IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v108y2023ics0304406823000654.html
   My bibliography  Save this article

Optimal tie-breaking rules

Author

Listed:
  • Goel, Sumit
  • Goyal, Amit

Abstract

We consider two-player contests with the possibility of ties and study the effect of different tie-breaking rules on effort. For ratio-form and difference-form contests that admit pure-strategy Nash equilibrium, we find that the effort of both players is monotone decreasing in the probability that ties are broken in favor of the stronger player. Thus, the effort-maximizing tie-breaking rule commits to breaking ties in favor of the weaker agent. With symmetric agents, we find that the equilibrium is generally symmetric and independent of the tie-breaking rule. We also study the design of random tie-breaking rules that are ex-ante fair and identify sufficient conditions under which breaking ties before the contest actually leads to greater expected effort than the more commonly observed practice of breaking ties after the contest.

Suggested Citation

  • Goel, Sumit & Goyal, Amit, 2023. "Optimal tie-breaking rules," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    • Handle: RePEc:eee:mateco:v:108:y:2023:i:c:s0304406823000654
    DOI: 10.1016/j.jmateco.2023.102872
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406823000654
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2023.102872?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Szech, Nora, 2015. "Tie-breaks and bid-caps in all-pay auctions," Games and Economic Behavior, Elsevier, vol. 92(C), pages 138-149.
    2. Che, Yeon-Koo & Gale, Ian, 2000. "Difference-Form Contests and the Robustness of All-Pay Auctions," Games and Economic Behavior, Elsevier, vol. 30(1), pages 22-43, January.
    3. Yizhaq Minchuk, 2022. "Winner‐pay contests with a no‐winner possibility," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(6), pages 1874-1879, September.
    4. Qiang Fu & Jingfeng Lu & Jun Zhang, 2016. "Disclosure policy in Tullock contests with asymmetric stochastic entry," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 49(1), pages 52-75, February.
    5. David Malueg & Andrew Yates, 2006. "Equilibria in rent-seeking contests with homogeneous success functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(3), pages 719-727, April.
    6. J. Amegashie, 2006. "A contest success function with a tractable noise parameter," Public Choice, Springer, vol. 126(1), pages 135-144, January.
    7. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
    8. Franke, Jörg & Leininger, Wolfgang & Wasser, Cédric, 2018. "Optimal favoritism in all-pay auctions and lottery contests," European Economic Review, Elsevier, vol. 104(C), pages 22-37.
    9. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    10. Imhof, Lorens & Kräkel, Matthias, 2014. "Tournaments with gaps," Economics Letters, Elsevier, vol. 122(2), pages 211-214.
    11. Jia, Hao & Skaperdas, Stergios & Vaidya, Samarth, 2013. "Contest functions: Theoretical foundations and issues in estimation," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 211-222.
    12. 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.
    13. Glenn C. Loury, 1979. "Market Structure and Innovation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(3), pages 395-410.
    14. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Biased contests for symmetric players," Games and Economic Behavior, Elsevier, vol. 103(C), pages 116-144.
    15. Maya Eden, 2006. "Optimal Ties in Contests," Discussion Paper Series dp430, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    16. Ewerhart, Christian, 2017. "Revenue ranking of optimally biased contests: The case of two players," Economics Letters, Elsevier, vol. 157(C), pages 167-170.
    17. Deng, Shanglyu & Wang, Xiruo & Wu, Zenan, 2018. "Incentives in lottery contests with draws," Economics Letters, Elsevier, vol. 163(C), pages 1-5.
    18. Lorens Imhof & Matthias Kräkel, 2016. "Ex post unbalanced tournaments," RAND Journal of Economics, RAND Corporation, vol. 47(1), pages 73-98, February.
    19. 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.
    20. Garfinkel, Michelle R. & Skaperdas, Stergios, 2007. "Economics of Conflict: An Overview," Handbook of Defense Economics, in: Keith Hartley & Todd Sandler (ed.), Handbook of Defense Economics, edition 1, volume 2, chapter 22, pages 649-709, Elsevier.
    21. Nti, Kofi O., 2004. "Maximum efforts in contests with asymmetric valuations," European Journal of Political Economy, Elsevier, vol. 20(4), pages 1059-1066, November.
    22. Zhu, Feng, 2021. "On optimal favoritism in all-pay contests," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    23. 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.
    24. Michael C. Fu, 2015. "Overview of the Handbook," International Series in Operations Research & Management Science, in: Michael C Fu (ed.), Handbook of Simulation Optimization, edition 127, chapter 0, pages 1-7, Springer.
    25. Hao Jia, 2012. "Contests with the Probability of a Draw: A Stochastic Foundation," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 391-406, September.
    26. Alberto Vesperoni & Anil Yildizparlak, 2019. "Contests With Draws: Axiomatization And Equilibrium," Economic Inquiry, Western Economic Association International, vol. 57(3), pages 1597-1616, July.
    27. Li, Bo & Wu, Zenan & Xing, Zeyu, 2023. "Optimally biased contests with draws," Economics Letters, Elsevier, vol. 226(C).
    28. Nti, Kofi O, 1997. "Comparative Statics of Contests and Rent-Seeking Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 43-59, February.
    29. Nti, Kofi O, 1999. "Rent-Seeking with Asymmetric Valuations," Public Choice, Springer, vol. 98(3-4), pages 415-430, March.
    30. Christian Ewerhart, 2021. "A typology of military conflict based on the Hirshleifer contest," ECON - Working Papers 400, Department of Economics - University of Zurich.
    31. Fu, Qiang & Wu, Zenan, 2020. "On the optimal design of biased contests," Theoretical Economics, Econometric Society, vol. 15(4), November.
    32. 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.
    33. Jack Hirshleifer, 1989. "Conflict and rent-seeking success functions: Ratio vs. difference models of relative success," Public Choice, Springer, vol. 63(2), pages 101-112, November.
    34. Alcalde, José & Dahm, Matthias, 2010. "Rent seeking and rent dissipation: A neutrality result," Journal of Public Economics, Elsevier, vol. 94(1-2), pages 1-7, February.
    35. 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.
    36. Baik, Kyung Hwan, 1998. "Difference-form contest success functions and effort levels in contests," European Journal of Political Economy, Elsevier, vol. 14(4), pages 685-701, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Li, Bo & Wu, Zenan & Xing, Zeyu, 2023. "Optimally biased contests with draws," Economics Letters, Elsevier, vol. 226(C).
    3. Jia, Hao & Skaperdas, Stergios & Vaidya, Samarth, 2013. "Contest functions: Theoretical foundations and issues in estimation," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 211-222.
    4. Ewerhart, Christian, 2017. "Contests with small noise and the robustness of the all-pay auction," Games and Economic Behavior, Elsevier, vol. 105(C), pages 195-211.
    5. Sakshi Gupta & Ram Singh, 2018. "On Existence and Properties of Pure-strategy Equilibria under Contests," Working Papers id:12840, eSocialSciences.
    6. Alberto Vesperoni, 2016. "A contest success function for rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 905-937, December.
    7. Franke, Jörg & Metzger, Lars P., 2023. "Repeated Contests with Draws," Ruhr Economic Papers 1016, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    8. Franke, Jörg & Leininger, Wolfgang & Wasser, Cédric, 2018. "Optimal favoritism in all-pay auctions and lottery contests," European Economic Review, Elsevier, vol. 104(C), pages 22-37.
    9. Hao Jia & Stergios Skaperdas, 2011. "Technologies of Conflict," Working Papers 101111, University of California-Irvine, Department of Economics.
    10. Raul Caruso, 2008. "Reciprocity in the shadow of threat," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 55(1), pages 91-111, April.
    11. Alan Gelder & Dan Kovenock & Brian Roberson, 2022. "All-pay auctions with ties," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(4), pages 1183-1231, November.
    12. Christian Ewerhart, 2014. "Elastic contests and the robustness of the all-pay auctions," ECON - Working Papers 155, Department of Economics - University of Zurich.
    13. Deng, Shanglyu & Wang, Xiruo & Wu, Zenan, 2018. "Incentives in lottery contests with draws," Economics Letters, Elsevier, vol. 163(C), pages 1-5.
    14. Alan Gelder & Dan Kovenock & Roman Sheremeta, 2015. "Behavior in All-Pay Auctions with Ties," Working Papers 15-22, Chapman University, Economic Science Institute.
    15. René Kirkegaard, 2020. "Microfounded Contest Design," Working Papers 2003, University of Guelph, Department of Economics and Finance.
    16. Luis Corchón, 2007. "The theory of contests: a survey," Review of Economic Design, Springer;Society for Economic Design, vol. 11(2), pages 69-100, September.
    17. Cubel, María & Sanchez-Pages, Santiago, 2016. "An axiomatization of difference-form contest success functions," Journal of Economic Behavior & Organization, Elsevier, vol. 131(PA), pages 92-105.
    18. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
    19. Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
    20. Helmut Dietl & Egon Franck & Martin Grossmann & Markus Lang, 2009. "Contest Theory and its Applications in Sports," Working Papers 0105, University of Zurich, Institute for Strategy and Business Economics (ISU).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:108:y:2023:i:c:s0304406823000654. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.