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On the probability of breakdown in participation games

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  • Pim Heijnen

Abstract

In this paper I analyze a participation game i.e. a public good game where contributions to the public good are binary (people either participate or not participate). Although variants of this game have been studied extensively, most previous work takes the benefit of provision of the public good to be independent of the number of players that contribute and show that the probability of breakdown, i.e. the probability that no one participates, is increasing in group size. Here this assumption is dropped. I show when the probability of breakdown is decreasing in group size and also present sufficient conditions under which the probability of breakdown is increasing in group size. Moreover I show that for large groups this probability is non-negligible and exceeding exp(−1) in the limit and that the expected number of participants is less than one. Also two economic examples, concerning R&D and debt overhang, are discussed.
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  • 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.
    • Handle: RePEc:spr:sochwe:v:32:y:2009:i:3:p:493-511
    DOI: 10.1007/s00355-008-0337-5
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    1. Mamoru Kaneko & Jacek Prokop, 1993. "A game theoretical approach to the international debt overhang," Journal of Economics, Springer, vol. 58(1), pages 1-24, February.
    2. 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.
    3. Thomas Palfrey & Howard Rosenthal, 1983. "A strategic calculus of voting," Public Choice, Springer, vol. 41(1), pages 7-53, January.
    4. Marco A. Haan & Peter Kooreman, 2003. "How majorities can lose the election Another voting paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 509-522, June.
    5. Joseph E Harrington Jr, 2001. "A Simple Game-Theoretic Explanation for the Relationship Between Group Size and Helping," Economics Working Paper Archive 417, The Johns Hopkins University,Department of Economics.
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    Cited by:

    1. 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.
    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. Takuma Wakayama & Takehiko Yamato, 2023. "Comparison of the voluntary contribution and Pareto-efficient mechanisms under voluntary participation," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 517-553, June.

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