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A sequential selection game with vetoes

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  • Alpern, Steve
  • Gal, Shmuel
  • Solan, Eilon

Abstract

We study a selection game between two committee members (the players). They interview candidates sequentially and have to decide, after each interview, whether to hire the candidate or to interview the next candidate. Each player can either accept or reject the candidate, and if he rejects the candidate while the other accepts her, he can cast a veto. The candidate is hired if accepted by at least one player and not vetoed. The total number of vetoes available for each player are fixed in advance. We prove the existence of a subgame perfect equilibrium if there are a finite number of candidates types. For a general candidate distribution we prove the existence of a subgame perfect [epsilon]-equilibrium. We exhibit situations in which a player prefers that the other player would have an extra veto, and even prefers to give one of his vetoes to the other player.

Suggested Citation

  • Alpern, Steve & Gal, Shmuel & Solan, Eilon, 2010. "A sequential selection game with vetoes," Games and Economic Behavior, Elsevier, vol. 68(1), pages 1-14, January.
    • Handle: RePEc:eee:gamebe:v:68:y:2010:i:1:p:1-14
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    References listed on IDEAS

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    1. David M., Ramsey & Krzysztof, Szajowski, 2000. "Bilateral Approach to the Secretary Problem," MPRA Paper 19888, University Library of Munich, Germany, revised 2003.
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    Cited by:

    1. Rohan DUTTA, 2016. "Joint Search with No Information: An Inefficient Immediate Agreement Theorem," Cahiers de recherche 12-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Alpern, Steve & Chen, Bo, 2017. "The importance of voting order for jury decisions by sequential majority voting," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1072-1081.
    3. Steve Alpern & Bo Chen, 2017. "Who should cast the casting vote? Using sequential voting to amalgamate information," Theory and Decision, Springer, vol. 83(2), pages 259-282, August.
    4. Francis X. Flanagan, 2015. "Peremptory Challenges and Jury Selection," Journal of Law and Economics, University of Chicago Press, vol. 58(2), pages 385-416.
    5. Longjian Li & Alexis Akira Toda, 2022. "Incentivizing Hidden Types in Secretary Problem," Papers 2208.05897, arXiv.org.
    6. Inukai, Keigo & Kawata, Keisuke & Sasaki, Masaru, 2017. "Committee Search with Ex-ante Heterogeneous Agents: Theory and Experimental Evidence," IZA Discussion Papers 10760, Institute of Labor Economics (IZA).
    7. Steve Alpern & Shmuel Gal, 2009. "Analysis and design of selection committees: a game theoretic secretary problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 377-394, November.
    8. Steve Alpern & Vic Baston, 2017. "The Secretary Problem with a Selection Committee: Do Conformist Committees Hire Better Secretaries?," Management Science, INFORMS, vol. 63(4), pages 1184-1197, April.
    9. Dutta, Rohan, 2017. "Joint search with no information: An immediate agreement theorem," Economics Letters, Elsevier, vol. 160(C), pages 43-45.
    10. Steve Alpern & Bo Chen, 2020. "Optimizing Voting Order on Sequential Juries: A Median Voter Theorem and Beyond," Papers 2006.14045, arXiv.org, revised Oct 2021.
    11. , & ,, 2013. "Specialization and partisanship in committee search," Theoretical Economics, Econometric Society, vol. 8(3), September.
    12. Steve Alpern & Bo Chen, 2022. "Optimizing voting order on sequential juries: a median voter theorem and beyond," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(3), pages 527-565, April.

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