TY - JOUR
T1 - Subgame perfect equilibria of sequential matching games
AU - Kawase, Yasushi
AU - Yamaguchi, Yutaro
AU - Yokoi, Yu
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grants No. JP16H06931, No. JP16K16005, and No. JP18K18004, by JST ACT-I Grant No. JPMJPR17U7, and by JST CREST Grant No. JPMJCR14D2.*%blankline%*
Funding Information:
A preliminary version [17] appeared in EC’18. This work was supported by JSPS KAKENHI Grants No. JP16H06931, No. JP16K16005, and No. JP18K18004, by JST ACT-I Grant No. JPMJPR17U7, and by JST CREST Grant No. JPMJCR14D2. Authors’ addresses: Y. Kawase, Tokyo Institute of Technology and RIKEN AIP Center, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8552, Japan; email: kawase.y.ab@m.titech.ac.jp; Y. Yamaguchi, Osaka University and RIKEN AIP Center, 1-5 Yamadaoka, Suita, Osaka, 565-0871, Japan; email: yutaro_yamaguchi@ist.osakau.ac.jp; Y. Yokoi, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan; email: yokoi@nii.ac.jp. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. © 2020 Association for Computing Machinery. 2167-8375/2020/01-ART21 $15.00 https://doi.org/10.1145/3373717
Publisher Copyright:
© 2020 Association for Computing Machinery.
PY - 2020/1/27
Y1 - 2020/1/27
N2 - We study a decentralized matching market in which firms sequentially make 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. We show a dichotomy result that characterizes the complexity of computing the SPE. The computation is tractable if each firm makes offers to at most two workers or each worker receives offers from at most two firms. In contrast, it is PSPACE-hard even if both firms and workers are related to at most three offers. We also study engineering aspects of this matching market. It is shown that, for any preference profile, we can design an offering schedule of firms so that the worker-optimal stable matching is realized in the SPE.
AB - We study a decentralized matching market in which firms sequentially make 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. We show a dichotomy result that characterizes the complexity of computing the SPE. The computation is tractable if each firm makes offers to at most two workers or each worker receives offers from at most two firms. In contrast, it is PSPACE-hard even if both firms and workers are related to at most three offers. We also study engineering aspects of this matching market. It is shown that, for any preference profile, we can design an offering schedule of firms so that the worker-optimal stable matching is realized in the SPE.
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U2 - 10.1145/3373717
DO - 10.1145/3373717
M3 - Article
AN - SCOPUS:85078945285
SN - 2167-8375
VL - 7
JO - ACM Transactions on Economics and Computation
JF - ACM Transactions on Economics and Computation
IS - 4
M1 - 21
ER -