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Optimal mechanism design for the private supply of a public good

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  • Csapó, G.

    (Quantitative Economics)

  • Müller, R.J.

    (Quantitative Economics)

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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Suggested Citation

  • Csapó, G. & Müller, R.J., 2012. "Optimal mechanism design for the private supply of a public good," Research Memorandum 037, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2012037
    DOI: 10.26481/umamet.2012037
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    Cited by:

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    3. Janke, Katharina & Johnston, David W. & Propper, Carol & Shields, Michael A., 2018. "The Causal Effect of Education on Chronic Health Conditions," IZA Discussion Papers 11353, Institute of Labor Economics (IZA).
    4. Nguyen, Hieu T.M., 2019. "Do more educated neighbourhoods experience less property crime? Evidence from Indonesia," International Journal of Educational Development, Elsevier, vol. 64(C), pages 27-37.
    5. Marc van der Steeg & Roel van Elk & Dinand Webbink, 2012. "Does intensive coaching reduce school dropout?," CPB Discussion Paper 224, CPB Netherlands Bureau for Economic Policy Analysis.
    6. repec:tir:wpaper:50 is not listed on IDEAS
    7. Nordin , Martin, 2014. "Does Eligibility for Tertiary Education Affect Crime Rates? Quasi-Experimental Evidence," Working Papers 2014:14, Lund University, Department of Economics.
    8. Povilas Lastauskas & Eirini Tatsi, 2017. "Spatial Nexus in Crime and Unemployement in Times of Crisis," Bank of Lithuania Working Paper Series 39, Bank of Lithuania.
    9. James, Jonathan & Vujić, Sunčica, 2019. "From high school to the high chair: Education and fertility timing," Economics of Education Review, Elsevier, vol. 69(C), pages 1-24.
    10. Ignacio Munyo, 2015. "The Juvenile Crime Dilemma," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(2), pages 201-211, April.
    11. Jin Xi & Haitian Xie, 2021. "Strength in Numbers: Robust Mechanisms for Public Goods with Many Agents," Papers 2101.02423, arXiv.org, revised Jul 2021.
    12. Rud, I & Van Klaveren, C. & Groot, W. and Maassen van den Brink, H., 2013. "Education and Youth Crime: a Review of the Empirical Literature," Working Papers 48, Top Institute for Evidence Based Education Research.
    13. Janke, Katharina & Johnston, David W. & Propper, Carol & Shields, Michael A., 2020. "The causal effect of education on chronic health conditions in the UK," Journal of Health Economics, Elsevier, vol. 70(C).
    14. Lindgren, Karl-Oskar & Oskarsson, Sven & Persson, Mikael, 2016. "How does access to education influence political candidacy? Lessons from school openings in Sweden," Working Paper Series 2016:7, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    15. Brugård, Kaja Høiseth & Falch, Torberg, 2013. "Post-compulsory education and imprisonment," Labour Economics, Elsevier, vol. 23(C), pages 97-106.
    16. Aoki, Yu, 2014. "More Schooling, Less Youth Crime? Learning from an Earthquake in Japan," IZA Discussion Papers 8619, Institute of Labor Economics (IZA).
    17. James, Jonathan, 2015. "Health and education expansion," Economics of Education Review, Elsevier, vol. 49(C), pages 193-215.

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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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