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Profit Maximizing in Auctions of Public Goods

Author

Listed:
  • Dirk Alboth

    (Paderborn University)

  • Anat Lerner

    (Tel-Aviv University)

  • Jonathan Shalev

    (CORE)

Abstract

A profit-maximizing auctioneer can provide a public good to a group of agents. Each group member has a private value for the good being provided to the group. We investigate an auction mechanism where the auctioneer provides the good to the group, only if the sum of their bids exceeds a reserve price declared previously by the auctioneer. For the two-bidder case with private values drawn from a uniform distribution we characterize the continuously differentiable symmetric equilibrium bidding functions for the agents, and find the optimal reserve price for the auctioneer when such functions are used by the bidders. We also examine another interesting family of equilibrium bidding functions for this case, with a discrete number of possible bids, and show the relation (in the limit) to the differentiable bidding functions.

Suggested Citation

  • Dirk Alboth & Anat Lerner & Jonathan Shalev, 1997. "Profit Maximizing in Auctions of Public Goods," Game Theory and Information 9707010, University Library of Munich, Germany, revised 01 Apr 1998.
  • Handle: RePEc:wpa:wuwpga:9707010
    Note: Type of Document - LaTeX; prepared on IBM PC; to print on PostScript; pages: 32 ; figures: 3 eps files included. Comments welcome
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    Cited by:

    1. 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.
    2. Matthew Ellman & Sjaak Hurkens, 2014. "Optimal Crowdfunding Design," Working Papers 14-21, NET Institute.
    3. Pengfei Liu & Stephen K. Swallow & Christopher M. Anderson, 2016. "Threshold-Level Public Goods Provision with Multiple Units: Experimental Effects of Disaggregated Groups with Rebates," Land Economics, University of Wisconsin Press, vol. 92(3), pages 515-533.
    4. 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.
    5. Ellman, Matthew & Hurkens, Sjaak, 2019. "Optimal crowdfunding design," Journal of Economic Theory, Elsevier, vol. 184(C).
    6. 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.
    7. Jehiel, Philippe & Moldovanu, Benny, 2005. "Allocative and Informational Externalities in Auctions and Related Mechanisms," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 142, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    8. 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.
    9. 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.
    10. 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.
    11. Murat Yilmaz, 2010. "Auctioning a Discrete Public Good under Incomplete Information," Working Papers 2010/14, Bogazici University, Department of Economics.
    12. Jingfeng Lu & Euston Quah, 2009. "Private Provisions of a Discrete Public Good with Voluntary Participation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(3), pages 343-362, June.
    13. 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.
    14. 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.
    15. 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.

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    More about this item

    Keywords

    public goods; auctions; externalities;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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