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Rationalizability and learning in games with strategic heterogeneity

Author

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  • Anne-Christine Barthel

    (West Texas A&M University)

  • Eric Hoffmann

    (West Texas A&M University)

Abstract

It is shown that in games of strategic heterogeneity (GSH), where both strategic complements and substitutes are present, there exist upper and lower serially undominated strategies which provide a bound for all other rationalizable strategies. By establishing a connection between learning in a repeated setting and the iterated deletion of strictly dominated strategies, we are able to provide necessary and sufficient conditions for dominance solvability and stability of equilibria. As a corollary, it is shown that only unique equilibria can be (globally) stable. Lastly, we provide conditions under which games that do not exhibit monotone best responses can be analyzed as a GSH. Applications to industrial organization, network games, and crime and punishment are given.

Suggested Citation

  • Anne-Christine Barthel & Eric Hoffmann, 2019. "Rationalizability and learning in games with strategic heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 565-587, April.
    • Handle: RePEc:spr:joecth:v:67:y:2019:i:3:d:10.1007_s00199-017-1092-6
    DOI: 10.1007/s00199-017-1092-6
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    Cited by:

    1. Rabah Amir, 2020. "Special Issue: Supermodularity and Monotonicity in Economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 907-911, November.
    2. He, Yong & Zhao, Xuan & Krishnan, Harish & Jin, Shibo, 2022. "Cooperation among suppliers of complementary products in repeated interactions," International Journal of Production Economics, Elsevier, vol. 252(C).
    3. Christian Ewerhart, 2020. "Ordinal potentials in smooth games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1069-1100, November.
    4. Xiao Luo & Xuewen Qian & Chen Qu, 2020. "Iterated elimination procedures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 437-465, September.
    5. Adriana Gama & Rim Lahmandi-Ayed & Ana Elisa Pereira, 2020. "Entry and mergers in oligopoly with firm-specific network effects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1139-1164, November.
    6. Anne-Christine Barthel & Eric Hoffmann, 2020. "On the existence and stability of equilibria in N-firm Cournot–Bertrand oligopolies," Theory and Decision, Springer, vol. 88(4), pages 471-491, May.
    7. Rabah Amir & Igor Evstigneev & Adriana Gama, 2021. "Oligopoly with network effects: firm-specific versus single network," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1203-1230, April.
    8. Lukasz Balbus & Wojciech Olszewski & Kevin Reffett & Lukasz Wozny, 2022. "Iterative Monotone Comparative Statics," KAE Working Papers 2022-072, Warsaw School of Economics, Collegium of Economic Analysis.
    9. Barthel, Anne-Christine & Hoffmann, Eric, 2022. "On dynamic adjustment and comparative statics via the implicit function theorem," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 52-57.
    10. Rabah Amir, 2019. "Supermodularity and Complementarity in Economic Theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 487-496, April.
    11. Anne-Christine Barthel & Eric Hoffmann, 2020. "Characterizing monotone games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1045-1068, November.

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    More about this item

    Keywords

    Strategic complements; Strategic substitutes; Learning;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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