IDEAS home Printed from https://ideas.repec.org/a/bla/jpbect/v3y2001i4p501-525.html
   My bibliography  Save this article

Profit Maximizing in Auctions of Public Goods

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1097-3923.00081
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1097-3923.00081?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Groves, Theodore & Ledyard, John O, 1977. "Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem," Econometrica, Econometric Society, vol. 45(4), pages 783-809, May.
    2. McAfee, R Preston & McMillan, John, 1992. "Bidding Rings," American Economic Review, American Economic Association, vol. 82(3), pages 579-599, June.
      • McAfee, R. Preston & McMillan, John., 1990. "Bidding Rings," Working Papers 726, California Institute of Technology, Division of the Humanities and Social Sciences.
    3. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
    4. d'Aspremont, C & Cremer, J & Gerard-Varet, L-A, 1997. "Unique Implementation in Auctions and in Public Goods Problems," G.R.E.Q.A.M. 97a15, Universite Aix-Marseille III.
    5. Michael H. Rothkopf, 1969. "A Model of Rational Competitive Bidding," Management Science, INFORMS, vol. 15(7), pages 362-373, March.
    6. Douglas K. Reece, 1978. "Competitive Bidding for Offshore Petroleum Leases," Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 369-384, Autumn.
    7. Philippe Jehiel & Benny Moldovanu, 2000. "Auctions with Downstream Interaction Among Buyers," RAND Journal of Economics, The RAND Corporation, vol. 31(4), pages 768-791, Winter.
    8. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1996. "How (Not) to Sell Nuclear Weapons," American Economic Review, American Economic Association, vol. 86(4), pages 814-829, September.
    9. Philippe Jehiel & Benny Moldovanu, 1998. "Auctions with Downstream Interaction," Discussion Papers 1243, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Jacob Rubinstein & Elmar Wolfstetter & Michael Landsberger & Shmuel Zamir, 2001. "First-price auctions when the ranking of valuations is common knowledge," Review of Economic Design, Springer;Society for Economic Design, vol. 6(3), pages 461-480.
    11. R. Isaac & James Walker & Susan Thomas, 1984. "Divergent evidence on free riding: An experimental examination of possible explanations," Public Choice, Springer, vol. 43(2), pages 113-149, January.
    12. Marwell, Gerald & Ames, Ruth E., 1981. "Economists free ride, does anyone else? : Experiments on the provision of public goods, IV," Journal of Public Economics, Elsevier, vol. 15(3), pages 295-310, June.
    13. Bliss, Christopher & Nalebuff, Barry, 1984. "Dragon-slaying and ballroom dancing: The private supply of a public good," Journal of Public Economics, Elsevier, vol. 25(1-2), pages 1-12, November.
    14. Brubaker, Earl R, 1975. "Free Ride, Free Revelation, or Golden Rule?," Journal of Law and Economics, University of Chicago Press, vol. 18(1), pages 147-161, April.
    15. Mark Isaac, R. & McCue, Kenneth F. & Plott, Charles R., 1985. "Public goods provision in an experimental environment," Journal of Public Economics, Elsevier, vol. 26(1), pages 51-74, February.
    16. M. E. Oren & A. C. Williams, 1975. "On Competitive Bidding," Operations Research, INFORMS, vol. 23(6), pages 1072-1079, December.
    17. Lerner, Anat, 1998. "A Pie Allocation Among Sharing Groups," Games and Economic Behavior, Elsevier, vol. 22(2), pages 316-330, February.
    18. Robert B. Wilson, 1967. "Competitive Bidding with Asymmetric Information," Management Science, INFORMS, vol. 13(11), pages 816-820, July.
    19. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
    20. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1999. "Multidimensional Mechanism Design for Auctions with Externalities," Journal of Economic Theory, Elsevier, vol. 85(2), pages 258-293, April.
    21. Cornes, Richard & Sandler, Todd, 1984. "Easy Riders, Joint Production, and Public Goods," Economic Journal, Royal Economic Society, vol. 94(375), pages 580-598, September.
    22. Friedrich Schneider & Werner W. Pommerehne, 1981. "Free Riding and Collective Action: An Experiment in Public Microeconomics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 96(4), pages 689-704.
    23. George J. Stigler, 1974. "Free Riders and Collective Action: An Appendix to Theories of Economic Regulation," Bell Journal of Economics, The RAND Corporation, vol. 5(2), pages 359-365, Autumn.
    24. Kalyan Chatterjee & William Samuelson, 1983. "Bargaining under Incomplete Information," Operations Research, INFORMS, vol. 31(5), pages 835-851, October.
    25. Michael H. Rothkopf, 1977. "Bidding in Simultaneous Auctions with a Constraint on Exposure," Operations Research, INFORMS, vol. 25(4), pages 620-629, August.
    26. Robert Wilson, 1977. "A Bidding Model of Perfect Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(3), pages 511-518.
    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. Barbieri, Stefano & Malueg, David A., 2010. "Threshold uncertainty in the private-information subscription game," Journal of Public Economics, Elsevier, vol. 94(11-12), pages 848-861, December.
    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. 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.
    5. 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.
    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. 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. 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.
    9. 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.
    10. Murat Yilmaz, 2010. "Auctioning a Discrete Public Good under Incomplete Information," Working Papers 2010/14, Bogazici University, Department of Economics.
    11. Philippe Jehiel & Benny Moldovanu, 2005. "Allocative and Informational Externalities in Auctions and Related Mechanisms," Levine's Bibliography 784828000000000490, UCLA 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. 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.
    14. 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.
    15. 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.
    16. 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.
    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.

    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. ALBOTH, Dirk & LERNER, Anat & SHALEV, Jonathan, 1997. "Auctioning public goods to groups of aghents," LIDAM Discussion Papers CORE 1997077, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Ledyard, John O., "undated". "Public Goods: A Survey of Experimental Research," Working Papers 861, California Institute of Technology, Division of the Humanities and Social Sciences.
    3. Laffont, Jean-Jacques, 1997. "Game theory and empirical economics: The case of auction data 1," European Economic Review, Elsevier, vol. 41(1), pages 1-35, January.
    4. Vincy Fon, 1988. "Free-Riding versus Paying under Uncertainty," Public Finance Review, , vol. 16(4), pages 464-481, October.
    5. Cramton, Peter C, 1995. "Money Out of Thin Air: The Nationwide Narrowband PCS Auction," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(2), pages 267-343, Summer.
    6. Harrison, Glenn W & Hirshleifer, Jack, 1989. "An Experimental Evaluation of Weakest Link/Best Shot Models of Public Goods," Journal of Political Economy, University of Chicago Press, vol. 97(1), pages 201-225, February.
    7. Philippe Jehiel & Benny Moldovanu, 2005. "Allocative and Informational Externalities in Auctions and Related Mechanisms," Levine's Bibliography 784828000000000490, UCLA Department of Economics.
    8. Committee, Nobel Prize, 2020. "Improvements to auction theory and inventions of new auction formats," Nobel Prize in Economics documents 2020-2, Nobel Prize Committee.
    9. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Jean-Jacques Laffont, 1998. "Théorie des jeux et économie empirique : le cas des données issues d'enchères," Économie et Prévision, Programme National Persée, vol. 132(1), pages 121-137.
    11. Isabelle Brocas, 2013. "Optimal allocation mechanisms with type-dependent negative externalities," Theory and Decision, Springer, vol. 75(3), pages 359-387, September.
    12. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    13. Jacob K. Goeree & Theo Offerman, 2003. "Competitive Bidding in Auctions with Private and Common Values," Economic Journal, Royal Economic Society, vol. 113(489), pages 598-613, July.
    14. Brocas, Isabelle, 2014. "Countervailing incentives in allocation mechanisms with type-dependent externalities," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 22-33.
    15. Thomas McCaleb & Richard Wagner, 1985. "The experimental search for free riders: Some reflections and observations," Public Choice, Springer, vol. 47(3), pages 479-490, January.
    16. Isabelle Brocas, 2003. "Endogenous entry in auctions with negative externalities," Theory and Decision, Springer, vol. 54(2), pages 125-149, March.
    17. Ronald M. Harstad & Aleksandar Saša Pekeč, 2008. "Relevance to Practice and Auction Theory: A Memorial Essay for Michael Rothkopf," Interfaces, INFORMS, vol. 38(5), pages 367-380, October.
    18. Runge, C. Ford, 1985. "The Assurance Problem And Conjectural Variation In Public Goods Provision," Staff Papers 13548, University of Minnesota, Department of Applied Economics.
    19. Sánchez, Isabel, 1991. "La provision voluntaria de bienes publicos: Resultados Experimentales," DE - Documentos de Trabajo. Economía. DE 3000, Universidad Carlos III de Madrid. Departamento de Economía.
    20. Bernard Lebrun, 2008. "First-Price, Second-Price, and English Auctions with Resale," Working Papers 2008_06, York University, Department of Economics.

    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

    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:bla:jpbect:v:3:y:2001:i:4:p:501-525. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/apettea.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.