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Allocation rules of indivisible prizes in team contests

Author

Listed:
  • Hideo Konishi

    (Boston College)

  • Nicolas Sahuguet

    (HEC Montreal)

  • Benoît S. Y. Crutzen

    (Erasmus School of Economics and Tinbergen Institute)

Abstract

We analyze contests in which teams compete to win indivisible homogeneous prizes. Teams are composed of members who may differ in their ability, and who exert effort to increase the success of their team. Each team member can obtain at most one prize as a reward. As effort is costly, teams use the allocation of prizes to give incentives and solve the free-riding problem. We develop a two-stage game. First, teams select a prize-allocation rule. Then, team members exert effort. Members take into account how their effort and the allocation rule influence the chance they receive a prize. We prove the existence and uniqueness of equilibrium. We characterize the optimal prize-assignment rule and individual and aggregate efforts. We then show that the optimal assignment rule is generally not monotonic.

Suggested Citation

  • Hideo Konishi & Nicolas Sahuguet & Benoît S. Y. Crutzen, 2024. "Allocation rules of indivisible prizes in team contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(1), pages 69-100, August.
    • Handle: RePEc:spr:joecth:v:78:y:2024:i:1:d:10.1007_s00199-023-01534-9
    DOI: 10.1007/s00199-023-01534-9
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    1. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    2. Shmuel Nitzan, 2008. "Collective Rent Dissipation," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 309-321, Springer.
    3. Pau Balart & Sabine Flamand & Orestis Troumpounis, 2016. "Strategic choice of sharing rules in collective contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 239-262, February.
    4. Stefano Barbieri & David Malueg, 2014. "Group efforts when performance is determined by the “best shot”," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 333-373, June.
    5. Kai A. Konrad & Dan Kovenock, 2022. "Introduction to the Special Issue on Contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(4), pages 1017-1023, November.
    6. Corchón, Luis C., 2007. "The theory of contests : a survey," UC3M Working papers. Economics we075126, Universidad Carlos III de Madrid. Departamento de Economía.
    7. Yano, Makoto, 1983. "Welfare aspects of the transfer problem," Journal of International Economics, Elsevier, vol. 15(3-4), pages 277-289, November.
    8. Stefano Barbieri & Iryna Topolyan, 2021. "Private‐information group contests with complementarities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(5), pages 772-800, October.
    9. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 324-340, Autumn.
    10. Galasso, Vincenzo & Nannicini, Tommaso, 2015. "So closed: Political selection in proportional systems," European Journal of Political Economy, Elsevier, vol. 40(PB), pages 260-273.
    11. Richard Cornes & Roger Hartley, 2005. "Asymmetric contests with general technologies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 923-946, November.
    12. Francesco Trevisan, 2020. "Optimal prize allocations in group contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(3), pages 431-451, October.
    13. Barut, Yasar & Kovenock, Dan, 1998. "The symmetric multiple prize all-pay auction with complete information," European Journal of Political Economy, Elsevier, vol. 14(4), pages 627-644, November.
    14. Alchian, Armen A & Demsetz, Harold, 1972. "Production , Information Costs, and Economic Organization," American Economic Review, American Economic Association, vol. 62(5), pages 777-795, December.
    15. Barbieri, Stefano & Serena, Marco, 2021. "Winner’s effort maximization in large contests," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    16. Nitzan, Shmuel & Ueda, Kaoru, 2011. "Prize sharing in collective contests," European Economic Review, Elsevier, vol. 55(5), pages 678-687, June.
    17. Luis Corchón, 2007. "The theory of contests: a survey," Review of Economic Design, Springer;Society for Economic Design, vol. 11(2), pages 69-100, September.
    18. 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.
    19. Ernesto Dal Bó & Frederico Finan & Olle Folke & Torsten Persson & Johanna Rickne, 2017. "Who Becomes A Politician?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(4), pages 1877-1914.
    20. Barry J. Nalebuff & Joseph E. Stiglitz, 1983. "Prices and Incentives: Towards a General Theory of Compensation and Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 21-43, Spring.
    21. Jagdish Bhagwati, 1958. "Immiserizing Growth: A Geometrical Note," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(3), pages 201-205.
    22. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603, Decembrie.
    23. Dana Sisak, 2009. "Multiple‐Prize Contests – The Optimal Allocation Of Prizes," Journal of Economic Surveys, Wiley Blackwell, vol. 23(1), pages 82-114, February.
    24. Qiang Fu & Jingfeng Lu & Yue Pan, 2015. "Team Contests with Multiple Pairwise Battles," American Economic Review, American Economic Association, vol. 105(7), pages 2120-2140, July.
    25. Thomas Fujiwara & Carlos Sanz, 2020. "Rank Effects in Bargaining: Evidence from Government Formation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(3), pages 1261-1295.
    26. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    27. Joan Esteban & Debraj Ray, 2008. "Collective Action and the Group Size Paradox," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 379-388, Springer.
    28. Shmuel Nitzan & Kaoru Ueda, 2014. "Intra-group heterogeneity in collective contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 219-238, June.
    29. Barbieri, Stefano & Malueg, David A., 2016. "Private-information group contests: Best-shot competition," Games and Economic Behavior, Elsevier, vol. 98(C), pages 219-234.
    30. Cirone, Alexandra & Cox, Gary W. & Fiva, Jon H., 2021. "Seniority-Based Nominations and Political Careers," American Political Science Review, Cambridge University Press, vol. 115(1), pages 234-251, February.
    31. Clark, Derek J & Riis, Christian, 1998. "Competition over More Than One Prize," American Economic Review, American Economic Association, vol. 88(1), pages 276-289, March.
    32. Cox, Gary W. & Fiva, Jon H. & Smith, Daniel M. & Sørensen, Rune J., 2021. "Moral hazard in electoral teams: List rank and campaign effort," Journal of Public Economics, Elsevier, vol. 200(C).
    33. 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).
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    More about this item

    Keywords

    Contest; Team; Moral hazard;
    All these keywords.

    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

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