On strategy-proofness and the salience of single-peakedness in a private goods economy

• Main Authors: CHATTERJI, Shurojit, MASSO Jordi, SERIZAWA Shigehiro
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2020
• Subjects: Strategy-proofness; semilattice single peakedness; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/2459; https://ink.library.smu.edu.sg/context/soe_research/article/3458/viewcontent/DP1112.pdf
• Institution: Singapore Management University

We consider strategy-proof rules operating on a rich domain of preference profiles in a set up where multiple private goods have to be assigned to a set of agents with entitlements where preferences display satiation. We show that if the rule is in addition "desirable", in that it is tops-only, continuous, same-sided and individually rational with respect to the entitlements, then the preferences in the domain have to satisfy a variant of single-peakedness (referred to as smilattice single-peakedness). We also provide a converse of this main finding. It turns our that this domain coincides with the one already identified in a general set up with a public good. Finally we relate semilattice single-peaked domains to well-known restricted domains under which strategy-proof and desirable rules do exist.