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Two-agent Nash implementation with partially-honest agents: Almost Full Characterizations

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  • Lombardi, Michele

Abstract

In a two-agent society with partially-honest agents, we extend Dutta and Sen (2009)'s results of Nash implementation to the domain of weak orders. We identify the class of Nash implementable social choice correspondences with a "gap" between necessary and sufficient conditions, both when exactly one agent is partially-honest and when both agents are partially-honest. We also show that, on the domain of linear orders, the "gap" between our conditions gets closed and they become equivalent to those devised by Dutta and Sen. New implementing mechanisms are devised. In line with earlier works, the classic condition of monotonicity is no longer required, whereas a weak version of the standard punishment condition is required even when both agents are known to be partially-honest. We derive simpler sufficient conditions that are satisfied in a wide range of applications.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 27834.

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Date of creation: 22 Dec 2010
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Handle: RePEc:pra:mprapa:27834

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Keywords: Two-agent Nash implementation; intrinsic preferences for honesty; permissive results;

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  1. Elisha A. Pazner & David Schmeidler, 1975. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 174, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, Springer, vol. 18(4), pages 655-708.
  3. Matsushima, Hitoshi, 2008. "Role of honesty in full implementation," Journal of Economic Theory, Elsevier, Elsevier, vol. 139(1), pages 353-359, March.
  4. 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.
  5. Lombardi, Michele & Yoshihara, Naoki, 2011. "A Full Characterization of Nash Implementation with Strategy Space Reduction," Discussion Paper Series, Institute of Economic Research, Hitotsubashi University a548, Institute of Economic Research, Hitotsubashi University.
  6. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, Econometric Society, vol. 58(5), pages 1083-99, September.
  7. Francesca Busetto & Giulio Codognato, 2009. "Reconsidering two-agent Nash implementation," Social Choice and Welfare, Springer, Springer, vol. 32(2), pages 171-179, February.
  8. Hannu Vartiainen, 2007. "Nash implementation and the bargaining problem," Social Choice and Welfare, Springer, Springer, vol. 29(2), pages 333-351, September.
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Cited by:
  1. Ahmed Doghmi & Abderrahmane ZIAD, 2012. "On Partial Honesty Nash Implementation," Economics Working Paper Archive (University of Rennes 1 & University of Caen), Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS 201201, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.

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