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Two-Player Asymmetric Contests with Ratio-Form Contest Success Functions

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  • Kyung Hwan Baik

Abstract

I examine players' equilibrium effort levels in two-player asymmetric contests with ratio-form contest success functions. I first characterize the Nash equilibrium of the simultaneous-move game. I show that the equilibrium effort ratio is equal to the valuation ratio, and that the prize dissipation ratios for the players are the same. I also show that the prize dissipation ratio for each player is less than or equal to the minimum of the players' probabilities of winning at the Nash equilibrium and thus never exceeds a half. Then I examine how the equilibrium effort ratio, the prize dissipation ratios, and the players' equilibrium effort levels respond when the players' valuations for the prize or their abilities change. (JEL D72, C72) Copyright 2004, Oxford University Press.

Suggested Citation

  • Kyung Hwan Baik, 2004. "Two-Player Asymmetric Contests with Ratio-Form Contest Success Functions," Economic Inquiry, Western Economic Association International, vol. 42(4), pages 679-689, October.
    • Handle: RePEc:oup:ecinqu:v:42:y:2004:i:4:p:679-689
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    File URL: http://hdl.handle.net/10.1093/ei/cbh089
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    Citations

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    Cited by:

    1. Kyung Hwan Baik & Jihyun Kim, 2014. "Contests with Bilateral Delegation: Unobservable Contracts," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 170(3), pages 387-405, September.
    2. Radhika Santhanam & De Liu & Wei-Cheng Milton Shen, 2016. "Research Note—Gamification of Technology-Mediated Training: Not All Competitions Are the Same," Information Systems Research, INFORMS, vol. 27(2), pages 453-465, June.
    3. Malueg, David A. & Yates, Andrew J., 2006. "Citizen participation in pollution permit markets," Journal of Environmental Economics and Management, Elsevier, vol. 51(2), pages 205-217, March.
    4. Robert Ridlon, 2016. "Does Manufacturer Advertising Crowd‐in or Crowd‐out Retailer Advertising? An Application of an Endogenous Prize Contest with Asymmetric Players," Southern Economic Journal, John Wiley & Sons, vol. 83(2), pages 364-379, October.
    5. Camilla Mastromarco & Marco Runkel, 2009. "Rule changes and competitive balance in Formula One motor racing," Applied Economics, Taylor & Francis Journals, vol. 41(23), pages 3003-3014.
    6. Gürtler, Oliver, 2006. "Contractual Incentive Provision and Commitment in Rent-Seeking Contests," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 100, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    7. Maria Arbatskaya & Hugo Mialon, 2010. "Multi-activity contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 23-43, April.
    8. Goel, Sumit & Goyal, Amit, 2023. "Optimal tie-breaking rules," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    9. Kyung Hwan Baik, 2007. "Equilibrium Contingent Compensation in Contests with Delegation," Southern Economic Journal, John Wiley & Sons, vol. 73(4), pages 986-1002, April.
    10. Giuseppe Dari-Mattiacci & Eric Langlais & Bruno Lovat & Francesco Parisi, 2013. "Asymmetries in Rent-Seeking," Working Papers hal-04141218, HAL.
    11. Wang Zhewei, 2010. "The Optimal Accuracy Level in Asymmetric Contests," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-18, April.
    12. Häfner, Samuel, 2017. "A tug-of-war team contest," Games and Economic Behavior, Elsevier, vol. 104(C), pages 372-391.
    13. Sakshi Gupta & Ram Singh, 2018. "On Existence and Properties of Pure-strategy Equilibria under Contests," Working papers 288, Centre for Development Economics, Delhi School of Economics.
    14. Robert Ridlon & Jiwoong Shin, 2013. "Favoring the Winner or Loser in Repeated Contests," Marketing Science, INFORMS, vol. 32(5), pages 768-785, September.
    15. Samuel Häfner & Georg Nöldeke, 2022. "Sorting in iterated incumbency contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(4), pages 1103-1140, November.
    16. Kyung Hwan Baik & Jong Hwa Lee, 2013. "Endogenous Timing In Contests With Delegation," Economic Inquiry, Western Economic Association International, vol. 51(4), pages 2044-2055, October.
    17. Yang-Ming Chang & Zijun Luo, 2017. "Endogenous Destruction In Conflict: Theory And Extensions," Economic Inquiry, Western Economic Association International, vol. 55(1), pages 479-500, January.
    18. Matthew D. Mitchell, 2019. "Uncontestable favoritism," Public Choice, Springer, vol. 181(1), pages 167-190, October.
    19. Blavatskyy, Pavlo R., 2010. "Contest success function with the possibility of a draw: Axiomatization," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 267-276, March.
    20. Malueg, David A. & Yates, Andrew J., 2005. "Equilibria and comparative statics in two-player contests," European Journal of Political Economy, Elsevier, vol. 21(3), pages 738-752, September.
    21. Kyung Hwan Baik & Dongryul Lee, 2012. "Do Rent‐Seeking Groups Announce Their Sharing Rules?," Economic Inquiry, Western Economic Association International, vol. 50(2), pages 348-363, April.
    22. Christian Ewerhart & Julian Teichgräber, 2019. "Multi-battle contests, finite automata, and the tug-of-war," ECON - Working Papers 318, Department of Economics - University of Zurich.
    23. Jaesoo Kim & Jongwoo Park, 2014. "Monitoring in Tournaments," Economics Bulletin, AccessEcon, vol. 34(3), pages 1431-1437.

    More about this item

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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