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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. Jacob Glazer & Ariel Rubinstein, 2004. "On Optimal Rules of Persuasion," Econometrica, Econometric Society, vol. 72(6), pages 1715-1736, November.
  2. F. Forges & Frederic Koessler, 2003. "Communication Equilibria with Partially Verifiable Types," THEMA Working Papers 2003-10, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  3. Glazer, Jacob & Rubinstein, Ariel, 2001. "Debates and Decisions: On a Rationale of Argumentation Rules," Games and Economic Behavior, Elsevier, vol. 36(2), pages 158-173, August.
  4. Kartik, Navin & Tercieux, Olivier, 2012. "Implementation with evidence," Theoretical Economics, Econometric Society, vol. 7(2), May.
  5. Ching-to Albert Ma & Ingela Alger, 1999. "Moral Hazard, Insurance and Some Collusion," FMG Discussion Papers dp318, Financial Markets Group.
  6. Francoise Forges & Frédéric Koessler, 2006. "Long Persuasion Games," CESifo Working Paper Series 1669, CESifo Group Munich.
  7. Bull, Jesse & Watson, Joel, 2007. "Hard evidence and mechanism design," Games and Economic Behavior, Elsevier, vol. 58(1), pages 75-93, January.
  8. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
  9. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  10. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  11. Bull, Jesse & Watson, Joel, 2000. "Evidence Disclosure and Verifiability," University of California at San Diego, Economics Working Paper Series qt6th0060j, Department of Economics, UC San Diego.
  12. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  13. Deneckere, Raymond & Severinov, Sergei, 2008. "Mechanism design with partial state verifiability," Games and Economic Behavior, Elsevier, vol. 64(2), pages 487-513, November.
  14. Itai Sher, 2008. "Persuasion and Limited Communication," Levine's Bibliography 122247000000002132, UCLA Department of Economics.
  15. 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.
  16. Sanford Grossman & Oliver Hart, . "Disclosure Laws and Takeover Bids," Rodney L. White Center for Financial Research Working Papers 23-79, Wharton School Rodney L. White Center for Financial Research.
  17. Paul Milgrom & John Roberts, 1986. "Relying on the Information of Interested Parties," RAND Journal of Economics, The RAND Corporation, vol. 17(1), pages 18-32, Spring.
  18. Daniel J. Seidmann & Eyal Winter, 1997. "Strategic Information Transmission with Verifiable Messages," Econometrica, Econometric Society, vol. 65(1), pages 163-170, January.
  19. 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.
  20. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  21. 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.
  22. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  23. Dutta, Bhaskar & Sen, Arunava, 2009. "Nash Implementation with Partially Honest Individuals," The Warwick Economics Research Paper Series (TWERPS) 920, University of Warwick, Department of Economics.
  24. 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.
  25. 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.
  26. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
  27. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  28. Okuno-Fujiwara, Masahiro & Postlewaite, Andrew & Suzumura, Kotaro, 1990. "Strategic Information Revelation," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 25-47, January.
  29. 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.
  30. 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.
  31. 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.
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Citations

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Cited by:
  1. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
  2. Sher, Itai & Vohra, Rakesh, 0. "Price discrimination through communication," Theoretical Economics, Econometric Society.
  3. 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.
  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. Sher, Itai, 2014. "Persuasion and dynamic communication," Theoretical Economics, Econometric Society, vol. 9(1), January.
  6. Midjord, Rune, 2013. "Full implementation of rank-dependent prizes," Economics Letters, Elsevier, vol. 119(3), pages 261-263.

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