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Profit maximizing in auctions of public goods

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  • ALBOTH, Dirk
  • LERNER, Anat
  • SHALEV, Jonathan

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.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number -1596.

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Handle: RePEc:cor:louvrp:-1596

Note: In : Journal of Public Economic Theory, 3(4), 501-525, 2001
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  1. Jehiel, Phillipe & Moldovanu, Benny & Stacchetti, E., 1997. "Multidimensional Mechanism Design for Auctions with Externalities," Sonderforschungsbereich 504 Publications 97-04, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  2. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1996. "How (Not) to Sell Nuclear Weapons," American Economic Review, American Economic Association, vol. 86(4), pages 814-29, September.
  3. McAfee, R. Preston & McMillan, John., 1990. "Bidding Rings," Working Papers 726, California Institute of Technology, Division of the Humanities and Social Sciences.
  4. repec:wop:humbsf:1996-36 is not listed on IDEAS
  5. 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.
  6. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
  7. 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.
  8. Jehiel, Phillipe & Moldovanu, Benny, 1997. "Auctions with Downstream Interaction among Buyers," Sonderforschungsbereich 504 Publications 97-06, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  9. 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, vol. 6(3), pages 461-480.
  10. Douglas K. Reece, 1978. "Competitive Bidding for Offshore Petroleum Leases," Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 369-384, Autumn.
  11. Theodore Groves & John Ledyard, 1976. "Optimal Allocation of Public Goods: A Solution to the 'Free Rider Problem'," Discussion Papers 144, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. 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.
  13. Schneider, Friedrich & Pommerehne, Werner W, 1981. "Free Riding and Collective Action: An Experiment in Public Microeconomics," The Quarterly Journal of Economics, MIT Press, vol. 96(4), pages 689-704, November.
  14. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
  15. Lerner, Anat, 1998. "A Pie Allocation Among Sharing Groups," Games and Economic Behavior, Elsevier, vol. 22(2), pages 316-330, February.
  16. Wilson, Robert, 1977. "A Bidding Model of Perfect Competition," Review of Economic Studies, Wiley Blackwell, vol. 44(3), pages 511-18, October.
  17. Isaac, R. Mark & McCue, Kenneth F. & Plott, Charles R., . "Public Goods Provision in an Experimental Environment," Working Papers 428, California Institute of Technology, Division of the Humanities and Social Sciences.
  18. Cornes, Richard & Sandler, Todd, 1984. "Easy Riders, Joint Production, and Public Goods," Economic Journal, Royal Economic Society, vol. 94(375), pages 580-98, September.
  19. 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.
  20. Philippe Jehiel & Benny Moldovanu, 1998. "Auctions with Downstream Interaction," Discussion Papers 1243, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  21. Robert B. Wilson, 1967. "Competitive Bidding with Asymmetric Information," Management Science, INFORMS, vol. 13(11), pages 816-820, July.
  22. Brubaker, Earl R, 1975. "Free Ride, Free Revelation, or Golden Rule?," Journal of Law and Economics, University of Chicago Press, vol. 18(1), pages 147-61, April.
  23. 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.
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Citations

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Cited by:
  1. Philippe Jehiel & Benny Moldovanu, 2005. "Allocative and Informational Externalities in Auctions and Related Mechanisms," Levine's Bibliography 784828000000000490, UCLA Department of Economics.
  2. Stefano Barbieri & David A. Malueg, 2009. "Threshold Uncertainty in the Private-Information Subscription Game," Working Papers 0903, Tulane University, Department of Economics.
  3. 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.
  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. Stefano Barbieri & David Malueg, 2008. "Private provision of a discrete public good: efficient equilibria in the private-information contribution game," Economic Theory, Springer, vol. 37(1), pages 51-80, October.
  6. Liu, Pengfei & Swallow, Stephen K. & Anderson, Christopher M., 2013. "Threshold Level Public Goods Provision with Multiple Units: Experimental Effects of Disaggregated Groups with Rebates," Working Papers 24, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
  7. Murat Yilmaz, 2010. "Auctioning a Discrete Public Good under Incomplete Information," Working Papers 2010/14, Bogazici University, Department of Economics.

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