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Implementation with partial provability

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  • Ben-Porath, Elchanan
  • Lipman, Barton L.

Abstract

We extend implementation theory by allowing the social choice function to depend on more than just the preferences of the agents and allowing agents to support their statements with hard evidence. We show that a simple condition on evidence is necessary for the implementation of a social choice function f when the preferences of the agents are state independent and sufficient for implementation for any preferences (including state dependent) with at least three agents if the social planner can perform small monetary transfers beyond those called for by f. If transfers can be large, f can be implemented in a game with perfect information when there are at least two players under a boundedness assumption. For both results, transfers only occur out of equilibrium. The use of evidence enables implementation which is robust in the sense that the planner needs little information about agentsʼ preferences or beliefs and agents need little information about each othersʼ preferences. Our results are robust to evidence forgery at any strictly positive cost.

Suggested Citation

  • Ben-Porath, Elchanan & Lipman, Barton L., 2012. "Implementation with partial provability," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1689-1724.
  • Handle: RePEc:eee:jetheo:v:147:y:2012:i:5:p:1689-1724
    DOI: 10.1016/j.jet.2012.01.017
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Caffera, Marcelo & Dubra, Juan & Figueroa, Nicolás, 2018. "Mechanism design when players’ preferences and information coincide," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 56-61.
    2. Shimoji, Makoto & Schweinzer, Paul, 2015. "Implementation without incentive compatibility: Two stories with partially informed planners," Games and Economic Behavior, Elsevier, vol. 91(C), pages 258-267.
    3. Sergiu Hart & Ilan Kremer & Motty Perry, 2017. "Evidence Games: Truth and Commitment," American Economic Review, American Economic Association, vol. 107(3), pages 690-713, March.
    4. Sher, Itai & Vohra, Rakesh, 2015. "Price discrimination through communication," Theoretical Economics, Econometric Society, vol. 10(2), May.
    5. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
    6. Ben-Porath, Elchanan & Lipman, Barton L., 2012. "Implementation with partial provability," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1689-1724.
    7. Konrad Stahl & Roland Strausz, 2017. "Certification and Market Transparency," Review of Economic Studies, Oxford University Press, vol. 84(4), pages 1842-1868.
    8. Hitoshi Matsushima, 2017. "Dynamic Implementation, Verification, and Detection," CARF F-Series CARF-F-416, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Midjord, Rune, 2012. "Full Implementation of Rank Dependent Prizes," DFAEII Working Papers 2012-15, University of the Basque Country - Department of Foundations of Economic Analysis II.
    10. Sher, Itai, 2014. "Persuasion and dynamic communication," Theoretical Economics, Econometric Society, vol. 9(1), January.
    11. Midjord, Rune, 2013. "Full implementation of rank-dependent prizes," Economics Letters, Elsevier, vol. 119(3), pages 261-263.
    12. Hitoshi Matsushima, 2015. "Implementation, Verification, and Detection," CIRJE F-Series CIRJE-F-991, CIRJE, Faculty of Economics, University of Tokyo.

    More about this item

    Keywords

    Implementation; Hard evidence; Mechanism design;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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