• Corpus ID: 251040207

Greedy Allocations and Equitable Matchings

@inproceedings{ValenzuelaStookey2022GreedyAA,
  title={Greedy Allocations and Equitable Matchings},
  author={Quitz'e Valenzuela-Stookey},
  year={2022}
}

• Quitz'e Valenzuela-Stookey
• Published 22 July 2022
• Economics

I study multi-item allocation problems when agents have capacity constraints. I first provide an approximate extension to the multi-item setting of Border’s characterization of realizable interim allocations. I identify necessary conditions for interim realizability, and show that these conditions are sufficient for realizability when the interim allocation in question is scaled by 12 . I then characterize a subset of the realizable polytope which contains all such scaled allocations. This polytope is generated by a majorization relationship between the scaled interim allocations and allocations induced by a certain “greedy algorithm”. I use these results to study mechanism design with equity concerns and model ambiguity. I also relate optimal mechanisms to the commonly used deferred acceptance and serial dictatorship matching algorithms. I provide conditions on the principal’s objective under which deferred acceptance is a 2-approximation to the optimal mechanism.