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Deep and shallow thinking in the long run

Author

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  • Nax, Heinrich Harald

    (Zurich Center for Market Design and SUZ, University of Zurich)

  • Newton, Jonathan

    (Kyoto Institute of Economic Research, Kyoto University)

Abstract

Humans differ in their strategic reasoning abilities and in beliefs about others’ strategic reasoning abilities. Studying such cognitive hierarchies has produced new insights regarding equilibrium analysis in economics. This paper investigates the effect of cognitive hierarchies on long run behavior. Despite short run behavior being highly sensitive to variation in strategic reasoning abilities, this variation is not replicated in the long run. In particular, when generalized risk dominant strategy profiles exist, they emerge in the long run independently of the strategic reasoning abilities of players. These abilities may be arbitrarily low or high, heterogeneous across players and evolve over time.

Suggested Citation

  • Nax, Heinrich Harald & Newton, Jonathan, 2022. "Deep and shallow thinking in the long run," Theoretical Economics, Econometric Society, vol. 17(4), November.
    • Handle: RePEc:the:publsh:4824
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    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    2. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    3. Peski, Marcin, 2010. "Generalized risk-dominance and asymmetric dynamics," Journal of Economic Theory, Elsevier, vol. 145(1), pages 216-248, January.
    4. Crawford, Vincent P, 1974. "Learning the Optimal Strategy in a Zero-Sum Game," Econometrica, Econometric Society, vol. 42(5), pages 885-891, September.
    5. Heller, Yuval, 2015. "Three steps ahead," Theoretical Economics, Econometric Society, vol. 10(1), January.
    6. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    7. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
    8. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    9. Abhimanyu Khan & Ronald Peeters, 2014. "Cognitive hierarchies in adaptive play," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 903-924, November.
    10. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    11. Duffy, John & Nagel, Rosemarie, 1997. "On the Robustness of Behaviour in Experimental "Beauty Contest" Games," Economic Journal, Royal Economic Society, vol. 107(445), pages 1684-1700, November.
    12. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 195-208.
    13. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    14. Blume, Lawrence E., 2003. "How noise matters," Games and Economic Behavior, Elsevier, vol. 44(2), pages 251-271, August.
    15. Vincent P. Crawford, 2019. "Experiments on Cognition, Communication, Coordination, and Cooperation in Relationships," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 167-191, August.
    16. Nikolaus Robalino & Arthur Robson, 2016. "The Evolution of Strategic Sophistication," American Economic Review, American Economic Association, vol. 106(4), pages 1046-1072, April.
    17. David Gill & Victoria Prowse, 2016. "Cognitive Ability, Character Skills, and Learning to Play Equilibrium: A Level-k Analysis," Journal of Political Economy, University of Chicago Press, vol. 124(6), pages 1619-1676.
    18. Battalio, Raymond & Samuelson, Larry & Van Huyck, John, 2001. "Optimization Incentives and Coordination Failure in Laboratory Stag Hunt Games," Econometrica, Econometric Society, vol. 69(3), pages 749-764, May.
    19. Matros, Alexander, 2003. "Clever agents in adaptive learning," Journal of Economic Theory, Elsevier, vol. 111(1), pages 110-124, July.
    20. Goeree, Jacob K. & Holt, Charles A., 2004. "A model of noisy introspection," Games and Economic Behavior, Elsevier, vol. 46(2), pages 365-382, February.
    21. 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.
    22. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    23. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    24. Stahl Dale O., 1993. "Evolution of Smartn Players," Games and Economic Behavior, Elsevier, vol. 5(4), pages 604-617, October.
    25. David Myatt & Chris Wallace, 2003. "Sophisticated play by idiosyncratic agents," Journal of Evolutionary Economics, Springer, vol. 13(3), pages 319-345, August.
    26. 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.
    27. Newton, Jonathan, 2017. "Shared intentions: The evolution of collaboration," Games and Economic Behavior, Elsevier, vol. 104(C), pages 517-534.
    28. Stahl, Dale O., 2000. "Rule Learning in Symmetric Normal-Form Games: Theory and Evidence," Games and Economic Behavior, Elsevier, vol. 32(1), pages 105-138, July.
    29. Conlisk, John, 1993. "Adaptive tactics in games : Further solutions to the Crawford puzzle," Journal of Economic Behavior & Organization, Elsevier, vol. 22(1), pages 51-68, September.
    30. Tang, Fang-Fang, 2001. "Anticipatory learning in two-person games: some experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 44(2), pages 221-232, February.
    31. H.D. Block & Jacob Marschak, 1959. "Random Orderings and Stochastic Theories of Response," Cowles Foundation Discussion Papers 66, Cowles Foundation for Research in Economics, Yale University.
    32. Rusch, Hannes, 2019. "The evolution of collaboration in symmetric 2×2-games with imperfect recognition of types," Games and Economic Behavior, Elsevier, vol. 114(C), pages 118-127.
    33. Dale O. Stahl, 1999. "Evidence based rules and learning in symmetric normal-form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 111-130.
    34. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
    35. Conlisk, John, 1993. "Adaptation in games : Two solutions to the Crawford puzzle," Journal of Economic Behavior & Organization, Elsevier, vol. 22(1), pages 25-50, September.
    36. Teck-Hua Ho & Xuanming Su, 2013. "A Dynamic Level-k Model in Sequential Games," Management Science, INFORMS, vol. 59(2), pages 452-469, March.
    37. Lim, Wooyoung & Neary, Philip R., 2016. "An experimental investigation of stochastic adjustment dynamics," Games and Economic Behavior, Elsevier, vol. 100(C), pages 208-219.
    38. Frank Heinemann & Rosemarie Nagel & Peter Ockenfels, 2004. "The Theory of Global Games on Test: Experimental Analysis of Coordination Games with Public and Private Information," Econometrica, Econometric Society, vol. 72(5), pages 1583-1599, September.
    39. Iijima, Ryota, 2015. "Iterated generalized half-dominance and global game selection," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 120-136.
    40. Johan Stennek, 2000. "The survival value of assuming others to be rational," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(2), pages 147-163.
    41. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," LSE Research Online Documents on Economics 65422, London School of Economics and Political Science, LSE Library.
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    More about this item

    Keywords

    Bounded rationality; level-k thinking; evolution;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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