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—Sa...
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Veröffentlicht in: | Social choice and welfare 2013-01, Vol.40 (1), p.41-63 |
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Sprache: | eng |
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Zusammenfassung: | 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). |
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ISSN: | 0176-1714 1432-217X |
DOI: | 10.1007/s00355-011-0586-6 |