Subgame perfect equilibria under the deferred acceptance algorithm

Yasushi Kawase, Keisuke Bando

Research output: Contribution to journalArticlepeer-review

Abstract

We analyze a subgame perfect equilibrium (SPE) of an extensive game with perfect information induced by the firm-oriented deferred acceptance (DA) algorithm in a one-to-one matching market between firms and workers. Our game repeats the following procedure until every firm in the market has a partner: (i) an unmatched firm strategically decides to which worker to make an offer or to exit the market, and (ii) the worker receiving the offer strategically decides whether to tentatively accept or reject it. When no agents are strategic, the resulting outcome is the firm-optimal stable matching. We show that the worker-optimal stable matching is the unique SPE outcome when only workers are strategic. By contrast, multiple SPE outcomes may exist, possibly including unstable matchings when only firms are strategic. We show that every firm weakly prefers any SPE outcome to the worker-optimal stable matching and that the matching induced by Kesten’s efficiency-adjusted DA algorithm can be achieved as an SPE. When both workers and firms are strategic, we also show that the worker-optimal stable matching is still the unique SPE outcome.

Original languageEnglish
Pages (from-to)503-546
Number of pages44
JournalInternational Journal of Game Theory
Volume50
Issue number2
DOIs
Publication statusPublished - 2021 Jun
Externally publishedYes

Keywords

  • Deferred acceptance algorithm
  • Subgame perfect equilibrium
  • Two-sided matching

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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