RIEB Discussion Paper Series No.2022-25

Title

Coordinated Strategic Manipulations and Mechanisms in School Choice*

Abstract

This study observes that no group strategy-proof mechanism satisfies even a fairly weak notion of stability in a school choice setting. In response to this result, we introduce two monotonicity axioms, which we call top-dropping monotonicity and extension monotonicity, as alternatives to group strategy-proofness. We prove that these two axioms are equivalent to the requirement that no group of students gains from a simple manipulation of their preferences. Replacing group strategy-proofness with the two axioms, we find that the Kesten's (2010) efficiency adjusted deferred acceptance mechanism is the unique mechanism satisfying the three criteria. We also provide several applications of the two monotonicity axioms, finding axiomatic characterizations of the deferred acceptance mechanism and a class of mechanisms in which stability and strategy-proofness are equivalent.

Keywords

Matching; School choice; Strategy-proofness; Group strategy-proofness; Monotonicity; Deferred acceptance; Efficiency adjusted deferred acceptance

JEL Classification

C78, D47

Inquiries

Ryo SHIRAKAWA
Graduate School of Economics, The Univerity of Tokyo
Junior Research Fellow, RIEB, Kobe University

*This Discussion Paper won the Kanematsu Prize (FY 2021).