IDEAS home Printed from https://ideas.repec.org/p/geo/guwopa/gueconwpa~21-21-07.html
   My bibliography  Save this paper

Disequilibrium Play in Tennis

Author

Abstract

Are the serves of the world’s best tennis pros consistent with the theoretical prediction of Nash equilibrium in mixed strategies? We analyze their serve direction choices (to the returner’s left, right or body) with data from an online database called the Match Charting Project. Using a new methodology, we test and decisively reject a key implication of a mixed strategy Nash equilibrium, namely, that the probability of winning a service game is the same for all serve directions. We also use dynamic programming (DP) to numerically solve for the best-response serve strategies to probability models of service game outcomes estimated for individual server-returner pairs, such as Novak Djokovic serving to Rafael Nadal. We show that for most elite pro servers, the DP serve strategy significantly increases their service game win probability compared to the mixed strategies they actually use, which we estimate using flexible reduced-form logit models. Stochastic simulations verify that our results are robust to estimation error. Classification- C61, C73, L21

Suggested Citation

  • Axel Anderson & Jeremy Rosen & John Rust & Kin-Ping Wong, 2021. "Disequilibrium Play in Tennis," Working Papers gueconwpa~21-21-07, Georgetown University, Department of Economics.
    • Handle: RePEc:geo:guwopa:gueconwpa~21-21-07
    as

    Download full text from publisher

    File URL: http://axelanderson.georgetown.domains/DynamicTennis.pdf
    File Function: Full text
    Download Restriction: None
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fedor Iskhakov & John Rust & Bertel Schjerning, 2016. "Recursive Lexicographical Search: Finding All Markov Perfect Equilibria of Finite State Directional Dynamic Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(2), pages 658-703.
    2. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    3. P.-A. Chiappori, 2002. "Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer," American Economic Review, American Economic Association, vol. 92(4), pages 1138-1151, September.
    4. Walker, Mark & Wooders, John & Amir, Rabah, 2011. "Equilibrium play in matches: Binary Markov games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 487-502, March.
    5. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    6. Romain Gauriot & Lionel Page & John Wooders, 2016. "Nash at Wimbledon: Evidence from Half a Million Serves," QuBE Working Papers 046, QUT Business School.
    7. Brown, James N & Rosenthal, Robert W, 1990. "Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment," Econometrica, Econometric Society, vol. 58(5), pages 1065-1081, September.
    8. S. L. George, 1973. "Optimal Strategy in Tennis: A Simple Probabilistic Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(1), pages 97-104, March.
    9. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 395-415.
    10. Klaassen, Franc J.G.M. & Magnus, Jan R., 2009. "The efficiency of top agents: An analysis through service strategy in tennis," Journal of Econometrics, Elsevier, vol. 148(1), pages 72-85, January.
    11. David Romer, 2006. "Do Firms Maximize? Evidence from Professional Football," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 340-365, April.
    12. Fedor Iskhakov & Thomas H. Jørgensen & John Rust & Bertel Schjerning, 2017. "The endogenous grid method for discrete‐continuous dynamic choice models with (or without) taste shocks," Quantitative Economics, Econometric Society, vol. 8(2), pages 317-365, July.
    13. Klaassen F. J G M & Magnus J. R., 2001. "Are Points in Tennis Independent and Identically Distributed? Evidence From a Dynamic Binary Panel Data Model," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 500-509, June.
    14. Shih-Hsun Hsu & Chen-Ying Huang & Cheng-Tao Tang, 2007. "Minimax Play at Wimbledon: Comment," American Economic Review, American Economic Association, vol. 97(1), pages 517-523, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wu, Tong & Lawell, C.Y. Cynthia Lin & Just, David R. & Zhao, Jiancheng & Fei, Zhangjun & Wei, Qiang, 2022. "Optimal Forest Management for Interdependent Products: A Nested Dynamic Bioeconomic Model and Application to Bamboo," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322164, Agricultural and Applied Economics Association.

    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. Emara, Noha & Owens, David & Smith, John & Wilmer, Lisa, 2017. "Serial correlation in National Football League play calling and its effects on outcomes," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 69(C), pages 125-132.
    2. Leonidas Spiliopoulos, 2018. "Randomization and serial dependence in professional tennis matches: Do strategic considerations, player rankings and match characteristics matter?," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(5), pages 413-427, September.
    3. repec:cup:judgdm:v:13:y:2018:i:5:p:413-427 is not listed on IDEAS
    4. Paserman, M. Daniele, 2023. "Gender Differences in Performance in Competitive Environments? Evidence from Professional Tennis Players," Journal of Economic Behavior & Organization, Elsevier, vol. 212(C), pages 590-609.
    5. Kenneth Kovash & Steven D. Levitt, 2009. "Professionals Do Not Play Minimax: Evidence from Major League Baseball and the National Football League," NBER Working Papers 15347, National Bureau of Economic Research, Inc.
    6. Joseph P. McGarrity & Brian Linnen, 2010. "Pass or Run: An Empirical Test of the Matching Pennies Game Using Data from the National Football League," Southern Economic Journal, John Wiley & Sons, vol. 76(3), pages 791-810, January.
    7. Steven D. Levitt & John A. List & David H. Reiley, 2010. "What Happens in the Field Stays in the Field: Exploring Whether Professionals Play Minimax in Laboratory Experiments," Econometrica, Econometric Society, vol. 78(4), pages 1413-1434, July.
    8. Duffy, Sean & Naddeo, JJ & Owens, David & Smith, John, 2016. "Cognitive load and mixed strategies: On brains and minimax," MPRA Paper 71878, University Library of Munich, Germany.
    9. Okano, Yoshitaka, 2013. "Minimax play by teams," Games and Economic Behavior, Elsevier, vol. 77(1), pages 168-180.
    10. Brian Goff & Stephen L. Locke, 2019. "Revisiting Romer: Digging Deeper Into Influences on NFL Managerial Decisions," Journal of Sports Economics, , vol. 20(5), pages 671-689, June.
    11. Romain Gauriot & Lionel Page, 2019. "Does Success Breed Success? a Quasi-Experiment on Strategic Momentum in Dynamic Contests," The Economic Journal, Royal Economic Society, vol. 129(624), pages 3107-3136.
    12. Emara, Noha & Owens, David & Smith, John & Wilmer, Lisa, 2014. "Minimax on the gridiron: Serial correlation and its effects on outcomes in the National Football League," MPRA Paper 58907, University Library of Munich, Germany.
    13. Germán Coloma, 2007. "Penalty Kicks in Soccer," Journal of Sports Economics, , vol. 8(5), pages 530-545, October.
    14. Van Essen, Matt & Wooders, John, 2015. "Blind stealing: Experience and expertise in a mixed-strategy poker experiment," Games and Economic Behavior, Elsevier, vol. 91(C), pages 186-206.
    15. Luigi Buzzacchi & Stefano Pedrini, 2014. "Does player specialization predict player actions? Evidence from penalty kicks at FIFA World Cup and UEFA Euro Cup," Applied Economics, Taylor & Francis Journals, vol. 46(10), pages 1067-1080, April.
    16. Heifetz, Aviad & Heller, Ruth & Ostreiher, Roni, 2021. "Do Arabian babblers play mixed strategies in a “volunteer’s dilemma”?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 91(C).
    17. Romain Gauriot & Lionel Page & John Wooders, 2016. "Nash at Wimbledon: Evidence from Half a Million Serves," QuBE Working Papers 046, QUT Business School.
    18. Spiliopoulos, Leonidas, 2012. "Pattern recognition and subjective belief learning in a repeated constant-sum game," Games and Economic Behavior, Elsevier, vol. 75(2), pages 921-935.
    19. Casilda Lasso de la Vega & Oscar Volij, 2020. "The value of a draw," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1023-1044, November.
    20. Jin-Hyuk Kim, 2013. "Does competition affect evolutionary dynamics? Evidence from a collegiate university," Applied Economics Letters, Taylor & Francis Journals, vol. 20(8), pages 781-785, May.
    21. Spiliopoulos, Leonidas, 2013. "Beyond fictitious play beliefs: Incorporating pattern recognition and similarity matching," Games and Economic Behavior, Elsevier, vol. 81(C), pages 69-85.

    More about this item

    Keywords

    tennis; games; Nash equilibrium; Minimax theorem; constant sum games; mixed strategies; dynamic directional games; binary Markov games; dynamic programming; structural estimation; muscle memory;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L21 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Business Objectives of the Firm

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:geo:guwopa:gueconwpa~21-21-07. 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: Marcia Suss (email available below). General contact details of provider: http://econ.georgetown.edu/ .

    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.