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Best response adaptation under dominance solvability

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  • Kukushkin, Nikolai S.

Abstract

Two new properties of a finite strategic game, strong and weak BR-dominance solvability, are introduced. The first property holds, e.g., if the game is strongly dominance solvable or if it is weakly dominance solvable and all best responses are unique. It ensures that every simultaneous best response adjustment path, as well as every non-discriminatory individual best response improvement path, reaches a Nash equilibrium in a finite number of steps. The second property holds, e.g., if the game is weakly dominance solvable; it ensures that every strategy profile can be connected to a Nash equilibrium with a simultaneous best response path and with an individual best response path (if there are more than two players, unmotivated switches from one best response to another may be needed). In a two person game, weak BR-dominance solvability is necessary for the acyclicity of simultaneous best response adjustment paths, as well as for the acyclicity of best response improvement paths provided the set of Nash equilibria is rectangular.

Suggested Citation

  • Kukushkin, Nikolai S., 2007. "Best response adaptation under dominance solvability," MPRA Paper 4108, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:4108
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    File URL: https://mpra.ub.uni-muenchen.de/11704/1/MPRA_paper_11704.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Dominance solvability; Best response dynamics; Potential game;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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