Strategy-Proofness Makes the Difference: Deferred-Acceptance with Responsive Priorities

Abstract

In college admissions and student placements at public schools, the admission decision can be thought of as assigning indivisible objects with capacity constraints to a set of students such that each student receives at most one object and monetary compensations are not allowed. In these important market design problems, the agent-proposing deferred-acceptance (DA-)mechanism with responsive strict priorities performs well and economists have successfully implemented DA-mechanisms or slight variants thereof. We show that almost all real-life mechanisms used in such environments-including the large classes of priority mechanisms and linear programming mechanisms-satisfy a set of simple and intuitive properties. Once we add strategy-proofness to these properties, DA-mechanisms are the only ones surviving. In market design problems that are based on weak priorities (like school choice), generally multiple tie-breaking (MTB) procedures are used and then a mechanism is implemented with the obtained strict priorities. By adding stability with respect to the weak priorities, we establish the first normative foundation for MTB-DA-mechanisms that are used in NYC. JEL Classification: D63, D70

Object allocation via deferred-acceptance: Strategy-proofness and comparative statics

“…2 Our allocation model is identical to that described in Ehlers and Klaus (2014). 3 Our results remain unchanged when O is infinite.…”

“…Ehlers and Klaus (2014) characterize the smaller class of responsive DA-mechanisms whereby each choice function is based on a strict order and chooses from any set of agents the k most preferred elements. In their main result, "two-agent consistent conflict resolution" plays a key role which says that at maximal conflict situations always the same agent should win the conflict (or receive the object).…”

Matching under Preferences

“…This theorem for hr is an extension of an earlier corresponding theorem for sm (Dubins and Freedman, 1981;Roth, 1982b). Strategy-proofness for all residents also turns out to be a key property in characterising the RGS mechanism (Ehlers and Klaus, 2014): almost all real-life mechanisms used in variants of hr (including sc) -including the large classes of priority mechanisms and linear programming mechanisms -satisfy a set of simple and intuitive properties, but once strategy-proofness is added to these properties, the RGS mechanism is the only one surviving (and characterised by the respective properties including strategy-proofness). For sc, since residents (aka students) are the only economic agents, Theorem 9 in fact establishes a possibility result.…”

On Capacity-Filling and Substitutable Choice Rules

“…6 Chambers and Yenmez (2017) use the MC representation of path independent choice rules to provide a new proof of a classical existence result for stable matching and a new result on welfare effects of expanding the choice rules in the matching context. Kojima and Manea (2010), Ehlers and Klaus (2014), and Ehlers and Klaus (2016) characterize deferred acceptance mechanisms where each school has a choice rule that satisfies capacity-filling and substitutability. Although the structure of capacityfilling and substitutable choice rules and their relation to matching mechanisms have been extensively studied, there is no direct implication of these studies for our con-struction of priority orderings that render a smallest size MC representation.…”