TY - JOUR
T1 - The relation between monotonicity and strategy-proofness
AU - Klaus, Bettina
AU - Bochet, Olivier
N1 - Funding Information:
The authors thank William Thomson and two anonymous referees for their very valuable comments. B. Klaus thank the Netherlands Organisation for Scientific Research (NWO) for its support under grant VIDI-452-06-013. O. Bochet thank the Swiss National Science Foundation (SNF) and the Netherlands Organisation for Scientific Research (NWO) for their support under, respectively, grants SNF-100014-126954 and VENI-451-07-021.
PY - 2013/1
Y1 - 2013/1
N2 - 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).
AB - 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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U2 - 10.1007/s00355-011-0586-6
DO - 10.1007/s00355-011-0586-6
M3 - Article
AN - SCOPUS:84872356163
SN - 0176-1714
VL - 40
SP - 41
EP - 63
JO - Social Choice and Welfare
JF - Social Choice and Welfare
IS - 1
ER -