IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v91y2023i6p2295-2331.html
   My bibliography  Save this article

Mixed Strategies in the Indefinitely Repeated Prisoner's Dilemma

Author

Listed:
  • Julian Romero
  • Yaroslav Rosokha

Abstract

Identifying the strategies that are played is critical to understanding behavior in repeated games. This process is difficult because only choices (not strategies) are observable. Recently, a debate has emerged regarding whether subjects play mixed strategies in the indefinitely repeated prisoner's dilemma. We use an experimental approach to elicit mixed strategies from human subjects, thereby providing direct empirical evidence. We find that a majority of subjects use mixed strategies. However, the data also suggest subjects' strategies are becoming less mixed over time, and move toward three focal pure strategies: Tit For Tat, Grim Trigger, and Always Defect. We use the elicited strategies to provide an empirically‐relevant foundation for analyzing commonly used mixture model estimation procedures.

Suggested Citation

  • Julian Romero & Yaroslav Rosokha, 2023. "Mixed Strategies in the Indefinitely Repeated Prisoner's Dilemma," Econometrica, Econometric Society, vol. 91(6), pages 2295-2331, November.
    • Handle: RePEc:wly:emetrp:v:91:y:2023:i:6:p:2295-2331
    DOI: 10.3982/ECTA17482
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA17482
    Download Restriction: no
    File URL: https://libkey.io/10.3982/ECTA17482?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
    ---><---

    References listed on IDEAS

    as
    1. Cason, Timothy N. & Mui, Vai-Lam, 2019. "Individual versus group choices of repeated game strategies: A strategy method approach," Games and Economic Behavior, Elsevier, vol. 114(C), pages 128-145.
    2. Julian Romero & Yaroslav Rosokha, 2019. "The Evolution of Cooperation: The Role of Costly Strategy Adjustments," American Economic Journal: Microeconomics, American Economic Association, vol. 11(1), pages 299-328, February.
    3. Drew Fudenberg & David G. Rand & Anna Dreber, 2012. "Slow to Anger and Fast to Forgive: Cooperation in an Uncertain World," American Economic Review, American Economic Association, vol. 102(2), pages 720-749, April.
    4. Cockburn, Iain & Henderson, Rebecca, 1994. "Racing to Invest? The Dynamics of Competition in Ethical Drug Discovery," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 3(3), pages 481-519, Fall.
    5. James R. Bland, 2020. "Heterogeneous trembles and model selection in the strategy frequency estimation method," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 6(2), pages 113-124, December.
    6. Jim Engle-Warnick & Robert Slonim, 2006. "Inferring repeated-game strategies from actions: evidence from trust game experiments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 603-632, August.
    7. Marina Agranov & Pietro Ortoleva, 2017. "Stochastic Choice and Preferences for Randomization," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 40-68.
    8. Ioannou, Christos A. & Romero, Julian, 2014. "A generalized approach to belief learning in repeated games," Games and Economic Behavior, Elsevier, vol. 87(C), pages 178-203.
    9. Kahn, Lawrence M, 1993. "Unions and Cooperative Behavior: The Effect of Discounting," Journal of Labor Economics, University of Chicago Press, vol. 11(4), pages 680-703, October.
    10. David Gill & Yaroslav Rosokha, 2024. "Beliefs, Learning, and Personality in the Indefinitely Repeated Prisoner's Dilemma," American Economic Journal: Microeconomics, American Economic Association, vol. 16(3), pages 259-283, August.
    11. Yves Breitmoser, 2015. "Cooperation, but No Reciprocity: Individual Strategies in the Repeated Prisoner's Dilemma," American Economic Review, American Economic Association, vol. 105(9), pages 2882-2910, September.
    12. Ernan Haruvy & Dale O. Stahl & Paul W. Wilson, 2001. "Modeling And Testing For Heterogeneity In Observed Strategic Behavior," The Review of Economics and Statistics, MIT Press, vol. 83(1), pages 146-157, February.
    13. Shachat, Jason M., 2002. "Mixed Strategy Play and the Minimax Hypothesis," Journal of Economic Theory, Elsevier, vol. 104(1), pages 189-226, May.
    14. Eugenio Proto & Aldo Rustichini & Andis Sofianos, 2019. "Intelligence, Personality, and Gains from Cooperation in Repeated Interactions," Journal of Political Economy, University of Chicago Press, vol. 127(3), pages 1351-1390.
    15. Charles Noussair & Marc Willinger, 2011. "Mixed strategies in an unprofitable game: an experiment," Working Papers 11-19, LAMETA, Universtiy of Montpellier, revised Nov 2011.
    16. Giovanni Maggi, 1999. "The Role of Multilateral Institutions in International Trade Cooperation," American Economic Review, American Economic Association, vol. 89(1), pages 190-214, March.
    17. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
    18. Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
    19. repec:bla:jemstr:v:3:y:1994:i:3:p:481-519:a is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yaroslav Rosokha & Chen Wei, 2024. "Cooperation in Queueing Systems," Management Science, INFORMS, vol. 70(11), pages 7597-7616, November.

    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. Fabian Dvorak, 2023. "stratEst: a software package for strategy frequency estimation," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 9(2), pages 337-349, December.
    2. Heller, Yuval & Tubul, Itay, 2023. "Strategies in the repeated prisoner’s dilemma: A cluster analysis," MPRA Paper 117444, University Library of Munich, Germany.
    3. Drouvelis, Michalis & Pearce, Graeme, 2023. "Leadership under the shadow of the future: Intelligence and strategy choice in infinitely repeated games," European Economic Review, Elsevier, vol. 152(C).
    4. Wright, Julian, 2013. "Punishment strategies in repeated games: Evidence from experimental markets," Games and Economic Behavior, Elsevier, vol. 82(C), pages 91-102.
    5. Breitmoser, Yves & Valasek, Justin, 2017. "A rationale for unanimity in committees," Discussion Papers, Research Unit: Economics of Change SP II 2017-308, WZB Berlin Social Science Center.
    6. Chowdhury Mohammad Sakib Anwar & Konstantinos Georgalos, 2024. "Position uncertainty in a sequential public goods game: an experiment," Experimental Economics, Springer;Economic Science Association, vol. 27(4), pages 820-853, September.
    7. repec:tiu:tiucen:200922 is not listed on IDEAS
    8. Ernesto Reuben & Sigrid Suetens, 2012. "Revisiting strategic versus non-strategic cooperation," Experimental Economics, Springer;Economic Science Association, vol. 15(1), pages 24-43, March.
    9. Normann, Hans-Theo & Sternberg, Martin, 2023. "Human-algorithm interaction: Algorithmic pricing in hybrid laboratory markets," European Economic Review, Elsevier, vol. 152(C).
    10. Ridinger, Garret & McBride, Michael, 2025. "Theory-of-mind ability and cooperation," Journal of Economic Behavior & Organization, Elsevier, vol. 230(C).
    11. Romero, Julian & Rosokha, Yaroslav, 2018. "Constructing strategies in the indefinitely repeated prisoner’s dilemma game," European Economic Review, Elsevier, vol. 104(C), pages 185-219.
    12. Marco Lambrecht & Eugenio Proto & Aldo Rustichini & Andis Sofianos, 2024. "Intelligence Disclosure and Cooperation in Repeated Interactions," American Economic Journal: Microeconomics, American Economic Association, vol. 16(3), pages 199-231, August.
    13. Evans, Alecia & Sesmero, Juan, 2022. "Cooperation in Social Dilemmas with Correlated Noisy Payoffs: Theory and Experimental Evidence," 2021 Annual Meeting, August 1-3, Austin, Texas 322804, Agricultural and Applied Economics Association.
    14. Stahl, Dale O. & Haruvy, Ernan, 2008. "Level-n bounded rationality in two-player two-stage games," Journal of Economic Behavior & Organization, Elsevier, vol. 65(1), pages 41-61, January.
    15. Gill, David & Knepper, Zachary & Prowse, Victoria & Zhou, Junya, 2023. "How Cognitive Skills Affect Strategic Behavior: Cognitive Ability, Fluid Intelligence and Judgment," CAGE Online Working Paper Series 690, Competitive Advantage in the Global Economy (CAGE).
    16. Normann, Hans-Theo & Sternberg, Martin, 2022. "Human-algorithm interaction: Algorithmic pricing in hybrid laboratory markets," DICE Discussion Papers 392, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    17. Gill, David & Knepper, Zachary & Prowse, Victoria & Zhou, Junya, 2025. "How cognitive skills affect strategic behavior: Cognitive ability, fluid intelligence and judgment," Games and Economic Behavior, Elsevier, vol. 149(C), pages 82-95.
    18. Somayeh Kokabisaghi & Eric J Pauwels & Andre B Dorsman, 2019. "To snipe or not to snipe, that is the question! Transitions in sniping behaviour among competing algorithmic traders," Papers 1912.04012, arXiv.org, revised Sep 2020.
    19. repec:tiu:tiucen:200833 is not listed on IDEAS
    20. Cason, Timothy N. & Mui, Vai-Lam, 2019. "Individual versus group choices of repeated game strategies: A strategy method approach," Games and Economic Behavior, Elsevier, vol. 114(C), pages 128-145.
    21. Kartal, Melis & Müller, Wieland & Tremewan, James, 2021. "Building trust: The costs and benefits of gradualism," Games and Economic Behavior, Elsevier, vol. 130(C), pages 258-275.
    22. Maximilian Andres, 2024. "Equilibrium selection in infinitely repeated games with communication," CEPA Discussion Papers 75, Center for Economic Policy Analysis.

    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:wly:emetrp:v:91:y:2023:i:6:p:2295-2331. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    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.