Another Characterisation of Deferred Acceptance

Abstract

We present a new characterisation of the agent-proposing deferred acceptance (APDA) rule (Gale and Shapley, 1962) in models of school choice. This is based on the notion of 'influence', introduced in Raghavan (2018), that agents may have on each other's welfare under bossy allocation rules. When priorities are substitutable, we show that the APDA rule is the unique strategy-proof, bossy, and unanimous allocation rule to satisfy weak mutual-best and three influence-related properties: acyclicity, positivity, and displacement. This result contributes to the literature on strategy-proofness for agents of the APDA rule, and is also the first characterisation in terms of bossiness.

Keywords: Deferred Acceptance, School Choice, Characterisation, Strategy-Proofness, Bossiness, Influence, Monotonicity

JEL Classification: C71, D78