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A Unified Approach to p-Dominance and its Generalizations in Games with Strategic Complements and Substitutes

Author

Listed:
  • 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

The concepts of p-dominance and its generalizations are useful to understand equilibrium selection and equilibrium stability in games. We prove that in games with strategic complements, games with strategic substitutes, and games with combinations of both, these concepts are logically equivalent to pure strategy Nash equilibria in a transformed game of complete information. The transformation process is easy to follow and implement and retains a natural connection to the original game. Therefore, our results make these solution concepts more tractable and accessible, and this is shown in many applications. The connection to Nash equilibrium helps us prove new results about the structure of classes of such solution concepts. Similar to the case of Nash equilibrium, these classes are complete lattices in games with strategic complements, but are totally unordered when we deviate from this case.

Suggested Citation

  • Anne-Christine Barthel & Eric Hoffmann & Tarun Sabarwal, 2021. "A Unified Approach to p-Dominance and its Generalizations in Games with Strategic Complements and Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202109, University of Kansas, Department of Economics.
    • Handle: RePEc:kan:wpaper:202109
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    File URL: http://www2.ku.edu/~kuwpaper/2021Papers/202109.pdf
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    References listed on IDEAS

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    Cited by:

    1. Tarun Sabarwal, 2023. "General theory of equilibrium in models with complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202307, University of Kansas, Department of Economics, revised Sep 2023.

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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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