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The relation between monotonicity and strategy-proofness

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  • Bettina Klaus

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  • Olivier Bochet

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Abstract

The Muller–Satterthwaite Theorem (J Econ Theory 14:412–418, 1977 ) establishes the equivalence between Maskin monotonicity and strategy-proofness, two cornerstone conditions for the decentralization of social choice rules. We consider a general model that covers public goods economies as in Muller–Satterthwaite (J Econ Theory 14:412–418, 1977 ) as well as private goods economies. For private goods economies, we use a weaker condition than Maskin monotonicity that we call unilateral monotonicity. We introduce two easy-to-check preference domain conditions which separately guarantee that (i) unilateral/Maskin monotonicity implies strategy-proofness (Theorem 1) and (ii) strategy-proofness implies unilateral/Maskin monotonicity (Theorem 2). We introduce and discuss various classical single-peaked preference domains and show which of the domain conditions they satisfy (see Propositions 1 and 2 and an overview in Table 1). As a by-product of our analysis, we obtain some extensions of the Muller–Satterthwaite Theorem as summarized in Theorem 3. We also discuss some new “Muller–Satterthwaite preference domains” (e.g., Proposition 3). Copyright The Author(s) 2013

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  • 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.
  • Handle: RePEc:spr:sochwe:v:40:y:2013:i:1:p:41-63
    DOI: 10.1007/s00355-011-0586-6
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    Cited by:

    1. William Thomson, 2016. "Non-bossiness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 665-696, October.
    2. Massó, Jordi & Moreno de Barreda, Inés, 2011. "On strategy-proofness and symmetric single-peakedness," Games and Economic Behavior, Elsevier, vol. 72(2), pages 467-484, June.
    3. Ryan Tierney, 2016. "The problem of multiple commons: A market design approach," ISER Discussion Paper 0986, Institute of Social and Economic Research, Osaka University.
    4. 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.
    5. 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.
    6. Bochet Olivier & Storcken Ton, 2006. "Maximal Domains for Strategy-Proof or Maskin Monotonic Choice Rules," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    7. Diss, Mostapha & Doghmi, Ahmed & Tlidi, Abdelmonaim, 2015. "Strategy proofness and unanimity in private good economies with single-peaked preferences," MPRA Paper 75469, University Library of Munich, Germany, revised 06 Dec 2016.
    8. 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.
    9. Felix Brandt, 2015. "Set-monotonicity implies Kelly-strategyproofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 793-804, December.
    10. Uuganbaatar Ninjbat, 2012. "Symmetry vs. complexity in proving the Muller-Satterthwaite theorem," Economics Bulletin, AccessEcon, vol. 32(2), pages 1434-1441.
    11. Cato, Susumu, 2011. "Maskin monotonicity and infinite individuals," Economics Letters, Elsevier, vol. 110(1), pages 56-59, January.

    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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