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Group size and collective action in a binary contribution game

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  • Nöldeke, Georg
  • Peña, Jorge

Abstract

We consider how group size affects the private provision of a public good with non-refundable binary contributions. A fixed amount of the good is provided if and only if the number of contributors reaches an exogenous threshold. The threshold, the group size, and the identical, non-refundable cost of contributing to the public good are common knowledge. Our focus is on the case in which the threshold is larger than one, so that teamwork is required to produce the public good. We show that both expected payoffs and the probability that the public good is obtained in the best symmetric equilibrium are decreasing in group size. We also characterize the limit outcome when group size converges to infinity and provide precise conditions under which the expected number of contributors is decreasing or increasing in group size for sufficiently large groups.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:mateco:v:88:y:2020:i:c:p:42-51
    DOI: 10.1016/j.jmateco.2020.02.003
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    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. Christos Mavridis & Marco Serena, 2018. "Complete information pivotal-voter model with asymmetric group size," Public Choice, Springer, vol. 177(1), pages 53-66, October.
    3. 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.
    4. Justin Pappas Johnson, 2002. "Open Source Software: Private Provision of a Public Good," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 11(4), pages 637-662, December.
    5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    6. Dixit, Avinash & Olson, Mancur, 2000. "Does voluntary participation undermine the Coase Theorem?," Journal of Public Economics, Elsevier, vol. 76(3), pages 309-335, June.
    7. Pim Heijnen, 2009. "On the probability of breakdown in participation games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 493-511, March.
    8. 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.
    9. Jean Hindriks & Romans Pancs, 2002. "Free Riding on Altruism and Group Size," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 4(3), pages 335-346, July.
    10. Tasos Kalandrakis, 2009. "Robust rational turnout," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(2), pages 317-343, November.
    11. Anderson, Simon P. & Engers, Maxim, 2007. "Participation games: Market entry, coordination, and the beautiful blonde," Journal of Economic Behavior & Organization, Elsevier, vol. 63(1), pages 120-137, May.
    12. Nöldeke, Georg & Peña, Jorge, 2018. "Group size effects in social evolution," IAST Working Papers 18-75, Institute for Advanced Study in Toulouse (IAST).
    13. Andreas Diekmann, 1985. "Volunteer's Dilemma," Journal of Conflict Resolution, Peace Science Society (International), vol. 29(4), pages 605-610, December.
    14. Martin McGuire, 1974. "Group size, group homo-geneity, and the aggregate provision of a pure public good under cournot behavior," Public Choice, Springer, vol. 18(1), pages 107-126, June.
    15. 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.
    16. David P. Myatt & Chris Wallace, 2002. "Equilibrium Selection and Public-good Provision: The Development of Open-source Software," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 18(4), pages 446-461.
    17. McBride, Michael, 2006. "Discrete public goods under threshold uncertainty," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1181-1199, August.
    18. Thomas Palfrey & Howard Rosenthal, 1983. "A strategic calculus of voting," Public Choice, Springer, vol. 41(1), pages 7-53, January.
    19. Amartya K. Sen, 1967. "Isolation, Assurance and the Social Rate of Discount," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 81(1), pages 112-124.
    20. Chamberlin, John, 1974. "Provision of Collective Goods As a Function of Group Size," American Political Science Review, Cambridge University Press, vol. 68(2), pages 707-716, June.
    21. repec:bla:jpbect:v:4:y:2002:i:3:p:335-46 is not listed on IDEAS
    22. Makris, Miltiadis, 2009. "Private provision of discrete public goods," Games and Economic Behavior, Elsevier, vol. 67(1), pages 292-299, September.
    23. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    24. Todd Sandler, 2015. "Collective action: fifty years later," Public Choice, Springer, vol. 164(3), pages 195-216, September.
    25. Palfrey, Thomas R. & Rosenthal, Howard, 1988. "Private incentives in social dilemmas : The effects of incomplete information and altruism," Journal of Public Economics, Elsevier, vol. 35(3), pages 309-332, April.
    26. 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.
    27. Schram, Arthur & Offerman, Theo & Sonnemans, Joep, 2008. "Explaining the Comparative Statics in Step-Level Public Good Games," Handbook of Experimental Economics Results, in: Charles R. Plott & Vernon L. Smith (ed.), Handbook of Experimental Economics Results, edition 1, volume 1, chapter 86, pages 817-824, Elsevier.
    28. Binmore, Ken & Samuelson, Larry, 2001. "Evolution and Mixed Strategies," Games and Economic Behavior, Elsevier, vol. 34(2), pages 200-226, February.
    29. David P. Myatt & Chris Wallace, 2008. "When Does One Bad Apple Spoil the Barrel? An Evolutionary Analysis of Collective Action," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(2), pages 499-527.
    30. Andreoni, James, 1988. "Privately provided public goods in a large economy: The limits of altruism," Journal of Public Economics, Elsevier, vol. 35(1), pages 57-73, February.
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    Cited by:

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    4. Ginzburg, Boris & Guerra, José-Alberto & Lekfuangfu, Warn N., 2023. "Critical Mass in Collective Action," MPRA Paper 117139, University Library of Munich, Germany.

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    More about this item

    Keywords

    Private provision of public goods; Group size effects; Collective action; Threshold games; Participation games; Teamwork dilemma;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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