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Implementation with Partial Provability

Author

Listed:
  • Barton L. Lipman

    () (Department of Economics, Boston University.)

  • Elchanan Ben-Porath

    () (Department of Economics and Center for Rationality, Hebrew University.)

Abstract

We extend implementation theory by allowing the social choice function to depend on more than just the profile of preferences of the agents and by allowing agents to support their statements with hard evidence. We show that a simple condition on the evidence structure which is necessary for the implementation of a social choice function f when the preferences of the agents are state independent is also sufficient for implementation for any preferences (including state dependent) if the social planner can perform small monetary transfers beyond those called for by f and there are at least three players. If transfers can be large, f can be implemented in a game with perfect information when there are at least two players under an additional boundedness assumption. In both cases, transfers only occur off the equilibrium path. In the special but important case of allocation problems, under weak conditions, f can be implemented in a perfect information game with at least two players and no transfers. In all cases, the use of evidence enables implementation which is robust in the sense that the social planner needs very little information about the preferences, beliefs, and evidence of the agents and the agents need little information about each others' preferences. Furthermore, our results still hold if evidence can be forged at an arbitrarily small but strictly positive cost. Finally, we relate our results to the classical work of Maskin (1977) and Moore and Repullo (1988) on implementation without evidence.

Suggested Citation

  • Barton L. Lipman & Elchanan Ben-Porath, 2010. "Implementation with Partial Provability," Boston University - Department of Economics - Working Papers Series WP2010-018, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2010-018
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    References listed on IDEAS

    as
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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. Sher, Itai & Vohra, Rakesh, 2015. "Price discrimination through communication," Theoretical Economics, Econometric Society, vol. 10(2), May.
    3. Konrad Stahl & Roland Strausz, 2017. "Certification and Market Transparency," Review of Economic Studies, Oxford University Press, vol. 84(4), pages 1842-1868.
    4. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
    5. 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.
    6. 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.
    7. 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.
    8. Midjord, Rune, 2013. "Full implementation of rank-dependent prizes," Economics Letters, Elsevier, vol. 119(3), pages 261-263.
    9. Hitoshi Matsushima, 2015. "Implementation, Verification, and Detection," CIRJE F-Series CIRJE-F-991, CIRJE, Faculty of Economics, University of Tokyo.
    10. Ben-Porath, Elchanan & Lipman, Barton L., 2012. "Implementation with partial provability," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1689-1724.
    11. Hitoshi Matsushima, 2018. "Implementation without Expected Utility: Ex-Post Verifiability," CARF F-Series CARF-F-443, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    12. 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.
    13. Sher, Itai, 2014. "Persuasion and dynamic communication," Theoretical Economics, Econometric Society, vol. 9(1), January.

    More about this item

    JEL classification:

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

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