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A General Framework for Studying Contests

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  • Spencer Bastani
  • Thomas Giebe
  • Oliver Gürtler

Abstract

We develop a general framework to study contests, containing the well-known models of Tullock (1980) and Lazear & Rosen (1981) as special cases. The contest outcome depends on players’ effort and skill, the latter being subject to symmetric uncertainty. The model is tractable, because a symmetric equilibrium exists under general assumptions regarding production technologies and skill distributions. We construct a link between our contest model and expected utility theory and exploit this link to revisit important comparative statics results of contest theory and show how these can be overturned. Finally, we apply our results to study optimal workforce composition.

Suggested Citation

  • Spencer Bastani & Thomas Giebe & Oliver Gürtler, 2019. "A General Framework for Studying Contests," CESifo Working Paper Series 7993, CESifo.
    • Handle: RePEc:ces:ceswps:_7993
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    1. Giebe, Thomas & Schweinzer, Paul, 2014. "Consuming your way to efficiency: Public goods provision through non-distortionary tax lotteries," European Journal of Political Economy, Elsevier, vol. 36(C), pages 1-12.
    2. Scott M Gilpatric, 2009. "Risk Taking In Contests And The Role Of Carrots And Sticks," Economic Inquiry, Western Economic Association International, vol. 47(2), pages 266-277, April.
    3. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    4. 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.
    5. David Bjerk, 2008. "Glass Ceilings or Sticky Floors? Statistical Discrimination in a Dynamic Model of Hiring and Promotion," Economic Journal, Royal Economic Society, vol. 118(530), pages 961-982, July.
    6. 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.
    7. Thomas Giebe & Paul Schweinzer, 2012. "Fuzzy Price-Quality Ratio Procurement under Incomplete Information," Discussion Papers 12/26, Department of Economics, University of York.
    8. Chowdhury, Subhasish M. & Kim, Sang-Hyun, 2017. "“Small, yet Beautiful”: Reconsidering the optimal design of multi-winner contests," Games and Economic Behavior, Elsevier, vol. 104(C), pages 486-493.
    9. Kräkel, Matthias, 2008. "Optimal risk taking in an uneven tournament game with risk averse players," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1219-1231, December.
    10. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    11. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    12. Dan Bernhardt, 1995. "Strategic Promotion and Compensation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(2), pages 315-339.
    13. Qiang Fu & Jingfeng Lu, 2012. "Micro foundations of multi-prize lottery contests: a perspective of noisy performance ranking," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 497-517, March.
    14. Christian Grund & Dirk Sliwka, 2005. "Envy and Compassion in Tournaments," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 14(1), pages 187-207, March.
    15. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Biased contests for symmetric players," Games and Economic Behavior, Elsevier, vol. 103(C), pages 116-144.
    16. Jed DeVaro & Antti Kauhanen, 2016. "An “Opposing Responses” Test of Classic versus Market-Based Promotion Tournaments," Journal of Labor Economics, University of Chicago Press, vol. 34(3), pages 747-779.
    17. Andrew Schotter & Keith Weigelt, 1992. "Asymmetric Tournaments, Equal Opportunity Laws, and Affirmative Action: Some Experimental Results," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 511-539.
    18. 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.
    19. Paul Schweinzer & Ella Segev, 2012. "The optimal prize structure of symmetric Tullock contests," Public Choice, Springer, vol. 153(1), pages 69-82, October.
    20. Lazear, Edward P, 1989. "Pay Equality and Industrial Politics," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 561-580, June.
    21. Hans K. Hvide, 2002. "Tournament Rewards and Risk Taking," Journal of Labor Economics, University of Chicago Press, vol. 20(4), pages 877-898, October.
    22. James M. Malcomson, 1986. "Rank-Order Contracts for a Principal with Many Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 807-817.
    23. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 291-305.
    24. Chen Cohen & Todd R. Kaplan & Aner Sela, 2008. "Optimal rewards in contests," RAND Journal of Economics, RAND Corporation, vol. 39(2), pages 434-451, June.
    25. Florian Morath & Johannes Münster, 2013. "Information acquisition in conflicts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 99-129, September.
    26. Matthias Kräkel & Dirk Sliwka, 2004. "Risk Taking in Asymmetric Tournaments," German Economic Review, Verein für Socialpolitik, vol. 5(1), pages 103-116, February.
    27. 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.
    28. Gürtler, Oliver & Kräkel, Matthias, 2010. "Optimal tournament contracts for heterogeneous workers," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 180-191, August.
    29. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    30. Gershkov, Alex & Li, Jianpei & Schweinzer, Paul, 2016. "How to share it out: The value of information in teams," Journal of Economic Theory, Elsevier, vol. 162(C), pages 261-304.
    31. Subhasish Chowdhury & Oliver Gürtler, 2015. "Sabotage in contests: a survey," Public Choice, Springer, vol. 164(1), pages 135-155, July.
    32. René Kirkegaard, 2020. "Microfounded Contest Design," Working Papers 2003, University of Guelph, Department of Economics and Finance.
    33. Jed DeVaro & Michael Waldman, 2012. "The Signaling Role of Promotions: Further Theory and Empirical Evidence," Journal of Labor Economics, University of Chicago Press, vol. 30(1), pages 91-147.
    34. Marc Gürtler & Oliver Gürtler, 2015. "The Optimality of Heterogeneous Tournaments," Journal of Labor Economics, University of Chicago Press, vol. 33(4), pages 1007-1042.
    35. Aner Sela, 2012. "Sequential two-prize contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 383-395, October.
    36. Kong-Pin Chen, 2003. "Sabotage in Promotion Tournaments," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 19(1), pages 119-140, April.
    37. Oliver Gürtler & Johannes Münster & Petra Nieken, 2013. "Information Policy in Tournaments with Sabotage," Scandinavian Journal of Economics, Wiley Blackwell, vol. 115(3), pages 932-966, July.
    38. Lorens Imhof & Matthias Kräkel, 2016. "Ex post unbalanced tournaments," RAND Journal of Economics, RAND Corporation, vol. 47(1), pages 73-98, February.
    39. Alex Gershkov & Jianpei Li & Paul Schweinzer, 2009. "Efficient tournaments within teams," RAND Journal of Economics, RAND Corporation, vol. 40(1), pages 103-119, March.
    40. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    41. Anja Schöttner & Veikko Thiele, 2010. "Promotion Tournaments and Individual Performance Pay," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 19(3), pages 699-731, September.
    42. Suman Ghosh & Michael Waldman, 2010. "Standard promotion practices versus up‐or‐out contracts," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 301-325, June.
    43. David Bjerk, 2008. "Glass Ceilings or Sticky Floors? Statistical Discrimination in a Dynamic Model of Hiring and Promotion," Economic Journal, Royal Economic Society, vol. 118(530), pages 961-982, July.
    44. Stefano Barbieri & David Malueg & Iryna Topolyan, 2014. "The best-shot all-pay (group) auction with complete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 603-640, November.
    45. Michael Waldman, 1984. "Job Assignments, Signalling, and Efficiency," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 255-267, Summer.
    46. Benny Moldovanu & Aner Sela & Xianwen Shi, 2007. "Contests for Status," Journal of Political Economy, University of Chicago Press, vol. 115, pages 338-363.
    47. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    48. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    49. 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.
    50. Florian Ederer, 2010. "Feedback and Motivation in Dynamic Tournaments," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 19(3), pages 733-769, September.
    51. Mathias Dewatripont & Ian Jewitt & Jean Tirole, 1999. "The Economics of Career Concerns, Part I: Comparing Information Structures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 183-198.
    52. Luis Corchón & Matthias Dahm, 2010. "Foundations for contest success functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 81-98, April.
    53. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    54. Emmanuelle Auriol & Guido Friebel & Lambros Pechlivanos, 2002. "Career Concerns in Teams," Journal of Labor Economics, University of Chicago Press, vol. 20(2), pages 289-307, Part.
    55. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
    56. Mathias Dewatripont & Ian Jewitt & Jean Tirole, 1999. "The Economics of Career Concerns, Part I: Comparing Information Structures," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 183-198.
    57. Thomas Giebe & Paul Schweinzer, 2015. "Probabilistic procurement auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 19(1), pages 25-46, March.
    58. Malcomson, James M, 1984. "Work Incentives, Hierarchy, and Internal Labor Markets," Journal of Political Economy, University of Chicago Press, vol. 92(3), pages 486-507, June.
    59. 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.
    60. Richard L. Fullerton & R. Preston McAfee, 1999. "Auctioning Entry into Tournaments," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 573-605, June.
    61. Aoyagi, Masaki, 2010. "Information feedback in a dynamic tournament," Games and Economic Behavior, Elsevier, vol. 70(2), pages 242-260, November.
    62. Fu, Qiang & Lu, Jingfeng, 2009. "The beauty of "bigness": On optimal design of multi-winner contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 146-161, May.
    63. Jan Zábojník & Dan Bernhardt, 2001. "Corporate Tournaments, Human Capital Acquisition, and the Firm Size—Wage Relation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 693-716.
    64. O'Keeffe, Mary & Viscusi, W Kip & Zeckhauser, Richard J, 1984. "Economic Contests: Comparative Reward Schemes," Journal of Labor Economics, University of Chicago Press, vol. 2(1), pages 27-56, January.
    65. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
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    Cited by:

    1. René Kirkegaard, 2020. "Microfounded Contest Design," Working Papers 2003, University of Guelph, Department of Economics and Finance.
    2. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    3. Hanming Fang & Ming Li & Zenan Wu, 2022. "Tournament-Style Political Competition and Local Protectionism: Theory and Evidence from China," PIER Working Paper Archive 22-031, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    4. Thomas Giebe & Oliver Gürtler, 2024. "Player Strength and Effort in Contests," ECONtribute Discussion Papers Series 285, University of Bonn and University of Cologne, Germany.
    5. Goel, Sumit & Goyal, Amit, 2023. "Optimal tie-breaking rules," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    6. Mikhail Drugov & Dmitry Ryvkin, 2020. "Hunting for the discouragement effect in contests," Working Papers w0278, New Economic School (NES).

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    More about this item

    Keywords

    contest theory; symmetric equilibrium; heterogeneity; risk; decision theory;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • J23 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Labor Demand
    • M51 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Firm Employment Decisions; Promotions

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