Sorted or pooled? Optimal tournament design for heterogeneous contestants

Article

Abstract

The optimal tournament for the heterogeneous contestants is described and developed in approach of game theory, which includes the sorted tournament between the strong contestants with high ability, the sorted tournament between the weak contestants with low ability, and the pooled tournament between the strong and the weak contestants. By comparing the equilibrium results of the incentive structure, the efforts level, and the expected profits in each kind of tournament, it is found that the strong contestants can get more utilities in the pooled tournament, and hence prefer to take part in the pooled tournament to compete with the weak competitors, while the weak contestants only can get the reservation utility in both the sorted and pooled tournament, and hence do not care about the abilities of competitors. The principal will choose and implement the sorted tournament because he can acquire more profits than that in the pooled tournament.

Keywords

Sorted tournament Pooled tournament Comparison Game theory 

Notes

Acknowledgements

This work is supported by Social Sciences and Humanities Foundation of Chongqing, China under Grant No. 17SKG079.

References

  1. 1.
    Lazear, E.P., Rosen, S.: Rank order tournaments as optimum labor contracts. J. Polit. Econ. 89(5), 841–864 (1981)CrossRefGoogle Scholar
  2. 2.
    Lazear, E.P.: Pay equality and industrial politics. J. Polit. Econ. 97(3), 561–580 (1989)CrossRefGoogle Scholar
  3. 3.
    Kräkel, M.: U-type versus J-type tournaments as alternative solutions to the unverifiability problem. Labor Econ. 10(3), 359–380 (2003)CrossRefGoogle Scholar
  4. 4.
    Hvide, H.K., Kristiansen, E.G.: Risk taking in selection contests. Games Econ. Behav. 42(2), 172–179 (2003)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Yun, J.: On the efficiency of the rank order contract under moral hazard and adverse selection. J. Labor Econ. 15(3), 466–494 (1997)CrossRefGoogle Scholar
  6. 6.
    Gurtler, O.: On sabotage in collective tournaments. J. Math. Econ. 44(3), 383–393 (2008)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Gurtler, O., Munster, J.: Sabotage in dynamic tournaments. J. Math. Econ. 46(2), 179–190 (2010)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Altmann, S., Falk, A., Wibral, M.: Promotions and incentives: the case of multistage elimination tournaments. J. Labor Econ. 30(1), 149–174 (2012)CrossRefGoogle Scholar
  9. 9.
    Moldovanu, B., Sela, A., Shi, X.W.: Carrots and sticks: prizes and punishments in contests. Econ. Inq. 50(2), 453–462 (2012)CrossRefGoogle Scholar
  10. 10.
    Dubey, P., Geanakoplos, J., Haimanko, O.: Prizes versus wages with envy and pride. Jpn. Econ. Rev. 64(1), 98–121 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Marinakis, K., Tsoulouhas, T.: Are tournaments optimal over piece rates under limited liability for the principal? Int. J. Ind. Organ. 31(3), 223–237 (2013)CrossRefGoogle Scholar
  12. 12.
    Klein, A.H., Armin, S.: Optimal effort incentives in dynamic tournaments. Games Econ. Behav. 103(5), 199–224 (2017)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Knyazev, D.: Optimal prize structures in elimination contests. J. Econ. Behav. Organ. 139(7), 32–48 (2017)CrossRefGoogle Scholar
  14. 14.
    Roland, P., Bertrand, T., Narcisse, T.: Properties of ladder tournaments. Eur. J. Oper. Res. 263(1), 203–213 (2017)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Kräkel, M.: Optimal risk taking in an uneven tournament game with risk averse players. J. Math. Econ. 44(11), 1219–1231 (2008)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Jost, P., Kräkel, M.: Human capital investments in asymmetric corporate tournaments. J. Econ. Bus. 60(4), 312–331 (2008)CrossRefGoogle Scholar
  17. 17.
    Gurtler, O., Krakel, M.: Optimal tournament contracts for heterogeneous workers. J. Econ. Behav. Organ. 75(2), 180–191 (2010)CrossRefGoogle Scholar
  18. 18.
    Parreiras, S.O., Rubinchik, A.: Contests with three or more heterogeneous contestants. Games Econ. Behav. 68(2), 703–715 (2010)CrossRefMATHGoogle Scholar
  19. 19.
    Fonseca, M.A.: An experimental investigation of asymmetric contests. Int. J. Ind. Organ. 27(5), 582–591 (2009)CrossRefGoogle Scholar
  20. 20.
    Hammond, R.G., Zheng, X.Y.: Heterogeneity in tournaments with incomplete information: an experimental analysis. Int. J. Ind. Organ. 31(3), 248–260 (2013)CrossRefGoogle Scholar
  21. 21.
    Ryvkin, D.: The optimal sorting of players in contests between groups. Games Econ. Behav. 73(2), 564–572 (2011)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Brookins, P., Lightle, J.P., Ryvkin, D.: Optimal sorting in group contests with complementarities. J. Econ. Behav. Organ. 112(C), 311–323 (2015)CrossRefGoogle Scholar
  23. 23.
    Dawid, H., Muehlheusser, G.: Repeated selection with heterogeneous individuals and relative age effects. J. Econ. Behav. Organ. 116(3), 387–406 (2015)CrossRefGoogle Scholar
  24. 24.
    Figueroa, A.P., Montellano-Ballesteros, J.J., Olsen, M.: Strong sub-tournaments and cycles of multipartite tournaments. Discret. Math. 339(11), 2793–2803 (2016)CrossRefMATHGoogle Scholar
  25. 25.
    Alexander, K.: A new knockout tournament seeding method and its axiomatic justification. Oper. Res. Lett. 44(6), 706–711 (2016)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Aras, E.: Constructing day-balanced round-robin tournaments with partitions. Discret. Appl. Math. 235(1), 81–91 (2018)MathSciNetMATHGoogle Scholar
  27. 27.
    Dixit, A.K.: Strategic behavior in contests. Am. Econ. Rev. 77(5), 891–898 (1987)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Economics and ManagementChongqing Jiaotong UniversityChongqingChina
  2. 2.School of ManagementChongqing University of TechnologyChongqingChina

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