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Optimal mechanism design for the private supply of a public good

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  • Csapó, Gergely
  • Müller, Rudolf

Abstract

We study the problem of finding the profit-maximizing mechanism for a monopolistic provider of a single, non-excludable public good. Our model covers the most general setting, namely, we allow for correlation in the signal distribution as well as for informational externalities in the valuations. We show that the optimal deterministic, ex-post incentive compatible, ex-post individual rational mechanism can be computed in polynomial time by reducing the problem to finding a maximal weight closure in a directed graph. Node weights in the graph correspond to conditional virtual values, while the network structure is arising from the monotonicity constraints. We discuss what can be achieved if we relax our core assumptions one by one, i.e., if we go for randomized, interim individual rational or Bayes–Nash implementable mechanisms. Finally, we demonstrate that our techniques can be adapted for the excludable public good problem as well.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 80 (2013)
Issue (Month): C ()
Pages: 229-242

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Handle: RePEc:eee:gamebe:v:80:y:2013:i:c:p:229-242

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Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: Public good provision; Mechanism design; Profit maximization;

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References

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  1. Laffont, Jean-Jacques & Martimort, David, 1998. "Mechanism Design with Collusion and Correlation," IDEI Working Papers 81, Institut d'Économie Industrielle (IDEI), Toulouse.
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  5. Schmitz, Patrick W., 1997. "Monopolistic Provision of Excludable Public Goods under Private Information," MPRA Paper 6549, University Library of Munich, Germany.
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  10. 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.
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  12. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
  13. Jean-Claude Picard, 1976. "Maximal Closure of a Graph and Applications to Combinatorial Problems," Management Science, INFORMS, vol. 22(11), pages 1268-1272, July.
  14. Alex Gershkov & Jacob Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2012. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Working Papers tecipa-445, University of Toronto, Department of Economics.
  15. 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.
  16. Fernando Branco, 1996. "Multiple unit auctions of an indivisible good," Economic Theory, Springer, vol. 8(1), pages 77-101.
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