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Simple equilibria in general contests

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  • Bastani, Spencer
  • Giebe, Thomas
  • Gürtler, Oliver

Abstract

We show how symmetric equilibria emerge in general two-player contests in which skill and effort are combined to produce output according to a general production technology and players have skills drawn from different distributions. The model includes the Tullock (1980) and Lazear and Rosen (1981) models as special cases. Our paper provides intuition regarding how the contest components interact to determine the incentive to exert effort and sheds new light on classic comparative statics results. In particular, we show that more heterogeneity can increase equilibrium effort.

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  • Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
  • Handle: RePEc:eee:gamebe:v:134:y:2022:i:c:p:264-280
    DOI: 10.1016/j.geb.2022.05.006
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    1. 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.
    2. Jennifer Brown, 2011. "Quitters Never Win: The (Adverse) Incentive Effects of Competing with Superstars," Journal of Political Economy, University of Chicago Press, vol. 119(5), pages 982-1013.
    3. 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.
    4. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603, Decembrie.
    5. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
    6. Dan Bernhardt, 1995. "Strategic Promotion and Compensation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(2), pages 315-339.
    7. Alex Krumer & Reut Megidish & Aner Sela, 2017. "Round‐Robin Tournaments with a Dominant Player," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(4), pages 1167-1200, October.
    8. 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.
    9. Mikhail Drugov & Dmitry Ryvkin, 2020. "Hunting for the discouragement effect in contests," Working Papers w0278, New Economic School (NES).
    10. Paul Schweinzer & Ella Segev, 2012. "The optimal prize structure of symmetric Tullock contests," Public Choice, Springer, vol. 153(1), pages 69-82, October.
    11. Hans K. Hvide, 2002. "Tournament Rewards and Risk Taking," Journal of Labor Economics, University of Chicago Press, vol. 20(4), pages 877-898, October.
    12. 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.
    13. Matthias Kräkel & Dirk Sliwka, 2004. "Risk Taking in Asymmetric Tournaments," German Economic Review, Verein für Socialpolitik, vol. 5(1), pages 103-116, February.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Michael Waldman, 1984. "Job Assignments, Signalling, and Efficiency," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 255-267, Summer.
    24. Benny Moldovanu & Aner Sela & Xianwen Shi, 2007. "Contests for Status," Journal of Political Economy, University of Chicago Press, vol. 115, pages 338-363.
    25. 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.
    26. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "How noise affects effort in tournaments," Journal of Economic Theory, Elsevier, vol. 188(C).
    27. Green, Jerry R & Stokey, Nancy L, 1983. "A Comparison of Tournaments and Contracts," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 349-364, June.
    28. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    29. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    30. Christian Grund & Dirk Sliwka, 2005. "Envy and Compassion in Tournaments," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 14(1), pages 187-207, March.
    31. 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.
    32. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
    33. Fu, Qiang & Wu, Zenan, 2020. "On the optimal design of biased contests," Theoretical Economics, Econometric Society, vol. 15(4), November.
    34. 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.
    35. Aoyagi, Masaki, 2010. "Information feedback in a dynamic tournament," Games and Economic Behavior, Elsevier, vol. 70(2), pages 242-260, November.
    36. 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.
    37. Subhasish Chowdhury & Oliver Gürtler, 2015. "Sabotage in contests: a survey," Public Choice, Springer, vol. 164(1), pages 135-155, July.
    38. Clark, D.J. & Riis, C., 1996. "On the Win Probability in Rent-Seeking Gemes," Memorandum 1996_005, Oslo University, Department of Economics.
    39. 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.
    40. 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.
    41. 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.
    42. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Biased contests for symmetric players," Games and Economic Behavior, Elsevier, vol. 103(C), pages 116-144.
    43. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
    44. 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.
    45. 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.
    46. 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.
    47. Heski Bar-Isaac & Raphaël Lévy, 2022. "Motivating Employees through Career Paths," Journal of Labor Economics, University of Chicago Press, vol. 40(1), pages 95-131.
    48. 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.
    49. 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.
    50. Lazear, Edward P, 1989. "Pay Equality and Industrial Politics," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 561-580, June.
    51. Ryvkin, Dmitry & Drugov, Mikhail, 2020. "The shape of luck and competition in winner-take-all tournaments," Theoretical Economics, Econometric Society, vol. 15(4), November.
    52. 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.
    53. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    54. 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.
    55. Hideo Owan, 2004. "Promotion, Turnover, Earnings, and Firm-Sponsored Training," Journal of Labor Economics, University of Chicago Press, vol. 22(4), pages 955-978, October.
    56. René Kirkegaard, 2020. "Microfounded Contest Design," Working Papers 2003, University of Guelph, Department of Economics and Finance.
    57. 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.
    58. Lorens Imhof & Matthias Kräkel, 2016. "Ex post unbalanced tournaments," RAND Journal of Economics, RAND Corporation, vol. 47(1), pages 73-98, February.
    59. Alex Gershkov & Jianpei Li & Paul Schweinzer, 2009. "Efficient tournaments within teams," RAND Journal of Economics, RAND Corporation, vol. 40(1), pages 103-119, March.
    60. David Pérez‐Castrillo & David Wettstein, 2016. "Discrimination In A Model Of Contests With Incomplete Information About Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 881-914, August.
    61. Yigal Gerchak & Qi-Ming He, 2003. "When will the Range of Prizes in Tournaments Increase in the Noise or in the Number of Players?," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 151-165.
    62. 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.
    63. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    64. 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.
    65. 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.
    66. Dawei Fang & Thomas Noe & Philipp Strack, 2020. "Turning Up the Heat: The Discouraging Effect of Competition in Contests," Journal of Political Economy, University of Chicago Press, vol. 128(5), pages 1940-1975.
    67. 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.
    68. David Pérez‐Castrillo & David Wettstein, 2016. "Discrimination In A Model Of Contests With Incomplete Information About Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 881-914, August.
    69. 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.
    70. 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.
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    Cited by:

    1. 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.
    2. Goel, Sumit & Goyal, Amit, 2023. "Optimal tie-breaking rules," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    3. Mikhail Drugov & Dmitry Ryvkin, 2020. "Hunting for the discouragement effect in contests," Working Papers w0278, New Economic School (NES).
    4. René Kirkegaard, 2020. "Microfounded Contest Design," Working Papers 2003, University of Guelph, Department of Economics and Finance.
    5. Thomas Giebe & Oliver Gürtler, 2024. "Player Strength and Effort in Contests," ECONtribute Discussion Papers Series 285, University of Bonn and University of Cologne, Germany.
    6. 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.

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    More about this item

    Keywords

    Contest theory; Symmetric equilibrium; Heterogeneity; Risk; Stochastic dominance;
    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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