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On rank dominance of tie-breaking rules

Author

Listed:
  • Allman, Maxwell

    (Department Management Science and Engineering, Stanford University)

  • Ashlagi, Itai

    (Department Management Science and Engineering, Stanford University)

  • Nikzad, Afshin

    (Department of Economics, University of Southern California)

Abstract

Lotteries are a common way to resolve ties in assignment mechanisms that ration resources. We consider a model with a continuum of agents and a finite set of re- sources with heterogeneous qualities, where the agents’ preferences are generated from a multinomial-logit (MNL) model based on the resource qualities. We show that all agents prefer a common lottery to independent lotteries at each resource if every resource is popular, meaning that the mass of agents ranking that resource as their first choice exceeds its capacity. We then prove a stronger result where the assumption that every resource is popular is not required and agents’ preferences are drawn from a (more general) nested MNL model. By appropriately adapting the notion of popularity to resource types, we show that a hybrid tie-breaking rule in which the objects in each popular type share a common lottery dominates independent lotteries at each resource.

Suggested Citation

  • Allman, Maxwell & Ashlagi, Itai & Nikzad, Afshin, 2023. "On rank dominance of tie-breaking rules," Theoretical Economics, Econometric Society, vol. 18(2), May.
    • Handle: RePEc:the:publsh:4762
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    References listed on IDEAS

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    1. Kenny Peng & Nikhil Garg, 2023. "Monoculture in Matching Markets," Papers 2312.09841, arXiv.org.

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    More about this item

    Keywords

    Matching; deferred acceptance; tiebreaking;
    All these keywords.

    JEL classification:

    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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