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Implementation with Partial Provability

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  • 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.

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2010-018.

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Length: 50 pages
Date of creation: Jan 2010
Date of revision:
Handle: RePEc:bos:wpaper:wp2010-018

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References

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  1. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  2. Itai Sher, 2008. "Persuasion and Limited Communication," Levine's Bibliography 122247000000002132, UCLA Department of Economics.
  3. Paul R. Milgrom, 1979. "Good Nevs and Bad News: Representation Theorems and Applications," Discussion Papers 407R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Lipman Barton L. & Seppi Duane J., 1995. "Robust Inference in Communication Games with Partial Provability," Journal of Economic Theory, Elsevier, vol. 66(2), pages 370-405, August.
  5. A. Rubinstein & J. Glazer, . "Debates and Decisions, On a Rationale of Argumentation Rules," Princeton Economic Theory Papers 00s7, Economics Department, Princeton University.
  6. Bull, Jesse & Watson, Joel, 2002. "Hard Evidence and Mechanism Design," University of California at San Diego, Economics Working Paper Series qt7715f08f, Department of Economics, UC San Diego.
  7. Grossman, S J & Hart, O D, 1980. " Disclosure Laws and Takeover Bids," Journal of Finance, American Finance Association, vol. 35(2), pages 323-34, May.
  8. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
  9. Ching-to Albert Ma & Ingela Alger, 1999. "Moral Hazard, Insurance and Some Collusion," FMG Discussion Papers dp318, Financial Markets Group.
  10. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
  11. Baliga, Sandeep, 1999. "Implementation in Economic Environments with Incomplete Information: The Use of Multi-Stage Games," Games and Economic Behavior, Elsevier, vol. 27(2), pages 173-183, May.
  12. Francoise Forges & Frédéric Koessler, 2006. "Long Persuasion Games," CESifo Working Paper Series 1669, CESifo Group Munich.
  13. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  14. Okuno-Fujiwara, Masahiro & Postlewaite, Andrew & Suzumura, Kotaro, 1990. "Strategic Information Revelation," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 25-47, January.
  15. Paul R. Milgrom & John Roberts, 1985. "Relying on the Information of Interested Parties," Cowles Foundation Discussion Papers 749, Cowles Foundation for Research in Economics, Yale University.
  16. Forges, Françoise & Koessler, Frédéric, 2005. "Communication equilibria with partially verifiable types," Economics Papers from University Paris Dauphine 123456789/168, Paris Dauphine University.
  17. Deneckere, Raymond & Severinov, Sergei, 2008. "Mechanism design with partial state verifiability," Games and Economic Behavior, Elsevier, vol. 64(2), pages 487-513, November.
  18. Kartik, Navin & Tercieux, Olivier, 2012. "Implementation with evidence," Theoretical Economics, Econometric Society, vol. 7(2), May.
  19. Abreu, Dilip & Sen, Arunava, 1990. "Subgame perfect implementation: A necessary and almost sufficient condition," Journal of Economic Theory, Elsevier, vol. 50(2), pages 285-299, April.
  20. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  21. Bull, Jesse & Watson, Joel, 2002. "Evidence Disclosure and Verfiability," University of California at San Diego, Economics Working Paper Series qt19p7z2gm, Department of Economics, UC San Diego.
  22. Green, Jerry R & Laffont, Jean-Jacques, 1986. "Partially Verifiable Information and Mechanism Design," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 447-56, July.
  23. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-42, November.
  24. Jacob Glazer & Ariel Rubinstein, 2004. "On Optimal Rules of Persuasion," Econometrica, Econometric Society, vol. 72(6), pages 1715-1736, November.
  25. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  26. Daniel J. Seidmann & Eyal Winter, 1997. "Strategic Information Transmission with Verifiable Messages," Econometrica, Econometric Society, vol. 65(1), pages 163-170, January.
  27. Rubinstein, Ariel & Glazer, Jacob, 2006. "A study in the pragmatics of persuasion: a game theoretical approach," Theoretical Economics, Econometric Society, vol. 1(4), pages 395-410, December.
  28. Fishman, Michael J & Hagerty, Kathleen M, 1990. "The Optimal Amount of Discretion to Allow in Disclosure," The Quarterly Journal of Economics, MIT Press, vol. 105(2), pages 427-44, May.
  29. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  30. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  31. Grossman, Sanford J, 1981. "The Informational Role of Warranties and Private Disclosure about Product Quality," Journal of Law and Economics, University of Chicago Press, vol. 24(3), pages 461-83, December.
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Citations

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Cited by:
  1. Itai Sher & Rakesh Vohra, 2011. "Price Discrimination Through Communication," Discussion Papers 1536, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
  3. Midjord, Rune, 2013. "Full implementation of rank-dependent prizes," Economics Letters, Elsevier, vol. 119(3), pages 261-263.
  4. Makoto Shimoji & Paul Schweinzer, 2012. "Implementation without Incentive Compatibility: Two Stories with Partially Informed Planners," Discussion Papers 12/21, Department of Economics, University of York.
  5. 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.
  6. Sher, Itai, 2014. "Persuasion and dynamic communication," Theoretical Economics, Econometric Society, vol. 9(1), January.

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