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Mixed Strategies in the Indefinitely Repeated Prisoner's Dilemma

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. Charles Noussair & Marc Willinger, 2011. "Mixed strategies in an unprofitable game: an experiment," Working Papers 11-19, LAMETA, Universtiy of Montpellier, revised Nov 2011.
    3. 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.
    4. 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.
    5. 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.
    6. Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. repec:bla:jemstr:v:3:y:1994:i:3:p:481-519:a is not listed on IDEAS
    12. 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.
    13. 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.
    14. Gill, David & Rosokha, Yaroslav, 2020. "Beliefs, learning, and personality in the indefinitely repeated prisoner’s dilemma," CAGE Online Working Paper Series 489, Competitive Advantage in the Global Economy (CAGE).
    15. 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.
    16. 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.
    17. Shachat, Jason M., 2002. "Mixed Strategy Play and the Minimax Hypothesis," Journal of Economic Theory, Elsevier, vol. 104(1), pages 189-226, May.
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