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Implementation with Partial Provability

  • Barton L. Lipman

    ()

    (Department of Economics, Boston University.)

  • Elchanan Ben-Porath

    ()

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

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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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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  1. Francoise Forges & Frédéric Koessler, 2006. "Long Persuasion Games," CESifo Working Paper Series 1669, CESifo Group Munich.
  2. Itai Sher, 2008. "Persuasion and Limited Communication," Levine's Bibliography 122247000000002132, UCLA Department of Economics.
  3. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  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. 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.
  6. Kartik, Navin & Tercieux, Olivier, 2012. "Implementation with evidence," Theoretical Economics, Econometric Society, vol. 7(2), May.
  7. 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.
  8. Alger, Ingela & Albert Ma, Ching-to, 2003. "Moral hazard, insurance, and some collusion," Journal of Economic Behavior & Organization, Elsevier, vol. 50(2), pages 225-247, February.
  9. Watson, Joel & Bull, Jesse, 2006. "Hard Evidence and Mechanism Design," University of California at San Diego, Economics Working Paper Series qt7973v805, Department of Economics, UC San Diego.
  10. 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.
  11. Jerry R. Green & Jean-Jacques Laffont, 1986. "Partially Verifiable Information and Mechanism Design," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 447-456.
  12. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  13. Forges, Francoise & Koessler, Frederic, 2005. "Communication equilibria with partially verifiable types," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 793-811, November.
  14. Andrew Postlewaite & David Wettstein, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 603-611.
  15. 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.
  16. Masahiro Okuno-Fujiwara & Andrew Postlewaite & Kotaro Suzumura, 1990. "Strategic Information Revelation," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 25-47.
  17. 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.
  18. 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.
  19. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  20. 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.
  21. repec:dau:papers:123456789/179 is not listed on IDEAS
  22. 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.
  23. Deneckere, Raymond & Severinov, Sergei, 2008. "Mechanism design with partial state verifiability," Games and Economic Behavior, Elsevier, vol. 64(2), pages 487-513, November.
  24. Michael J. Fishman & Kathleen M. Hagerty, 1990. "The Optimal Amount of Discretion to Allow in Disclosure," The Quarterly Journal of Economics, Oxford University Press, vol. 105(2), pages 427-444.
  25. 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.
  26. 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.
  27. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  28. Daniel J. Seidmann & Eyal Winter, 1997. "Strategic Information Transmission with Verifiable Messages," Econometrica, Econometric Society, vol. 65(1), pages 163-170, January.
  29. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
  30. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  31. repec:dau:papers:123456789/168 is not listed on IDEAS
  32. Jacob Glazer & Ariel Rubinstein, 2004. "On Optimal Rules of Persuasion," Econometrica, Econometric Society, vol. 72(6), pages 1715-1736, November.
  33. 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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