Dynamic Combinatorial Assignment

TL;DR

This paper introduces a new dynamic assignment model and mechanism that ensures approximate market clearing over time without money, with applications in refugee resettlement, daycare, and airport slots.

Contribution

It develops the DACEEI concept and the OCAM mechanism, ensuring high-probability market clearing and strategic properties in dynamic, indivisible object assignment.

Findings

OCAM is group-strategyproof up to one object

OCAM is envy-free up to one object for most agents

Markets clear approximately in most periods with high probability

Abstract

We study a model of dynamic combinatorial assignment of indivisible objects without money. We introduce a new solution concept called ``dynamic approximate competitive equilibrium from equal incomes'' (DACEEI), which stipulates that markets must approximately clear in almost all time periods. A naive repeated application of approximate competitive equilibrium from equal incomes (Budish, 2011) does not yield a desirable outcome because the approximation error in market-clearing compounds quickly over time. We therefore develop a new version of the static approximate competitive equilibrium from carefully constructed random budgets which ensures that, in expectation, markets clear exactly. We then use it to design the ``online combinatorial assignment mechanism'' (OCAM) which implements a DACEEI with high probability. The OCAM is (i) group-strategyproof up to one object (ii) envy-free up to one object for almost all agents (iii) approximately market-clearing in almost all periods with high probability when the market is large and arrivals are random. Applications include refugee resettlement, daycare assignment, and airport slot allocation.