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Nash Implementation with Partially Honest Individuals

  • Dutta, Bhaskar

    (Department of Economics, University of Warwick)

  • Sen, Arunava

    (Planning Unit, Indian Statistical Institute)

We investigate the problem of Nash implementation in the presence of "partially honest" individuals. A partially honest player is one who has a strict preference for revealing the true state over lying when truthtelling does not lead to a worse outcome (according to preferences in the true state) than that which obtains when lying. We show that when there are at least three individuals, the presence of even a single partially honest individual (whose identity is not known to the planner) can lead to a dramatic increase in the class of Nash implementable social choice correspondences. In particular, all social choice correspondences satisfying No Veto Power can be implemented. We also provide necessary and sufficient conditions for implementation in the two-person case when there is exactly one partially honest individual and when both individuals are partially honest. We describe some implications of the characterization conditions for the two-person case. Finally, we extend our three or more individual result to the case where there is an individual with an arbitrary small but strictly positive probability of being partially honest.

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File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2009/twerp_920.pdf
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Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 920.

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Date of creation: 2009
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Handle: RePEc:wrk:warwec:920
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  1. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
  2. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  3. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September.
  4. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-93, November.
  5. Matthew, Jackson O. & Palfrey, Thomas R. & Srivastava, Sanjay., 1990. "Undominated Nash Implementation in Bounded Mechanism," Working Papers 754, California Institute of Technology, Division of the Humanities and Social Sciences.
  6. Fehr, Ernst & Schmidt, Klaus M., . "A theory of fairness, competition, and cooperation," Chapters in Economics, University of Munich, Department of Economics.
  7. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  8. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," Discussion Paper Series 555, Institute of Economic Research, Hitotsubashi University.
  9. Luis Corchón & Carmen Herrero Blanco, 1995. "A Decent Proposal," Working Papers. Serie AD 1995-25, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  10. Shigehiro Serizawa & John A. Weymark, 2002. "Efficient Strategy-Proof Exchange and Minimum Consumption Guarantees," Vanderbilt University Department of Economics Working Papers 0216, Vanderbilt University Department of Economics, revised Aug 2002.
  11. Sjostrom, T., 1991. "Implementation in Undominated Nash Equilibria without Integer Games," Papers 491, Stockholm - International Economic Studies.
  12. Hitoshi Matsushima, 2007. "Behavioral Aspects of Implementation Theory," CIRJE F-Series CIRJE-F-523, CIRJE, Faculty of Economics, University of Tokyo.
  13. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 59(4), pages 757-75, October.
  14. Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. M. Rabin, 2001. "Incorporating Fairness into Game Theory and Economics," Levine's Working Paper Archive 511, David K. Levine.
  16. Kartik, Navin & Tercieux, Olivier, 2012. "Implementation with evidence," Theoretical Economics, Econometric Society, vol. 7(2), May.
  17. Hurwicz, Leonid & Schmeidler, David, 1978. "Construction of Outcome Functions Guaranteeing Existence and Pareto Optimality of Nash Equilibria," Econometrica, Econometric Society, vol. 46(6), pages 1447-74, November.
  18. Hitoshi Matsushima, 2006. "Role of Honesty in Full Implementation," CIRJE F-Series CIRJE-F-405, CIRJE, Faculty of Economics, University of Tokyo.
  19. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  20. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  21. Saijo, Tatsuyoshi, 1987. "On constant maskin monotonic social choice functions," Journal of Economic Theory, Elsevier, vol. 42(2), pages 382-386, August.
  22. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
  23. Kahneman, Daniel & Knetsch, Jack L & Thaler, Richard, 1986. "Fairness as a Constraint on Profit Seeking: Entitlements in the Market," American Economic Review, American Economic Association, vol. 76(4), pages 728-41, September.
  24. Dutta, Bhaskar & Sen, Arunava, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," Review of Economic Studies, Wiley Blackwell, vol. 58(1), pages 121-28, January.
  25. Francesca Busetto & Giulio Codognato, 2009. "Reconsidering two-agent Nash implementation," Social Choice and Welfare, Springer, vol. 32(2), pages 171-179, February.
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