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Proportional individual rationality and the provision of a public good in a large economy

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  • Rong, Kang

Abstract

This paper studies the public good provision problem in which a non-excludable public good can be provided and payments can be collected from agents only if the proportion of agents who obtain nonnegative interim expected utilities from the public good provision mechanism weakly exceeds a prespecified ratio α. We call this requirement “α proportional individual rationality”. We identify a key threshold such that if α is less than this threshold, then efficiency obtains asymptotically. If α is greater than the threshold, then inefficiency obtains asymptotically. In addition, we obtain the convergence rate of the probability of provision to its efficient/inefficient level. Moreover, as a methodological contribution of this paper, we propose the standard deviation of an agent’s interim expected provision as a measure of the agent’s influence in a mechanism. We find that as the economy becomes large, an agent’s influence in any sequence of anonymous mechanisms converges to zero, and thus any sequence of anonymous feasible mechanisms must converge to a constant mechanism. We obtain uniform bounds for those rates of convergence.

Suggested Citation

  • Rong, Kang, 2014. "Proportional individual rationality and the provision of a public good in a large economy," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 187-196.
    • Handle: RePEc:eee:mateco:v:51:y:2014:i:c:p:187-196
    DOI: 10.1016/j.jmateco.2013.11.004
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    1. Tilman Börgers & Peter Norman, 2009. "A note on budget balance under interim participation constraints: the case of independent types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 477-489, June.
    2. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    3. Peter Norman, 2004. "Efficient Mechanisms for Public Goods with Use Exclusions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(4), pages 1163-1188.
    4. Ledyard, John O. & Palfrey, Thomas R., 2002. "The approximation of efficient public good mechanisms by simple voting schemes," Journal of Public Economics, Elsevier, vol. 83(2), pages 153-171, February.
    5. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    6. George J. Mailath & Andrew Postlewaite, 1990. "Asymmetric Information Bargaining Problems with Many Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 351-367.
    7. Rob, Rafael, 1989. "Pollution claim settlements under private information," Journal of Economic Theory, Elsevier, vol. 47(2), pages 307-333, April.
    8. Martin F. Hellwig, 2003. "Public-Good Provision with Many Participants," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(3), pages 589-614.
    9. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    10. Al-Najjar, Nabil I. & Smorodinsky, Rann, 2000. "Pivotal Players and the Characterization of Influence," Journal of Economic Theory, Elsevier, vol. 92(2), pages 318-342, June.
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