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Minimax across a population of games

Author

Listed:
  • Ido Erev

    (The Technion)

  • Alvin E. Roth

    (Stanford University)

  • Robert Slonim

    (The University of Sydney)

Abstract

Most economic experiments designed to test theories carefully choose specific games. This paper reports on an experimental design to evaluate how well the minimax hypothesis describes behavior across a population of games. Past studies suggest that the hypothesis is more accurate the closer the equilibrium is to equal probability play of all actions, but many differences between the designs makes direct comparison impossible. We examine the minimax hypothesis by randomly sampling constant sum games with two players and two actions with a unique equilibrium in mixed strategies. Only varying the games, we find behavior is more consistent with minimax play the closer the mixed strategy equilibrium is to equal probability play of each action. The results are robust over all iterations as well as early and final play. Experimental designs in which the game is a variable allow some conclusions to be drawn that cannot be drawn from more conventional experimental designs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jesaex:v:2:y:2016:i:2:d:10.1007_s40881-016-0029-3
    DOI: 10.1007/s40881-016-0029-3
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    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. Wooders, John & Shachat, Jason M., 2001. "On the Irrelevance of Risk Attitudes in Repeated Two-Outcome Games," Games and Economic Behavior, Elsevier, vol. 34(2), pages 342-363, February.
    4. Ochs, Jack & Roth, Alvin E, 1989. "An Experimental Study of Sequential Bargaining," American Economic Review, American Economic Association, vol. 79(3), pages 355-384, June.
    5. Axel Ockenfels & Gary E. Bolton, 2000. "ERC: A Theory of Equity, Reciprocity, and Competition," American Economic Review, American Economic Association, vol. 90(1), pages 166-193, March.
    6. 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.
    7. Stahl, Dale O., 1996. "Boundedly Rational Rule Learning in a Guessing Game," Games and Economic Behavior, Elsevier, vol. 16(2), pages 303-330, October.
    8. Robert Slonim & Alvin E. Roth, 1998. "Learning in High Stakes Ultimatum Games: An Experiment in the Slovak Republic," Econometrica, Econometric Society, vol. 66(3), pages 569-596, May.
    9. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency, Heterogeneity, and Granularity of Individual Behavior under Uncertainty," Economics Working Papers 0076, Institute for Advanced Study, School of Social Science.
    10. 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.
    11. Roth, Alvin E. & Vesna Prasnikar & Masahiro Okuno-Fujiwara & Shmuel Zamir, 1991. "Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An Experimental Study," American Economic Review, American Economic Association, vol. 81(5), pages 1068-1095, December.
    12. Ido Erev & Alvin Roth & Robert Slonim & Greg Barron, 2007. "Learning and equilibrium as useful approximations: Accuracy of prediction on randomly selected constant sum games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(1), pages 29-51, October.
    13. Erev, Ido & Roth, Alvin E. & Slonim, Robert L. & Barron, Greg, 2002. "Predictive value and the usefulness of game theoretic models," International Journal of Forecasting, Elsevier, vol. 18(3), pages 359-368.
    14. Ido Erev & Eyal Ert & Alvin E. Roth, 2010. "A Choice Prediction Competition for Market Entry Games: An Introduction," Games, MDPI, vol. 1(2), pages 1-20, May.
    15. Erev, I. & Roth, Alvin E., 2014. "Maximization, learning, and economic behavior," Scholarly Articles 30831199, Harvard University Department of Economics.
    16. Ochs Jack, 1995. "Games with Unique, Mixed Strategy Equilibria: An Experimental Study," Games and Economic Behavior, Elsevier, vol. 10(1), pages 202-217, July.
    17. Yoella Bereby-Meyer & Alvin E. Roth, 2006. "The Speed of Learning in Noisy Games: Partial Reinforcement and the Sustainability of Cooperation," American Economic Review, American Economic Association, vol. 96(4), pages 1029-1042, September.
    18. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency and Heterogeneity of Individual Behavior under Uncertainty," American Economic Review, American Economic Association, vol. 97(5), pages 1921-1938, December.
    19. Roth, Alvin E. & Herzog, Stefan & Hau, Robin & Hertwig, Ralph & Erev, Ido & Ert, Eyal & Haruvy, Ernan & Stewart, Terrence & West, Robert & Lebiere, Christian, 2009. "A Choice Prediction Competition: Choices From Experience and From Description," Scholarly Articles 5343169, Harvard University Department of Economics.
    20. Nick Feltovich, 2000. "Reinforcement-Based vs. Belief-Based Learning Models in Experimental Asymmetric-Information," Econometrica, Econometric Society, vol. 68(3), pages 605-642, May.
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    More about this item

    Keywords

    Game theory; Experimental design; Equilibrium;
    All these keywords.

    JEL classification:

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

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