Computing a subgame perfect equilibrium of a sequential matching game

Yasushi Kawase, Yutaro Yamaguchi, Yu Yokoi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

We study a decentralized matching market in which each firm sequentially makes offers to potential workers. For each offer, the worker can choose "accept" or "reject," but the decision is irrevocable. The acceptance of an offer guarantees her job at the firm, but it may also eliminate chances of better offers from other firms in the future. We formulate this market as a perfect-information extensive-form game played by the workers. Each instance of this game has a unique subgame perfect equilibrium (SPE), which does not necessarily lead to a stable matching and has some perplexing properties. Our aim is to establish the complexity of computing the SPE, or more precisely, deciding whether each offer is accepted in the SPE. We show that the tractability of this problem drastically changes according to the number of potential offers related to each firm and worker. If each firm makes offers to at most two workers (or each worker receives offers from at most two firms), then the problem is efficiently solved by a variant of the deferred acceptance algorithm. In contrast, the problem is PSPACE-hard even if both firms and workers are related to at most three offers.

Original languageEnglish
Title of host publicationACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Pages131-148
Number of pages18
ISBN (Electronic)9781450358293
DOIs
Publication statusPublished - Jun 11 2018
Event19th ACM Conference on Economics and Computation, EC 2018 - Ithaca, United States
Duration: Jun 18 2018Jun 22 2018

Publication series

NameACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation

Conference

Conference19th ACM Conference on Economics and Computation, EC 2018
CountryUnited States
CityIthaca
Period6/18/186/22/18

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Statistics and Probability
  • Computational Mathematics
  • Economics and Econometrics

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  • Cite this

    Kawase, Y., Yamaguchi, Y., & Yokoi, Y. (2018). Computing a subgame perfect equilibrium of a sequential matching game. In ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation (pp. 131-148). (ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation). Association for Computing Machinery, Inc. https://doi.org/10.1145/3219166.3219200