Subgame Perfect Equilibria Under the Deferred Acceptance Algorithm

25 Pages Posted: 29 Aug 2018

See all articles by Yasushi Kawase

Yasushi Kawase

Tokyo Institute of Technology

Keisuke Bando

Shinshu University

Date Written: August 20, 2018

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. 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 a SPE. When both workers and firms are strategic, we also show that the worker-optimal stable matching is still the unique SPE outcome. Hence, the strategic behavior of workers yields the worker-optimal stable matching in a dynamic implementation of the firm-oriented DA algorithm. Our results reveal that the workers strategic behavior yields a reversal property in a dynamic implementation of the firm-oriented DA algorithm.

Keywords: Two-Sided Matching, Deferred Acceptance Algorithm, Subgame Perfect Equilibrium, Reversal Property

JEL Classification: C70, C78

Suggested Citation

Kawase, Yasushi and Bando, Keisuke, Subgame Perfect Equilibria Under the Deferred Acceptance Algorithm (August 20, 2018). Available at SSRN: https://ssrn.com/abstract=3235068 or http://dx.doi.org/10.2139/ssrn.3235068

Yasushi Kawase

Tokyo Institute of Technology ( email )

2-12-1 O-okayama, Meguro-ku
Tokyo 152-8550, 52-8552
Japan

Keisuke Bando (Contact Author)

Shinshu University ( email )

Nagano, 390-8621
Japan

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