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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, 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; if the set of Nash equilibria is rectangular, it is also necessary for the acyclicity of best response mprovement paths.

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

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Date of creation: 20 Nov 2008
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Handle: RePEc:pra:mprapa:4108

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Related research
Keywords: Dominance solvability; Best response dynamics; Potential game;

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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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  3. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September. [Downloadable!] (restricted)
  4. 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)
  5. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March. [Downloadable!] (restricted)
  6. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April. [Downloadable!] (restricted)
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  8. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321. [Downloadable!] (restricted)
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  9. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July. [Downloadable!] (restricted)
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