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Do we detect and exploit mixed strategy play by opponents?

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  • Jason Shachat
  • J. Todd Swarthout

Abstract

We conducted an experiment in which each subject repeatedly played a game with a unique Nash equilibrium in mixed strategies against some computer-implemented mixed strategy. The results indicate subjects are successful at detecting and exploiting deviations from Nash equilibrium. However, there is heterogeneity in subject behavior and performance. We present a one variable model of dynamic random belief formation which rationalizes observed heterogeneity and other features of the data. Copyright Springer-Verlag 2004

Suggested Citation

  • Jason Shachat & J. Todd Swarthout, 2004. "Do we detect and exploit mixed strategy play by opponents?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 359-373, July.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:3:p:359-373
    DOI: 10.1007/s001860400354
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    Cited by:

    1. 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.
    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. Duffy, Sean & Naddeo, JJ & Owens, David & Smith, John, 2016. "Cognitive load and mixed strategies: On brains and minimax," MPRA Paper 89720, University Library of Munich, Germany.
    4. Shachat, Jason & Swarthout, J. Todd, 2012. "Learning about learning in games through experimental control of strategic interdependence," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 383-402.
    5. Shachat, Jason & Swarthout, J. Todd & Wei, Lijia, 2015. "A Hidden Markov Model For The Detection Of Pure And Mixed Strategy Play In Games," Econometric Theory, Cambridge University Press, vol. 31(4), pages 729-752, August.
    6. 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.
    7. repec:wyi:journl:002151 is not listed on IDEAS
    8. 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.
    9. Alcocer, Christian Diego & Jeitschko, Thomas D. & Shupp, Robert, 2020. "Naive and sophisticated mixing: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 170(C), pages 157-173.
    10. Spiliopoulos, Leonidas, 2008. "Humans versus computer algorithms in repeated mixed strategy games," MPRA Paper 6672, University Library of Munich, Germany.
    11. Spiliopoulos, Leonidas, 2008. "Do repeated game players detect patterns in opponents? Revisiting the Nyarko & Schotter belief elicitation experiment," MPRA Paper 6666, University Library of Munich, Germany.
    12. repec:cup:judgdm:v:13:y:2018:i:5:p:413-427 is not listed on IDEAS
    13. Aurora García-Gallego & Penelope Hernández-Rojas & Amalia Rodrigo-González, 2015. "An experimental online matching pennies game," Working Papers 2015/03, Economics Department, Universitat Jaume I, Castellón (Spain).
    14. Steven Levitt & John List & David Reiley, 2010. "What happens in the field stays in the field: Professionals do not play minimax in laboratory experiments," Artefactual Field Experiments 00080, The Field Experiments Website.
    15. Cardella, Eric, 2012. "Learning to make better strategic decisions," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 382-392.
    16. 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.
    17. March, Christoph, 2021. "Strategic interactions between humans and artificial intelligence: Lessons from experiments with computer players," Journal of Economic Psychology, Elsevier, vol. 87(C).
    18. 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.
    19. Frederic Moisan & Cleotilde Gonzalez, 2017. "Security under Uncertainty : Adaptive Attackers Are More Challenging to Human Defenders than Random Attackers," Post-Print hal-03188217, HAL.
    20. Jason Shachat & J. Todd Swarthout & Lijia Wei, 2011. "Man versus Nash An experiment on the self-enforcing nature of mixed strategy equilibrium," Working Papers 1101, Xiamen Unversity, The Wang Yanan Institute for Studies in Economics, Finance and Economics Experimental Laboratory, revised 21 Feb 2011.
    21. Jan Libich & Dat Thanh Nguyen, 2022. "When a compromise gets compromised by another compromise," Australian Economic Papers, Wiley Blackwell, vol. 61(4), pages 678-716, December.
    22. Ido Erev & Alvin E. Roth & Robert Slonim, 2016. "Minimax across a population of games," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 2(2), pages 144-156, November.

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    JEL classification:

    • C9 - Mathematical and Quantitative Methods - - Design of Experiments

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