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Optimal mechanism design for the private supply of a public good

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  • Csapó Gergely
  • Müller Rudolf

    (METEOR)

Abstract

We study the problem of finding the profit-maximizing mechanism for a monopolistic provider of asingle, non-excludable public good. This problem has been well studied for the case when agents''types are independently distributed, but the literature is almost silent about the case of generaljoint distributions. We investigate the problem from an automated mechanism design perspective,meaning that we want to understand the algorithmic complexity of finding the optimal mechanismwhen we are given a finite set of type profiles and their distribution. We show that the optimaldeterministic, dominant strategy incentive compatible, ex-post individual rational mechanism canbe computed in polynomial time by reducing the problem to finding a maximal weight closure in adirected graph. Node weights in the graph correspond to conditional virtual values. Whenvaluations are independently distributed, the constructed mechanism is also optimal among allBayes-Nash implementable and ex-interim individual rational mechanisms. In contrast, for dependentvaluations strictly higher profit can be achieved if one allows for ex-interim individualrationality. By invoking techniques due to Crémer and McLean, we show that optimal deterministic,ex-interim individual rational, Bayes-Nash implementable or dominant strategy implementablemechanisms still can be found in polynomial time if the joint distribution of types satisfiescertain regularity conditions.

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Bibliographic Info

Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 038.

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Date of creation: 2012
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Handle: RePEc:unm:umamet:2012038

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Keywords: operations research and management science;

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  1. Werner Güth & Martin Hellwig, 1986. "The private supply of a public good," Journal of Economics, Springer, vol. 46(1), pages 121-159, December.
  2. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Jehiel, Philippe & Moldovanu, Benny, 2006. "Allocative and Informational Externalities in Auctions and Related Mechanisms," CEPR Discussion Papers 5558, C.E.P.R. Discussion Papers.
  4. Jean-Jacques Laffont & David Martimort, 2000. "Mechanism Design with Collusion and Correlation," Econometrica, Econometric Society, vol. 68(2), pages 309-342, March.
  5. Jean-Claude Picard, 1976. "Maximal Closure of a Graph and Applications to Combinatorial Problems," Management Science, INFORMS, vol. 22(11), pages 1268-1272, July.
  6. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2011. "Bayesian and Dominant Strategy Implementation Revisited," Working Papers tecipa-422, University of Toronto, Department of Economics.
  7. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2006. "The Limits of ex post Implementation," Econometrica, Econometric Society, vol. 74(3), pages 585-610, 05.
  8. Schmitz, Patrick W., 1997. "Monopolistic Provision of Excludable Public Goods under Private Information," MPRA Paper 6549, University Library of Munich, Germany.
  9. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, 01.
  10. McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, vol. 60(2), pages 395-421, March.
  11. Bruce Faaland & Kiseog Kim & Tom Schmitt, 1990. "A New Algorithm for Computing the Maximal Closure of a Graph," Management Science, INFORMS, vol. 36(3), pages 315-331, March.
  12. Fernando Branco, 1996. "Multiple unit auctions of an indivisible good," Economic Theory, Springer, vol. 8(1), pages 77-101.
  13. Alejandro M. Manelli & Daniel R. Vincent, 2010. "Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model," Econometrica, Econometric Society, vol. 78(6), pages 1905-1938, November.
  14. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
  15. Robert B. Wilson, 1967. "Competitive Bidding with Asymmetric Information," Management Science, INFORMS, vol. 13(11), pages 816-820, July.
  16. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-57, November.
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