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Characterizing Robust Solutions in Monotone Games

Author

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  • Anne-Christine Barthel

    (Department of Economics, *West Texas A&M University, Canyon, TX 79016, USA)

  • Eric Hoffmann

    (Department of Economics, *West Texas A&M University, Canyon, TX 79016, USA)

  • Tarun Sabarwal

    (Department of Economics, University of Kansas, Lawrence, KS 66045, USA)

Abstract

In game theory, p-dominance and its set-valued generalizations serve as important robust solution concepts. We show that in monotone games, (which include the broad classes of super-modular games, sub-modular games, and their combinations,) these concepts can be characterized in terms of pure strategy Nash equilibria in an auxiliary game of complete information. The auxiliary game is constructed in a transparent manner that is easy to follow and retains a natural connection to the original game. Our results show explicitly how to map these concepts to a corresponding Nash equilibrium thereby identifying a new bijection between robust solutions in the original game and equilibrium notions in the auxiliary game. Moreover, our characterizations lead to new results about the structure of entire classes of such solution concepts. In games with strategic complements, these classes are complete lattices. More generally, they are totally unordered. We provide several examples to highlight these results.

Suggested Citation

  • Anne-Christine Barthel & Eric Hoffmann & Tarun Sabarwal, 2021. "Characterizing Robust Solutions in Monotone Games," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202121, University of Kansas, Department of Economics, revised Oct 2021.
    • Handle: RePEc:kan:wpaper:202121
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    File URL: http://www2.ku.edu/~kuwpaper/2021Papers/202121.pdf
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    References listed on IDEAS

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    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.

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    More about this item

    Keywords

    p-dominance; p-best response set; minimal p-best response set; strategic complements; strategic substitutes;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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