IDEAS home Printed from https://ideas.repec.org/a/spr/jesaex/v2y2016i2d10.1007_s40881-016-0029-3.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40881-016-0029-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40881-016-0029-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Stahl, Dale O., 1996. "Boundedly Rational Rule Learning in a Guessing Game," Games and Economic Behavior, Elsevier, vol. 16(2), pages 303-330, October.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Nick Feltovich, 2000. "Reinforcement-Based vs. Belief-Based Learning Models in Experimental Asymmetric-Information," Econometrica, Econometric Society, vol. 68(3), pages 605-642, May.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Erev, I. & Roth, Alvin E., 2014. "Maximization, learning, and economic behavior," Scholarly Articles 30831199, Harvard University Department of Economics.
    19. Ochs Jack, 1995. "Games with Unique, Mixed Strategy Equilibria: An Experimental Study," Games and Economic Behavior, Elsevier, vol. 10(1), pages 202-217, July.
    20. 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.
    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. 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.
    2. Olivier Armantier, 2006. "Do Wealth Differences Affect Fairness Considerations?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 391-429, May.
    3. 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.
    4. David Cooper & Nick Feltovich & Alvin Roth & Rami Zwick, 2003. "Relative versus Absolute Speed of Adjustment in Strategic Environments: Responder Behavior in Ultimatum Games," Experimental Economics, Springer;Economic Science Association, vol. 6(2), pages 181-207, October.
    5. Camerer, Colin F. & Ho, Teck-Hua, 2015. "Behavioral Game Theory Experiments and Modeling," Handbook of Game Theory with Economic Applications,, Elsevier.
    6. James Andreoni & Marco Castillo & Ragan Petrie, 2009. "Revealing Preferences for Fairness in Ultimatum Bargaining," Korean Economic Review, Korean Economic Association, vol. 25, pages 35-63.
    7. repec:wyi:journl:002151 is not listed on IDEAS
    8. Olivier Armantier, 2001. "Does Wealth Affect Fairness Considerations?," Department of Economics Working Papers 01-05, Stony Brook University, Department of Economics.
    9. Andreoni,J. & Castillo,M. & Petrie,R., 2000. "What do bargainers' preferences look like? : exploring a convex ultimatum game," Working papers 25, Wisconsin Madison - Social Systems.
    10. 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.
    11. Yi, Kang-Oh, 2005. "Quantal-response equilibrium models of the ultimatum bargaining game," Games and Economic Behavior, Elsevier, vol. 51(2), pages 324-348, May.
    12. James Andreoni & Emily Blanchard, 2006. "Testing subgame perfection apart from fairness in ultimatum games," Experimental Economics, Springer;Economic Science Association, vol. 9(4), pages 307-321, December.
    13. Charness, Gary & Kuhn, Peter, 2011. "Lab Labor: What Can Labor Economists Learn from the Lab?," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 3, pages 229-330, Elsevier.
    14. Ori Plonsky & Yefim Roth & Ido Erev, 2021. "Underweighting of rare events in social interactions and its implications to the design of voluntary health applications," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(2), pages 267-289, March.
    15. 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.
    16. 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.
    17. Committee, Nobel Prize, 2012. "Alvin E. Roth and Lloyd S. Shapley: Stable allocations and the practice of market design," Nobel Prize in Economics documents 2012-1, Nobel Prize Committee.
    18. Fisman, Raymond & Jakiela, Pamela & Kariv, Shachar, 2017. "Distributional preferences and political behavior," Journal of Public Economics, Elsevier, vol. 155(C), pages 1-10.
    19. repec:cup:judgdm:v:16:y:2021:i:2:p:267-289 is not listed on IDEAS
    20. 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.
    21. Cooper, David J. & Stockman, Carol Kraker, 2002. "Fairness and learning: an experimental examination," Games and Economic Behavior, Elsevier, vol. 41(1), pages 26-45, October.
    22. Irlenbusch, Bernd, 2004. "Relying on a man's word?: An experimental study on non-binding contracts," International Review of Law and Economics, Elsevier, vol. 24(3), pages 299-332, September.

    More about this item

    Keywords

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

    JEL classification:

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

    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:spr:jesaex:v:2:y:2016:i:2:d:10.1007_s40881-016-0029-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.