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Optimal mechanism design for the private supply of a public good

Author

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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.

Suggested Citation

  • Csapó, Gergely & Müller, Rudolf, 2013. "Optimal mechanism design for the private supply of a public good," Games and Economic Behavior, Elsevier, vol. 80(C), pages 229-242.
  • Handle: RePEc:eee:gamebe:v:80:y:2013:i:c:p:229-242
    DOI: 10.1016/j.geb.2013.03.014
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    References listed on IDEAS

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    More about this item

    Keywords

    Public good provision; Mechanism design; Profit maximization;

    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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