Fair and Consistent Prize Allocation in Competitions

Published Online:https://doi.org/10.1287/mnsc.2022.4520

References

  • Airiau S, Aziz H, Caragiannis I, Kruger J, Lang J, Peters D (2019) Portioning using ordinal preferences: Fairness and efficiency. Kraus S, ed. Proc. Twenty-Eighth Internat. Joint Conf. Artificial Intelligence, IJCAI 2019, August 10–16 (International Joint Conferences on Artificial Intelligence, Macao, China), 11–17.Google Scholar
  • Archak N, Sundararajan A (2009) Optimal design of crowdsourcing contests. Nunamaker Jr. JF, Currie WL, eds. Proc. Thirtieth Internat. Conf. Inform. Systems, ICIS 2009, December 15–18 (Association for Information Systems, Phoenix, AZ).Google Scholar
  • Aumann R, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the Talmud. J. Econom. Theory 36(2):195–213.CrossrefGoogle Scholar
  • Azmat G, Möller M (2009) Competition among contests. RAND J. Econom. 40(4):743–768.CrossrefGoogle Scholar
  • Azmat G, Möller M (2018) The distribution of talent across contests. Econom. J. 128(609):471–509.Google Scholar
  • Balinski M, Young H (1982) Fair Representation: Meeting the Ideal of One Man, One Vote (Yale University Press, New Haven, CT).Google Scholar
  • Balinski ML, Young HP (2001) Fair Representation: Meeting the Ideal of One Man, One Vote. 2nd ed. (Brookings Institution Press, Washington, D.C.).Google Scholar
  • Barut Y, Kovenock D (1998) The symmetric multiple prize all-pay auction with complete information. Eur. J. Political Econom. 14(4):627–644.CrossrefGoogle Scholar
  • Bergantiños G, Moreno-Ternero J (2020a) Allocating extra revenues from broadcasting sports leagues. J. Math. Econom. 90:65–73.CrossrefGoogle Scholar
  • Bergantiños G, Moreno-Ternero J (2020b) Sharing the revenues from broadcasting sport events. Management Sci. 66(6):2417–2431.LinkGoogle Scholar
  • Bergantiños G, Moreno-Ternero J (2021) Compromising to share the revenues from broadcasting sports leagues. J. Econom. Behav. Organ. 183:57–74.CrossrefGoogle Scholar
  • Bergantiños G, Moreno-Ternero J (2022a) Monotonicity in sharing the revenues from broadcasting sports leagues. Eur. J. Oper. Res. 297(1):338–346.CrossrefGoogle Scholar
  • Bergantiños G, Moreno-Ternero J (2022b) On the axiomatic approach to sharing the revenues from broadcasting sports leagues. Soc. Choice Welfare 58(2):321–347.CrossrefGoogle Scholar
  • Bergantiños G, Moreno-Ternero J (2022c) Separable rules to share the revenues from broadcasting sports leagues. Econom. Lett. 211:110233.CrossrefGoogle Scholar
  • Brandl F, Brandt F, Seedig HG (2016) Consistent probabilistic social choice. Econometrica 84(5):1839–1880.CrossrefGoogle Scholar
  • Chambers C, Moreno-Ternero J (2017) Taxation and poverty. Soc. Choice Welfare 48(1):153–175.CrossrefGoogle Scholar
  • Chambers C, Thomson W (2002) Group order preservation and the proportional rule for the adjudication of conflicting claims. Math. Soc. Sci. 44(3):235–252.CrossrefGoogle Scholar
  • Csató L (2021) Tournament Design: How Operations Research Can Improve Sports Rules (Palgrave Macmillan, Cham, Switzerland).CrossrefGoogle Scholar
  • Csató L (2022) The unfairness of the revenue distribution system used in the UEFA club competitions. Preprint, submitted June 23, https://arxiv.org/abs/2206.11746.Google Scholar
  • Fishburn P (1984) Probabilistic social choice based on simple voting comparisons. Rev. Econom. Stud. 51(4):683–692.CrossrefGoogle Scholar
  • Flores-Szwagrzak K, Treibich R (2020) Teamwork and individual productivity. Management Sci. 66(6):2523–2544.LinkGoogle Scholar
  • Galton F (1902) The most suitable proportion between the value of first and second prizes. Biometrika 1(4):385–399.CrossrefGoogle Scholar
  • Gershkov A, Li J, Schweinzer P (2009) Efficient tournaments within teams. RAND J. Econom. 40(1):103–119.CrossrefGoogle Scholar
  • Glazer A, Hassin R (1988) Optimal contests. Econom. Inquiry 26(1):133–143.CrossrefGoogle Scholar
  • Hart S, Mas-Colell A (1989) Potential, value, and consistency. Econometrica 57(3):589–614.CrossrefGoogle Scholar
  • Hougaard J, Moreno-Ternero J, Tvede M, Østerdal L (2017) Sharing the proceeds from a hierarchical venture. Games Econom. Behav. 102:98–110.CrossrefGoogle Scholar
  • Kalra A, Shi M (2001) Designing optimal sales contests: A theoretical perspective. Marketing Sci. 20(2):170–193.LinkGoogle Scholar
  • Kendall G, Lenten L (2017) When sports rules go awry. Eur. J. Oper. Res. 257(2):377–394.CrossrefGoogle Scholar
  • Kondratev A, Ianovski E, Nesterov A (2022) How should we score athletes and candidates: Geometric scoring rules. Preprint, submitted February 4, https://arxiv.org/abs/1907.05082v4.Google Scholar
  • Kreweras G (1965) Aggregation of preference orderings. Math. Soc. Sci. I Proc. Seminars Menthon-Saint-Bernard, France (1–July 27, 1960) Gösing, Austria (3–July 27, 1962), 73–79.Google Scholar
  • Lazear E, Rosen S (1981) Rank-order tournaments as optimum labor contracts. J. Political Econom. 89(5):841–864.CrossrefGoogle Scholar
  • Lensberg T (1987) Stability and collective rationality. Econometrica 55(4):935–961.CrossrefGoogle Scholar
  • Lensberg T (1988) Stability and the Nash solution. J. Econom. Theory 45(2):330–341.CrossrefGoogle Scholar
  • Lenten L, Kendall G (2021) Scholarly sports: Influence of social science academe on sports rules and policy. J. Oper. Res. Soc. http://doi.org/10.1080/01605682.2021.2000896CrossrefGoogle Scholar
  • Maschler M, Owen G (1989) The consistent Shapley value for hyperplane games. Internat. J. Game Theory 18(4):389–407.CrossrefGoogle Scholar
  • Moldovanu B, Sela A (2001) The optimal allocation of prizes in contests. Amer. Econom. Rev. 91(3):542–558.CrossrefGoogle Scholar
  • Moldovanu B, Sela A (2006) Contest architecture. J. Econom. Theory 126(1):70–96.CrossrefGoogle Scholar
  • Moldovanu B, Sela A, Shi X (2007) Contests for status. J. Political Econom. 115(2):338–363.CrossrefGoogle Scholar
  • Moreno-Ternero J, Roemer J (2006) Impartiality, priority, and solidarity in the theory of justice. Econometrica 74(5):1419–1429.CrossrefGoogle Scholar
  • Moulin H (1985) The separability axiom and equal-sharing methods. J. Econom. Theory 36(1):120–148.CrossrefGoogle Scholar
  • Moulin H (2000) Priority rules and other asymmetric rationing methods. Econometrica 68(3):643–684.CrossrefGoogle Scholar
  • Moulin H (2003) Fair Division and Collective Welfare (MIT Press, Cambridge, MA).CrossrefGoogle Scholar
  • Newman A, Tafkov I (2014) Relative performance information in tournaments with different prize structures. Accounting Organ. Soc. 39(5):348–361.CrossrefGoogle Scholar
  • O’Keeffe M, Viscusi W, Zeckhauser R (1984) Economic contests: Comparative reward schemes. J. Labor Econom. 2(1):27–56.CrossrefGoogle Scholar
  • Olszewski W, Siegel R (2020) Performance-maximizing large contests. Theoretical Econom. 15(1):57–88.CrossrefGoogle Scholar
  • Osório A (2017) Self-interest and equity concerns: A behavioural allocation rule for operational problems. Eur. J. Oper. Res. 261(1):205–213.CrossrefGoogle Scholar
  • Peleg B (1986) On the reduced game property and its converse. Internat. J. Game Theory 15(3):187–200.CrossrefGoogle Scholar
  • Petróczy D, Csató L (2021) Revenue allocation in Formula One: A pairwise comparison approach. Internat. J. General Systems 50(3):243–261.CrossrefGoogle Scholar
  • Potters J, Sudhölter P (1999) Airport problems and consistent allocation rules. Math. Social Sci. 38(1):83–102.CrossrefGoogle Scholar
  • Skaperdas S (1996) Contest success functions. Econom. Theory 7(2):283–290.CrossrefGoogle Scholar
  • Szymanski S (2003) The economic design of sporting contests. J. Econom. Literature 41(4):1137–1187.CrossrefGoogle Scholar
  • Terwiesch C, Xu Y (2008) Innovation contests, open innovation, and multiagent problem solving. Management Sci. 54(9):1529–1543.LinkGoogle Scholar
  • Thomson W (1988) A study of choice correspondences in economies with a variable number of agents. J. Econom. Theory 46(2):237–254.CrossrefGoogle Scholar
  • Thomson W (1994) Consistent solutions to the problem of fair division when preferences are single-peaked. J. Econom. Theory 63(2):219–245.CrossrefGoogle Scholar
  • Thomson W (2011) Consistency and its converse: An introduction. Rev. Econom. Design 15(4):257–291.CrossrefGoogle Scholar
  • Thomson W (2012) On the axiomatics of resource allocation: Interpreting the consistency principle. Econom. Philos. 28(3):385–421.CrossrefGoogle Scholar
  • Thomson W, Zhou L (1993) Consistent solutions in atomless economies. Econometrica 61(3):575–587.CrossrefGoogle Scholar
  • Wright M (2014) OR analysis of sporting rules: A survey. Eur. J. Oper. Res. 232(1):1–8.CrossrefGoogle Scholar
  • Xiao J (2016) Asymmetric all-pay contests with heterogeneous prizes. J. Econom. Theory 163:178–221.CrossrefGoogle Scholar
  • Young H (1987) On dividing an amount according to individual claims or liabilities. Math. Oper. Res. 12(3):398–414.LinkGoogle Scholar
  • Young H (1988) Condorcet’s theory of voting. Amer. Political Sci. Rev. 82(4):1231–1244.CrossrefGoogle Scholar
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