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When Does One Bad Apple Spoil the Barrel? An Evolutionary Analysis of Collective Action

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  • David P. Myatt
  • Chris Wallace

Abstract

This paper studies n-player collective-action games in which a public good is produced if and only if m or more volunteers contribute to it. Quantal-response strategy revisions allow play to move between equilibria in which a team of m players successfully provide, and an equilibrium in which the collective action fails. A full characterisation of long-run play reveals the determinants of success. These include the correlation between players` costs of provision and their valuations for the good. The addition of an extra bad apple player can spoil the barrel by destabilising successful teams. A contemporary application is the team-based provision of open-source software. The analysis reveals the features of successful open-source projects, and suggests a rationale for limiting the pool of possible contributors.

Suggested Citation

  • David P. Myatt & Chris Wallace, 2006. "When Does One Bad Apple Spoil the Barrel? An Evolutionary Analysis of Collective Action," Economics Series Working Papers 269, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:269
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    Cited by:

    1. Boosey, Luke A., 2017. "Conditional cooperation in network public goods experiments," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 69(C), pages 108-116.
    2. 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.
    3. Gee, Laura K. & Schreck, Michael J., 2018. "Do beliefs about peers matter for donation matching? Experiments in the field and laboratory," Games and Economic Behavior, Elsevier, vol. 107(C), pages 282-297.
    4. Myatt, David P. & Wallace, Chris, 2008. "An evolutionary analysis of the volunteer's dilemma," Games and Economic Behavior, Elsevier, vol. 62(1), pages 67-76, January.
    5. Grund, Christian & Harbring, Christine & Thommes, Kirsten, 2018. "Group (Re-) formation in public good games: The tale of the bad apple?," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 306-319.
    6. Laura Gee & Michael Schreck, 2016. "Do Beliefs About Peers Matter for Donation Matching? Experiments in the Field and Laboratory," Framed Field Experiments 00538, The Field Experiments Website.
    7. Toshimasa Maruta & Akira Okada, 2015. "Formation and long-run stability of cooperative groups in a social dilemma situation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 11(1), pages 121-135, March.
    8. 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.
    9. Benndorf, Volker & Martínez-Martínez, Ismael & Normann, Hans-Theo, 2021. "Games with coupled populations: An experiment in continuous time," Journal of Economic Theory, Elsevier, vol. 195(C).
    10. Pradelski, Bary S.R., 2023. "Social influence: The Usage History heuristic," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 105-113.
    11. Josephson, Jens & Wärneryd, Karl, 2008. "Long-run selection and the work ethic," Games and Economic Behavior, Elsevier, vol. 63(1), pages 354-365, May.
    12. Angelovski, Andrej & Di Cagno, Daniela & Güth, Werner & Marazzi, Francesca & Panaccione, Luca, 2018. "Does heterogeneity spoil the basket? The role of productivity and feedback information on public good provision," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 77(C), pages 40-49.
    13. 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.
    14. Wallace, Chris & Young, H. Peyton, 2015. "Stochastic Evolutionary Game Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    15. Carlos Alós-Ferrer & Nick Netzer, 2015. "Robust stochastic stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 31-57, January.
    16. Gee, Laura Katherine & Schreck, Michael J., 2017. "Do Beliefs about Peers Matter for Donation Matching? Experiments in the Field and Laboratory," IZA Discussion Papers 10956, Institute of Labor Economics (IZA).
    17. DavidP. Myatt & Chris Wallace, 2009. "Evolution, Teamwork and Collective Action: Production Targets in the Private Provision of Public Goods," Economic Journal, Royal Economic Society, vol. 119(534), pages 61-90, January.
    18. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.
    19. Aggarwal, Ishani & Woolley, Anita Williams, 2013. "Do you see what I see? The effect of members’ cognitive styles on team processes and errors in task execution," Organizational Behavior and Human Decision Processes, Elsevier, vol. 122(1), pages 92-99.
    20. Newton, Jonathan, 2017. "Shared intentions: The evolution of collaboration," Games and Economic Behavior, Elsevier, vol. 104(C), pages 517-534.
    21. Antoci, Angelo & Russu, Paolo & Zarri, Luca, 2014. "Tax evasion in a behaviorally heterogeneous society: An evolutionary analysis," Economic Modelling, Elsevier, vol. 42(C), pages 106-115.

    More about this item

    Keywords

    Collective Action; Evolution; Teams; Equilibrium Selection; Concordance; Open-Source Software;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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