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Humans versus computer algorithms in repeated mixed strategy games

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  • Spiliopoulos, Leonidas

Abstract

This paper is concerned with the modeling of strategic change in humans’ behavior when facing different types of opponents. In order to implement this efficiently a mixed experimental setup was used where subjects played a game with a unique mixed strategy Nash equilibrium for 100 rounds against 3 preprogrammed computer algorithms (CAs) designed to exploit different modes of play. In this context, substituting human opponents with computer algorithms designed to exploit commonly occurring human behavior increases the experimental control of the researcher allowing for more powerful statistical tests. The results indicate that subjects significantly change their behavior conditional on the type of CA opponent, exhibiting within-sub jects heterogeneity, but that there exists comparatively little between-subjects heterogeneity since players seemed to follow very similar strategies against each algorithm. Simple heuristics, such as win-stay/lose-shift, were found to model subjects and make out of sample predictions as well as, if not better than, more complicated models such as individually estimated EWA learning models which suffered from overfitting. Subjects modified their strategies in the direction of better response as calculated from CA simulations of various learning models, albeit not perfectly. Examples include the observation that subjects randomized more effectively as the pattern recognition depth of the CAs increased, and the drastic reduction in the use of the win-stay/lose-shift heuristic when facing a CA designed to exploit this behavior.

Suggested Citation

  • Spiliopoulos, Leonidas, 2008. "Humans versus computer algorithms in repeated mixed strategy games," MPRA Paper 6672, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:6672
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    File URL: https://mpra.ub.uni-muenchen.de/6672/1/MPRA_paper_6672.pdf
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    References listed on IDEAS

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    1. 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.
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    3. Atanasios Mitropoulos, 2001. "On the Measurement of the Predictive Success of Learning Theories in Repeated Games," Experimental 0110001, University Library of Munich, Germany.
    4. Smith, Vernon L & Walker, James M, 1993. "Rewards, Experience and Decision Costs in First Price Auctions," Economic Inquiry, Western Economic Association International, vol. 31(2), pages 237-245, April.
    5. Harrison, Glenn W, 1989. "Theory and Misbehavior of First-Price Auctions," American Economic Review, American Economic Association, vol. 79(4), pages 749-762, September.
    6. 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.
    7. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    8. 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.
    9. Walker, James M. & Smith, Vernon L. & Cox, James C., 1987. "Bidding behavior in first price sealed bid auctions : Use of computerized Nash competitors," Economics Letters, Elsevier, vol. 23(3), pages 239-244.
    10. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    11. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
    12. Dürsch, Peter & Kolb, Albert & Oechssler, Jörg & Schipper, Burkhard C., 2005. "Rage Against the Machines: How Subjects Learn to Play Against Computers," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 63, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    13. repec:spr:compst:v:59:y:2004:i:3:p:359-373 is not listed on IDEAS
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    Cited by:

    1. 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.
    2. 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.
    3. repec:wyi:journl:002151 is not listed on IDEAS
    4. 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.

    More about this item

    Keywords

    Behavioral game theory; Learning; Experimental economics; Simulations; Experience weighted attraction learning; Simulations; Repeated games; Mixed Strategy Nash equilibria; Economics and psychology;

    JEL classification:

    • C9 - Mathematical and Quantitative Methods - - Design of Experiments
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior

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