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Profit Maximizing in Auctions of Public Goods

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  • Dirk Alboth
  • Anat Lerner
  • Jonathan Shalev

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 we 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, 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.
    • Handle: RePEc:bla:jpbect:v:3:y:2001:i:4:p:501-525
    DOI: 10.1111/1097-3923.00081
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    Cited by:

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    2. 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.
    3. Ellman, Matthew & Hurkens, Sjaak, 2019. "Optimal crowdfunding design," Journal of Economic Theory, Elsevier, vol. 184(C).
    4. 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.
    5. Stefano Barbieri, 2023. "Complementarity and information in collective action," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 167-206, January.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Murat Yilmaz, 2010. "Auctioning a Discrete Public Good under Incomplete Information," Working Papers 2010/14, Bogazici University, Department of Economics.
    16. Philippe Jehiel & Benny Moldovanu, 2005. "Allocative and Informational Externalities in Auctions and Related Mechanisms," Levine's Bibliography 784828000000000490, UCLA Department of Economics.
    17. Zhi Li & Pengfei Liu & Stephen K. Swallow, 2021. "Assurance Contracts to Support Multi-Unit Threshold Public Goods in Environmental Markets," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 80(2), pages 339-378, October.
    18. 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.
    19. 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.
    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.

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    More about this item

    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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