IDEAS home Printed from https://ideas.repec.org/a/oup/restud/v70y2003i2p395-415.html
   My bibliography  Save this article

Professionals Play Minimax

Author

Listed:
  • Ignacio Palacios-Huerta

Abstract

The implications of the Minimax theorem are tested using natural data. The tests use a unique data set from penalty kicks in professional soccer games. In this natural setting experts play a one-shot two-person zero-sum game. The results of the tests are remarkably consistent with equilibrium play in every respect: (i) winning probabilities are statistically identical across strategies for players; (ii) players' choices are serially independent. The tests have substantial power to distinguish equilibrium play from disequilibrium alternatives. These results represent the first time that both implications of von Neumann's Minimax theorem are supported under natural conditions. Copyright 2003, Wiley-Blackwell.

Suggested Citation

  • Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 395-415.
  • Handle: RePEc:oup:restud:v:70:y:2003:i:2:p:395-415
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/1467-937X.00249
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    2. Mookherjee Dilip & Sopher Barry, 1994. "Learning Behavior in an Experimental Matching Pennies Game," Games and Economic Behavior, Elsevier, vol. 7(1), pages 62-91, July.
    3. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    4. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    5. 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.
    6. Stahl, Dale O., 2000. "Rule Learning in Symmetric Normal-Form Games: Theory and Evidence," Games and Economic Behavior, Elsevier, vol. 32(1), pages 105-138, July.
    7. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    8. Rapoport, Amnon & Boebel, Richard B., 1992. "Mixed strategies in strictly competitive games: A further test of the minimax hypothesis," Games and Economic Behavior, Elsevier, vol. 4(2), pages 261-283, April.
    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. Ofer Azar & Michael Bar-Eli, 2011. "Do soccer players play the mixed-strategy Nash equilibrium?," Applied Economics, Taylor & Francis Journals, vol. 43(25), pages 3591-3601.
    2. Isabelle Brocas & Juan D. Carrillo, 2022. "The development of randomization and deceptive behavior in mixed strategy games," Quantitative Economics, Econometric Society, vol. 13(2), pages 825-862, May.
    3. 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.
    4. Kyoo il Kim, 2006. "Semiparametric Estimation of Signaling Games," Labor Economics Working Papers 22452, East Asian Bureau of Economic Research.
    5. Gallice, Andrea, 2007. "Best Responding to What? A Behavioral Approach to One Shot Play in 2x2 Games," Discussion Papers in Economics 1365, University of Munich, Department of Economics.
    6. Camerer, Colin F. & Ho, Teck-Hua, 2015. "Behavioral Game Theory Experiments and Modeling," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. Friedman, Daniel & Zhao, Shuchen, 2021. "When are mixed equilibria relevant?," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 51-65.
    8. 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.
    9. Spiliopoulos, Leonidas, 2013. "Beyond fictitious play beliefs: Incorporating pattern recognition and similarity matching," Games and Economic Behavior, Elsevier, vol. 81(C), pages 69-85.
    10. Rapoport, Amnon & Amaldoss, Wilfred, 2000. "Mixed strategies and iterative elimination of strongly dominated strategies: an experimental investigation of states of knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 42(4), pages 483-521, August.
    11. Ho, Teck H. & Camerer, Colin F. & Chong, Juin-Kuan, 2007. "Self-tuning experience weighted attraction learning in games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 177-198, March.
    12. Sean Duffy & J. J. Naddeo & David Owens & John Smith, 2024. "Cognitive Load and Mixed Strategies: On Brains and Minimax," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 26(03), pages 1-34, September.
    13. Scroggin, Steven, 2007. "Exploitable actions of believers in the "law of small numbers" in repeated constant-sum games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 219-235, March.
    14. Hanaki, Nobuyuki & Sethi, Rajiv & Erev, Ido & Peterhansl, Alexander, 2005. "Learning strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 56(4), pages 523-542, April.
    15. Armantier, Olivier, 2004. "Does observation influence learning?," Games and Economic Behavior, Elsevier, vol. 46(2), pages 221-239, February.
    16. Okano, Yoshitaka, 2013. "Minimax play by teams," Games and Economic Behavior, Elsevier, vol. 77(1), pages 168-180.
    17. Asim Ansari & Ricardo Montoya & Oded Netzer, 2012. "Dynamic learning in behavioral games: A hidden Markov mixture of experts approach," Quantitative Marketing and Economics (QME), Springer, vol. 10(4), pages 475-503, December.
    18. Robert W. Rosenthal & Jason Shachat & Mark Walker, 2003. "Hide and seek in Arizona," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 273-293, December.
    19. Camerer, Colin F. & Ho, Teck-Hua & Chong, Juin-Kuan, 2002. "Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games," Journal of Economic Theory, Elsevier, vol. 104(1), pages 137-188, May.
    20. Pangallo, Marco & Sanders, James B.T. & Galla, Tobias & Farmer, J. Doyne, 2022. "Towards a taxonomy of learning dynamics in 2 × 2 games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 1-21.

    More about this item

    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:oup:restud:v:70:y:2003:i:2:p:395-415. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/restud .

    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.