve, Jeremy, 2015. "Social evolution and genetic interactions in the short and long term," Theoretical Population Biology, Elsevier, vol. 103(C), pages 2-26.
    17. Isaac, R. Mark & Walker, James M. & Williams, Arlington W., 1994. "Group size and the voluntary provision of public goods : Experimental evidence utilizing large groups," Journal of Public Economics, Elsevier, vol. 54(1), pages 1-36, May.
    18. Guy Beauchamp, 2008. "What is the magnitude of the group-size effect on vigilance?," Behavioral Ecology, International Society for Behavioral Ecology, vol. 19(6), pages 1361-1368.
    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. Nöldeke, Georg & Peña, Jorge, 2020. "Group size and collective action in a binary contribution game," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 42-51.
    2. Jorge Peña & Georg Nöldeke, 2023. "Cooperative Dilemmas with Binary Actions and Multiple Players," Dynamic Games and Applications, Springer, vol. 13(4), pages 1156-1193, December.
    3. D. Timothy Bishop & Mark Broom & Richard Southwell, 2020. "Chris Cannings: A Life in Games," Dynamic Games and Applications, Springer, vol. 10(3), pages 591-617, September.
    4. Wang, Mengyao & Pan, Qiuhui & He, Mingfeng, 2020. "Individuals with the firm heart are conducive to cooperation in social dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Jann, Ole & Schottmüller, Christoph, 2021. "Regime change games with an active defender," Games and Economic Behavior, Elsevier, vol. 129(C), pages 96-113.
    6. Marta C. Couto & Saptarshi Pal, 2023. "Introspection Dynamics in Asymmetric Multiplayer Games," Dynamic Games and Applications, Springer, vol. 13(4), pages 1256-1285, December.

    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. Jorge Peña & Georg Nöldeke, 2023. "Cooperative Dilemmas with Binary Actions and Multiple Players," Dynamic Games and Applications, Springer, vol. 13(4), pages 1156-1193, December.
    2. Peña, Jorge & Heifetz, Aviad & Nöldeke, Georg, 2023. "The shirker’s dilemma and the prospect of cooperation in large groups," IAST Working Papers 23-152, Institute for Advanced Study in Toulouse (IAST), revised Oct 2023.
    3. Nöldeke, Georg & Peña, Jorge, 2020. "Group size and collective action in a binary contribution game," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 42-51.
    4. Pol Campos-Mercade, 2020. "When are groups less moral than individuals?," CEBI working paper series 20-26, University of Copenhagen. Department of Economics. The Center for Economic Behavior and Inequality (CEBI).
    5. Hong, Fuhai & Lim, Wooyoung, 2016. "Voluntary participation in public goods provision with Coasian bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 126(PA), pages 102-119.
    6. Campos-Mercade, Pol, 2022. "When are groups less moral than individuals?," Games and Economic Behavior, Elsevier, vol. 134(C), pages 20-36.
    7. Martin Kolmar & Hendrik Rommeswinkel, 2020. "Group size and group success in conflicts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 777-822, December.
    8. Paul Pecorino, 2015. "Olson’s Logic of Collective Action at fifty," Public Choice, Springer, vol. 162(3), pages 243-262, March.
    9. Friehe, Tim & Tabbach, Avraham, 2018. "A comparison of simple action-based and outcome-based policies for emergency-like situations," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 22-34.
    10. Martimort, David, 2019. ""When Olson Meets Dahl": From Inefficient Groups Formation to Inefficient Policy-Making," CEPR Discussion Papers 13843, C.E.P.R. Discussion Papers.
    11. Dripto Bakshi & Indraneel Dasgupta, 2021. "A Subscription vs. Appropriation Framework for Natural Resource Conflicts," World Scientific Book Chapters, in: Anil Markandya & Dirk Rübbelke (ed.), CLIMATE AND DEVELOPMENT, chapter 9, pages 257-307, World Scientific Publishing Co. Pte. Ltd..
    12. Cheikbossian, Guillaume, 2021. "Evolutionarily stable in-group altruism in intergroup conflict over (local) public goods," Games and Economic Behavior, Elsevier, vol. 127(C), pages 206-226.
    13. Sung Ha Hwang, 2009. "Larger groups may alleviate collective action problems," UMASS Amherst Economics Working Papers 2009-05, University of Massachusetts Amherst, Department of Economics.
    14. Katsuya Kobayashi & Hideo Konishi, 2021. "Effort complementarity and sharing rules in group contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 205-221, February.
    15. Todd Sandler, 2015. "Collective action: fifty years later," Public Choice, Springer, vol. 164(3), pages 195-216, September.
    16. Friedel Bolle, 2014. "Binary Threshold Public Goods," Discussion Paper Series RECAP15 14, RECAP15, European University Viadrina, Frankfurt (Oder).
    17. Stefano Barbieri & David Malueg & Iryna Topolyan, 2014. "The best-shot all-pay (group) auction with complete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 603-640, November.
    18. Roman M. Sheremeta, 2011. "Perfect-Substitutes, Best-Shot, and Weakest-Link Contests between Groups," Korean Economic Review, Korean Economic Association, vol. 27, pages 5-32.
    19. Thierry Pénard & Sylvain Dejean & Raphaël Suire, 2011. "Olson’s Paradox Revisited: An Empirical Analysis of Incentives to Contribute in P2P File-sharing Communities," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201105, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    20. Shakun D. Mago & Jennifer Pate, 2023. "Greed and fear: Competitive and charitable priming in a threshold volunteer's dilemma," Economic Inquiry, Western Economic Association International, vol. 61(1), pages 138-161, January.

    More about this item

    Keywords

    evolution of cooperation; evolutionary game theory; replicator dynamics; public goods games;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tse:iastwp:32651. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/iasttfr.html .

    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.