IDEAS home Printed from https://ideas.repec.org/p/tul/wpaper/0903.html
   My bibliography  Save this paper

Threshold Uncertainty in the Private-Information Subscription Game

Author

Listed:
  • Stefano Barbieri

    (Department of Economics, Tulane University)

  • David A. Malueg

    (Department of Economics, UC Riverside)

Abstract

We introduce threshold uncertainty, a la Nitzan and Romano (1990), into a private-values model of voluntary provision of a discrete public good. Players are allowed to make any level of contribution toward funding the good, which is provided only if the cost threshold is reached. Otherwise, contributions are refunded. Conditions ensuring existence and uniqueness of a Bayesian equilibrium are established. Further restricting the threshold uncertainty to a uniform distribution, we show the equilibrium strategies are very simple, even allowing for any number of players with asymmetric distributions of values. Comparative statics with respect to changes in players' distributions are derived, allowing changes in both the intensity and the dispersion of values. Finally, we show the equilibrium is interim incentive inefficient. The sharpness of our results greatly contrasts with the more qualified insights of earlier private-values models with known cost threshold, which relied on there being two symmetric players and generally exhibited multiple equilibria.

Suggested Citation

  • Stefano Barbieri & David A. Malueg, 2009. "Threshold Uncertainty in the Private-Information Subscription Game," Working Papers 0903, Tulane University, Department of Economics.
  • Handle: RePEc:tul:wpaper:0903
    as

    Download full text from publisher

    File URL: http://repec.tulane.edu/RePEc/pdf/tul0903.pdf
    File Function: First version, 2009
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. Alberto Alesina & Eliana La Ferrara, 2000. "Participation in Heterogeneous Communities," The Quarterly Journal of Economics, Oxford University Press, vol. 115(3), pages 847-904.
    3. , & ,, 2010. "Common agency and public good provision under asymmetric information," Theoretical Economics, Econometric Society, vol. 5(2), May.
    4. Anat R. Admati & Motty Perry, 1991. "Joint Projects without Commitment," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 259-276.
    5. Richard Cornes & Roger Hartley, 2007. "Aggregative Public Good Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(2), pages 201-219, April.
    6. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    7. Potters, Jan & Sloof, Randolph, 1996. "Interest groups: A survey of empirical models that try to assess their influence," European Journal of Political Economy, Elsevier, vol. 12(3), pages 403-442, November.
    8. Ledyard, John O. & Palfrey, Thomas R., 2007. "A general characterization of interim efficient mechanisms for independent linear environments," Journal of Economic Theory, Elsevier, vol. 133(1), pages 441-466, March.
    9. Dirk Alboth & Anat Lerner & Jonathan Shalev, 2001. "Profit Maximizing in Auctions of Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(4), pages 501-525, October.
    10. Satterthwaite, Mark A. & Williams, Steven R., 1989. "Bilateral trade with the sealed bid k-double auction: Existence and efficiency," Journal of Economic Theory, Elsevier, vol. 48(1), pages 107-133, June.
    11. Alberto Alesina & Eliana La Ferrara, 2003. "Ethnic Diversity and Economic Performance," Harvard Institute of Economic Research Working Papers 2028, Harvard - Institute of Economic Research.
    12. John O. Ledyard & Thomas R. Palfrey, 1999. "A Characterization of Interim Efficiency with Public Goods," Econometrica, Econometric Society, vol. 67(2), pages 435-448, March.
    13. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    14. Stefano Barbieri & David Malueg, 2008. "Private provision of a discrete public good: efficient equilibria in the private-information contribution game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(1), pages 51-80, October.
    15. McBride, Michael, 2006. "Discrete public goods under threshold uncertainty," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1181-1199, August.
    16. Menezes, Flavio M. & Monteiro, Paulo K. & Temimi, Akram, 2001. "Private provision of discrete public goods with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 35(4), pages 493-514, July.
    17. Didier Laussel & Thomas R. Palfrey, 2003. "Efficient Equilibria in the Voluntary Contributions Mechanism with Private Information," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 5(3), pages 449-478, July.
    18. George J. Mailath & Andrew Postlewaite, 1990. "Asymmetric Information Bargaining Problems with Many Agents," Review of Economic Studies, Oxford University Press, vol. 57(3), pages 351-367.
    19. Cadsby, Charles Bram & Maynes, Elizabeth, 1999. "Voluntary provision of threshold public goods with continuous contributions: experimental evidence," Journal of Public Economics, Elsevier, vol. 71(1), pages 53-73, January.
    20. Stefano Barbieri & David A. Malueg, 2008. "Private Provision of a Discrete Public Good: Continuous‐Strategy Equilibria in the Private‐Information Subscription Game," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(4), pages 529-545, August.
    21. Alboth, Dirk & Lerner, Anat & Shalev, Jonathan, 2001. "Profit Maximizing in Auctions of Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(4), pages 501-525.
    22. Nitzan, Shmuel & Romano, Richard E., 1990. "Private provision of a discrete public good with uncertain cost," Journal of Public Economics, Elsevier, vol. 42(3), pages 357-370, August.
    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. Guilfoos, Todd & Miao, Haoran & Trandafir, Simona & Uchida, Emi, 2019. "Social learning and communication with threshold uncertainty," Resource and Energy Economics, Elsevier, vol. 55(C), pages 81-101.
    2. Boris Ginzburg, 2023. "Slacktivism," Journal of Theoretical Politics, , vol. 35(2), pages 126-143, April.
    3. Billur Aksoy & Silvana Krasteva, 2020. "When does less information translate into more giving to public goods?," Experimental Economics, Springer;Economic Science Association, vol. 23(4), pages 1148-1177, December.
    4. Zhi Li & Christopher Anderson & Stephen K. Swallow, 2012. "Uniform Price Mechanisms for Threshold Public Goods Provision: An Experimental Investigation," Working Papers 14, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
    5. Ben Balmford & Madeleine Marino & Oliver P. Hauser, 2024. "Voting Sustains Intergenerational Cooperation, Even When the Tipping Point Threshold is Ambiguous," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 87(1), pages 167-190, January.
    6. Matros, Alexander & Smirnov, Vladimir, 2011. "Treasure game," Working Papers 2011-10, University of Sydney, School of Economics, revised May 2014.
    7. Zhi Li & Dongsheng Chen & Pengfei Liu, 2023. "Assurance payments on the coordination of threshold public goods provision: An experimental investigation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(2), pages 407-436, April.
    8. Krasteva, Silvana & Yildirim, Huseyin, 2014. "Reprint of: (Un)Informed charitable giving," Journal of Public Economics, Elsevier, vol. 114(C), pages 108-120.
    9. Li, Zhi & Anderson, Christopher M. & Swallow, Stephen K., 2016. "Uniform price mechanisms for threshold public goods provision with complete information: An experimental investigation," Journal of Public Economics, Elsevier, vol. 144(C), pages 14-26.
    10. Stefano Barbieri & David A. Malueg, 2014. "Increasing Fundraising Success by Decreasing Donor Choice," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(3), pages 372-400, June.
    11. Anwesha Banerjee & Stefano Barbieri & Kai A. Konrad, 2022. "Climate Policy, Irreversibilities and Global Economic Shocks," Working Papers tax-mpg-rps-2022-11, Max Planck Institute for Tax Law and Public Finance.
    12. Krasteva, Silvana & Yildirim, Huseyin, 2013. "(Un)Informed charitable giving," Journal of Public Economics, Elsevier, vol. 106(C), pages 14-26.
    13. Li, Zhi & Anderson, Christopher M. & Swallow, Stephen, 2012. "Uniform Price Mechanisms for Threshold Public Goods Provision: An Experimental Investigation," Working Paper series 148349, University of Connecticut, Charles J. Zwick Center for Food and Resource Policy.

    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. Stefano Barbieri & David A. Malueg, 2014. "Increasing Fundraising Success by Decreasing Donor Choice," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(3), pages 372-400, June.
    2. Krasteva, Silvana & Yildirim, Huseyin, 2013. "(Un)Informed charitable giving," Journal of Public Economics, Elsevier, vol. 106(C), pages 14-26.
    3. Murat Yilmaz, 2010. "Auctioning a Discrete Public Good under Incomplete Information," Working Papers 2010/14, Bogazici University, Department of Economics.
    4. Krasteva, Silvana & Yildirim, Huseyin, 2014. "Reprint of: (Un)Informed charitable giving," Journal of Public Economics, Elsevier, vol. 114(C), pages 108-120.
    5. Zhi Li & Dongsheng Chen & Pengfei Liu, 2023. "Assurance payments on the coordination of threshold public goods provision: An experimental investigation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(2), pages 407-436, April.
    6. Zhi Li & Christopher Anderson & Stephen K. Swallow, 2012. "Uniform Price Mechanisms for Threshold Public Goods Provision: An Experimental Investigation," Working Papers 14, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
    7. Barbieri Stefano & Malueg David A., 2010. "Profit-Maximizing Sale of a Discrete Public Good via the Subscription Game in Private-Information Environments," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-31, February.
    8. Stefano Barbieri & David Malueg, 2008. "Private provision of a discrete public good: efficient equilibria in the private-information contribution game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(1), pages 51-80, October.
    9. Li, Zhi & Anderson, Christopher M. & Swallow, Stephen, 2012. "Uniform Price Mechanisms for Threshold Public Goods Provision: An Experimental Investigation," Working Paper series 148349, University of Connecticut, Charles J. Zwick Center for Food and Resource Policy.
    10. Li, Zhi & Anderson, Christopher M. & Swallow, Stephen K., 2016. "Uniform price mechanisms for threshold public goods provision with complete information: An experimental investigation," Journal of Public Economics, Elsevier, vol. 144(C), pages 14-26.
    11. Stefano Barbieri & David A. Malueg, 2008. "Private Provision of a Discrete Public Good: Continuous‐Strategy Equilibria in the Private‐Information Subscription Game," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(4), pages 529-545, August.
    12. Altınok, Ahmet & Yılmaz, Murat, 2018. "Dynamic voluntary contribution to a public project under time inconsistency," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 114-140.
    13. An, Yonghong & Hu, Yingyao & Liu, Pengfei, 2018. "Estimating heterogeneous contributing strategies in threshold public goods provision: A structural analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 152(C), pages 124-146.
    14. Federica Alberti & Anna Cartwright & Edward Cartwright, 2021. "Predicting Efficiency in Threshold Public Good Games: A Learning Direction Theory Approach," Working Papers in Economics & Finance 2021-01, University of Portsmouth, Portsmouth Business School, Economics and Finance Subject Group.
    15. Ellman, Matthew & Hurkens, Sjaak, 2019. "Optimal crowdfunding design," Journal of Economic Theory, Elsevier, vol. 184(C).
    16. Peyman Khezr & Flavio M. Menezes, 2019. "Funding natural monopoly infrastructure expansion: auctions versus regulated uniform access prices," Journal of Regulatory Economics, Springer, vol. 55(2), pages 193-213, April.
    17. Boris Ginzburg, 2023. "Slacktivism," Journal of Theoretical Politics, , vol. 35(2), pages 126-143, April.
    18. Toth, Sandor F. & Rabotyagov, Sergey S. & Ettl, Gregory J., 2009. "Experimental Testbeds for ECOSEL: A Market Framework for Private Provision of Forest Ecosystem Services," 2009 Annual Meeting, July 26-28, 2009, Milwaukee, Wisconsin 49565, Agricultural and Applied Economics Association.
    19. Laffont, Jean-Jacques & Martimort, David, 2005. "The design of transnational public good mechanisms for developing countries," Journal of Public Economics, Elsevier, vol. 89(2-3), pages 159-196, February.
    20. 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.

    More about this item

    Keywords

    discrete public good; subscription game; threshold uncertainty;
    All these keywords.

    JEL classification:

    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:tul:wpaper:0903. 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: Kerui Geng (email available below). General contact details of provider: https://edirc.repec.org/data/detulus.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.