Local Priority Mechanisms

TL;DR

This paper introduces local priority mechanisms, a flexible framework for constrained allocation problems, unifying several known mechanisms and providing new insights into their properties and strategy-proofness.

Contribution

It defines local priority mechanisms, characterizes them axiomatically, and shows how many classic mechanisms are special cases, offering new tools for designing and analyzing constrained allocations.

Findings

Local priority mechanisms exist for any constraint type.

Several well-known mechanisms are instances of local priority mechanisms.

Conditions for group strategy-proofness and welfare comparisons are established.

Abstract

We introduce a novel family of mechanisms for constrained allocation problems which we call local priority mechanisms. These mechanisms are parameterized by a function which assigns a set of agents, the local compromisers, to every infeasible allocation. The mechanism then greedily attempts to match agents with their top choices. Whenever it reaches an infeasible allocation, the local compromisers move to their next favorite alternative. Local priority mechanisms exist for any constraint, so this provides a method of constructing new designs for any constrained allocation problem. We give axioms which characterize local priority mechanisms. Since constrained allocation includes many canonical problems as special constraints, we apply this characterization to show that several well-known mechanisms, including deferred acceptance for school choice, top trading cycles for house allocation, and serial dictatorship can be understood as instances of local priority mechanisms. Other mechanisms, including the Boston mechanism, are not local priority mechanisms. We give sufficient conditions for a local priority mechanism to be group strategy-proof. We also provide conditions which enable welfare comparisons across local priority mechanisms.