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Nash implementation in private good economies with single-plateaued preferences and in matching problems

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  • Doghmi, Ahmed
  • Ziad, Abderrahmane

Abstract

In this paper we explore the problem of Nash implementation providing two new properties called I-monotonicity and I-weak no-veto power. These properties form together with unanimity a new sufficient condition for a social choice correspondence to be implementable in Nash equilibria with at least three agents. As applications, we prove that: (1) In private good economies with single-plateaued preferences, each solution of the problem of fair division that has a full range is Nash implementable if and only if it satisfies Maskin monotonicity, (2) In matching problems, Maskin monotonicity is a necessary and sufficient condition for implementation.

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  • Doghmi, Ahmed & Ziad, Abderrahmane, 2015. "Nash implementation in private good economies with single-plateaued preferences and in matching problems," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 32-39.
    • Handle: RePEc:eee:matsoc:v:73:y:2015:i:c:p:32-39
    DOI: 10.1016/j.mathsocsci.2014.11.002
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    1. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
    2. William Thomson, 2010. "Implementation of solutions to the problem of fair division when preferences are single-peaked," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 1-15, March.
    3. Matsushima, Hitoshi, 2008. "Role of honesty in full implementation," Journal of Economic Theory, Elsevier, vol. 139(1), pages 353-359, March.
    4. Bossert, Walter & Peters, Hans, 2014. "Single-basined choice," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 162-168.
    5. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    6. Lars Ehlers, 2002. "Strategy-proof allocation when preferences are single-plateaued," Review of Economic Design, Springer;Society for Economic Design, vol. 7(1), pages 105-115.
    7. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    8. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Reexamination of Maskin's Theorem on Nash implementability," Economics Letters, Elsevier, vol. 100(1), pages 150-152, July.
    9. Claus-Jochen Haake & Bettina Klaus, 2009. "Monotonicity and Nash implementation in matching markets with contracts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 393-410, December.
    10. Bossert, Walter & Peters, Hans, 2013. "Single-plateaued choice," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 134-139.
    11. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    12. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(1), pages 151-159, February.
    13. Matsushima, Hitoshi, 2008. "Behavioral aspects of implementation theory," Economics Letters, Elsevier, vol. 100(1), pages 161-164, July.
    14. Doghmi Ahmed & Ziad Abderrahmane, 2013. "On Partially Honest Nash Implementation in Private Good Economies with Restricted Domains: A Sufficient Condition," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 415-428, September.
    15. Lombardi, Michele & Yoshihara, Naoki & 吉原, 直毅, 2011. "Partially-honest Nash implementation: Characterization results," CCES Discussion Paper Series 43, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
    16. Ziad, Abderrahmane, 1998. "A new necessary condition for Nash implementation," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 381-387, May.
    17. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 197-218.
    18. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    19. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    20. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
    21. Dolors Berga & Bernardo Moreno, 2009. "Strategic requirements with indifference: single-peaked versus single-plateaued preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 275-298, February.
    22. Sonmez, Tayfun, 1996. "Implementation in generalized matching problems," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 429-439.
    23. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(5), pages 687-698, October.
    24. Korpela, Ville, 2010. "Nash implementation theory -- A note on full characterizations," Economics Letters, Elsevier, vol. 108(3), pages 283-285, September.
    25. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    26. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Nash implementation in exchange economies with single-peaked preferences," Economics Letters, Elsevier, vol. 100(1), pages 157-160, July.
    27. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(3), pages 381-386, June.
    28. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(4), pages 525-537, August.
    29. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(2), pages 285-292, April.
    30. Bhaskar Dutta & Arunava Sen, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 121-128.
    31. Bettina Klaus & Olivier Bochet, 2013. "The relation between monotonicity and strategy-proofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 41-63, January.
    32. Ziad, Abderrahmane, 1997. "On the necessary and sufficient conditions for Nash implementation," Economics Letters, Elsevier, vol. 56(2), pages 209-213, October.
    33. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
    34. Tadenuma, Koichi & Toda, Manabu, 1998. "Implementable stable solutions to pure matching problems," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 121-132, March.
    35. Ahmed Doghmi & Abderrahmane Ziad, 2013. "Nash Implementation in Private Good Economies with Single-Plateaued Preferences," Economics Working Paper Archive (University of Rennes & University of Caen) 201311, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    36. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February.
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    Cited by:

    1. Mostapha Diss & Ahmed Doghmi & Abdelmonaim Tlidi, 2015. "Strategy proofness and unanimity in private good economies with single-peaked preferences," Working Papers halshs-01226803, HAL.
    2. Diss, Mostapha & Doghmi, Ahmed & Tlidi, Abdelmonaim, 2016. "Strategy proofness and unanimity in many-to-one matching markets," MPRA Paper 75927, University Library of Munich, Germany, revised 08 Dec 2016.
    3. Doghmi Ahmed, 2016. "On Nash Implementability in Allotment Economies under Domain Restrictions with Indifference," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(2), pages 767-795, June.
    4. Michele Lombardi & Foivos Savva & Nikolas Zivanas, 2023. "Implementation in strong core by codes of rights," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(3), pages 503-515, April.
    5. Hagiwara, Makoto, 2019. "Double implementation without no-veto-power," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 124-130.

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