Université de Lausanne
Faculté des HEC
Département d'économétrie et d'économie politique

Cahier de recherches économiques du DEEP No. 10.01
Bettina Klaus and Olivier Bochet

The Relation between Monotonicity and Strategy-Proofness

January 2010

Abstract
The Muller-Satterthwaite Theorem (Muller and Satterthwaite, 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 and Satterthwaite (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 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 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 domains" (e.g.,Proposition 3).

Keywords: Muller-Satterthwaite Theorem; restricted domains; rich domains; single-peaked domains; strategy-proofness; unilateral/Maskin monotonicity.

JEL classification: D71