The relation between monotonicity and strategy-proofness
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
Volume (Year): 40 (2013)
Issue (Month): 1 (January)
|Contact details of provider:|| Web page: http://link.springer.de/link/service/journals/00355/index.htm|
|Order Information:||Web: http://link.springer.de/orders.htm|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Michel Breton & Vera Zaporozhets, 2009.
"On the equivalence of coalitional and individual strategy-proofness properties,"
Social Choice and Welfare,
Springer, vol. 33(2), pages 287-309, August.
- Le Breton, Michel & Zaporozhets, Vera, 2006. "On the Equivalence of Coalitional and Individual Strategy-Proofness Properties," IDEI Working Papers 408, Institut d'Économie Industrielle (IDEI), Toulouse.
- M. Fleurbaey & F. Maniquet, 1997. "Implementability and Horizontal Equity Imply No-Envy," Econometrica, Econometric Society, vol. 65(5), pages 1215-1220, September.
- Dolors Berga & Bernardo Moreno, 2008.
"Strategic Requirements with Indifference: Single-Peaked versus Single-Plateaued Preferences,"
2008-7, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
- Dolors Berga & Bernardo Moreno, 2009. "Strategic requirements with indifference: single-peaked versus single-plateaued preferences," Social Choice and Welfare, Springer, vol. 32(2), pages 275-298, February.
- Dolors Berga & Bernardo Moreno, 2007. "Strategic Requirements with Indifference: Single-Peaked versus Single-Plateaued Preferences," Working Papers 325, Barcelona Graduate School of Economics.
- H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
- Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
- Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
- Takamiya, Koji, 2007. "Domains of social choice functions on which coalition strategy-proofness and Maskin monotonicity are equivalent," Economics Letters, Elsevier, vol. 95(3), pages 348-354, June.
- Mark A. Satterthwaite & Hugo Sonnenschein, 1979. "Strategy-Proof Allocation Mechanisms," Discussion Papers 395, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Maskin, Eric, 1999.
"Nash Equilibrium and Welfare Optimality,"
Review of Economic Studies,
Wiley Blackwell, vol. 66(1), pages 23-38, January.
- Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
- David Cantala, 2004. "Choosing the level of a public good when agents have an outside option," Social Choice and Welfare, Springer, vol. 22(3), pages 491-514, 06.
- Dasgupta, Partha S & Hammond, Peter J & Maskin, Eric S, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 185-216, April.
- Takamiya, Koji, 2001. "Coalition strategy-proofness and monotonicity in Shapley-Scarf housing markets," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 201-213, March.
- Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
- Border, Kim C & Jordan, J S, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 153-70, January.
- Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Wiley Blackwell, vol. 48(4), pages 587-97, October.
- Koji Takamiya, 2003. "On strategy-proofness and essentially single-valued cores: A converse result," Social Choice and Welfare, Springer, vol. 20(1), pages 77-83.
When requesting a correction, please mention this item's handle: RePEc:spr:sochwe:v:40:y:2013:i:1:p:41-63. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn)or (Christopher F Baum)
If references are entirely missing, you can add them using this form.