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A simple model of competition between teams

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  • Eliaz, Kfir
  • Wu, Qinggong

Abstract

We model competition between two teams (that may differ in size) as an all-pay contest with incomplete information where team members exert effort to increase the performance of their own team. The team with the higher performance wins, and its members enjoy the prize as a public good. The value of the prize is identical to members of the same team but is unknown to those of the other team. We focus on the case in which a team's performance is the sum of its individual members' performances and analyze monotone equilibria in which members of the same team exert the same effort. We find that the bigger team is more likely to win if individual performance is a concave function of effort, less likely if convex, and equally likely if linear. We also provide a complete characterization of the equilibria for the case in which individual performance is a power function of effort and team value is uniformly distributed. For this case we also investigate how probabilities of winning, total team performance and individual payoffs are affected by the size of the team. The results shed light on the “group-size paradox”.

Suggested Citation

  • Eliaz, Kfir & Wu, Qinggong, 2018. "A simple model of competition between teams," Journal of Economic Theory, Elsevier, vol. 176(C), pages 372-392.
  • Handle: RePEc:eee:jetheo:v:176:y:2018:i:c:p:372-392
    DOI: 10.1016/j.jet.2018.04.006
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    Cited by:

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    3. Martin Kolmar & Hendrik Rommeswinkel, 0. "Group size and group success in conflicts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 0, pages 1-46.
    4. Crutzen, Beno�t SY & Flamand, Sabine & Sahuguet, Nicolas, 2017. "Prize allocation and incentives in team contests," CEPR Discussion Papers 12493, C.E.P.R. Discussion Papers.
    5. Crutzen, Benoît S Y & Flamand, Sabine & Sahuguet, Nicolas, 2020. "A model of a team contest, with an application to incentives under list proportional representation," Journal of Public Economics, Elsevier, vol. 182(C).
    6. Vasudha Chopra & Hieu M. Nguyen & Christian A. Vossler, 2020. "Heterogeneous group contests with incomplete information," Working Papers 2020-05, University of Tennessee, Department of Economics.
    7. Barbieri, Stefano & Kovenock, Dan & Malueg, David A. & Topolyan, Iryna, 2019. "Group contests with private information and the “Weakest Link”," Games and Economic Behavior, Elsevier, vol. 118(C), pages 382-411.

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    More about this item

    Keywords

    Team contests; Group size paradox;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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