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Characterizing Robust Solutions to 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)

Abstract

In game theory, p-dominance and p-best response sets serve as important robustness solution concepts by allowing for deviations from the stringent common knowledge requirements of Nash equilibrium. However, solving for such sets remains largely intractable beyond the simplest of settings. The contributions of this paper are twofold: First, in monotone games, (which include the broad class of supermodular games, submodular games, and their combinations,) we show that these concepts can be characterized in terms of pure strategy Nash equilibria in an auxiliary game of complete information. This makes it considerably easier to compute such sets, facilitating their broader use. Second, these characterizations lead to new results about the structure of entire classes of such solution concepts, including minimal p-best response (p-MBR) sets, which generalize well known results for pure strategy Nash equilibria. In games with strategic complements, these classes are complete lattices. More generally, they are totally unordered. Several examples highlight the results.

Suggested Citation

  • Anne-Christine Barthel & Eric Hoffmann & Tarun Sabarwal, 2020. "Characterizing Robust Solutions to Monotone Games," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202012, University of Kansas, Department of Economics.
  • Handle: RePEc:kan:wpaper:202012
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    File URL: http://www2.ku.edu/~kuwpaper/2020Papers/202012.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

    Strategic complements; Strategic substitutes; Monotone games; p-dominance; p-best response set;
    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
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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