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Best response adaptation under dominance solvability

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Author Info
Kukushkin, Nikolai S.

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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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 4108.

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Date of creation: 13 Jul 2007
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Handle: RePEc:pra:mprapa:4108

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Related research
Keywords: Dominance solvability Best response dynamics Potential game

Find related papers by 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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  7. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July. [Downloadable!] (restricted)
  8. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February. [Downloadable!] (restricted)
  9. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July. [Downloadable!] (restricted)
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  13. Nikolai S. Kukushkin & Satoru Takahashi & Tetsuo Yamamori, 2005. "Improvement dynamics in games with strategic complementarities," International Journal of Game Theory, Springer, vol. 33(2), pages 229-238, 06. [Downloadable!] (restricted)
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