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Dynamic Combinatorial Assignment

Author

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  • Th`anh Nguyen
  • Alexander Teytelboym
  • Shai Vardi

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.

Suggested Citation

  • Th`anh Nguyen & Alexander Teytelboym & Shai Vardi, 2023. "Dynamic Combinatorial Assignment," Papers 2303.13967, arXiv.org.
    • Handle: RePEc:arx:papers:2303.13967
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    References listed on IDEAS

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