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Three steps ahead

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  • Heller, Yuval

Abstract

Experimental evidence suggest that people only use 1-3 iterations of strategic reasoning, and that some people systematically use less iterations than others. In this paper, we present a novel evolutionary foundation for these stylized facts. In our model, agents interact in finitely repeated Prisoner's Dilemma, and each agent is characterized by the number of steps he thinks ahead. When two agents interact, each of them has an independent probability to observe the opponent's type. We show that if this probability is not too close to 0 or 1, then the evolutionary process admits a unique stable outcome, in which the population includes a mixture of “naive” agents who think 1 step ahead, and “sophisticated” agents who think 2-3 steps ahead.

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  • Heller, Yuval, 2012. "Three steps ahead," MPRA Paper 40714, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:40714
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    Cited by:

    1. Nax, Heinrich Harald & Newton, Jonathan, 2022. "Deep and shallow thinking in the long run," Theoretical Economics, Econometric Society, vol. 17(4), November.
    2. Herold, Florian & Kuzmics, Christoph, 2020. "The evolution of taking roles," Journal of Economic Behavior & Organization, Elsevier, vol. 174(C), pages 38-63.
    3. Kevin He & Jonathan Libgober, 2020. "Evolutionarily Stable (Mis)specifications: Theory and Applications," Papers 2012.15007, arXiv.org, revised Feb 2023.
    4. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 997-1026, August.
    5. Rampal, Jeevant, 2022. "Limited Foresight Equilibrium," Games and Economic Behavior, Elsevier, vol. 132(C), pages 166-188.
    6. Sivan Frenkel & Yuval Heller & Roee Teper, 2018. "The Endowment Effect As Blessing," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(3), pages 1159-1186, August.
    7. Heller, Yuval & Mohlin, Erik, 2019. "Coevolution of deception and preferences: Darwin and Nash meet Machiavelli," Games and Economic Behavior, Elsevier, vol. 113(C), pages 223-247.
    8. Heller, Yuval, 2014. "Stability and trembles in extensive-form games," Games and Economic Behavior, Elsevier, vol. 84(C), pages 132-136.
    9. Sawa, Ryoji, 2021. "A stochastic stability analysis with observation errors in normal form games," Games and Economic Behavior, Elsevier, vol. 129(C), pages 570-589.
    10. Anujit Chakraborty, 2022. "Motives Behind Cooperation in Finitely Repeated Prisoner's Dilemma," Working Papers 353, University of California, Davis, Department of Economics.
    11. Heller, Yuval & Mohlin, Erik, 2015. "Stable Observable Behavior," MPRA Paper 63013, University Library of Munich, Germany.
    12. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    13. Chakraborty, Anujit, 2023. "Motives behind cooperation in finitely repeated prisoner's dilemma," Games and Economic Behavior, Elsevier, vol. 141(C), pages 105-132.

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    More about this item

    Keywords

    Indirect evolution; cognitive hierarchy; bounded forward-looking; Prisoner's Dilemma; Cooperation;
    All these keywords.

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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