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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.

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Bibliographic Info

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

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  1. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, Elsevier, vol. 64(3), pages 279-283, September.
  2. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, Elsevier, vol. 7(1), pages 83-102, February.
  3. Friedman, James W. & Mezzetti, Claudio, 2001. "Learning in Games by Random Sampling," Journal of Economic Theory, Elsevier, Elsevier, vol. 98(1), pages 55-84, May.
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  7. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 14(1), pages 124-143, May.
  8. M. Kandori & R. Rob, 2010. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Levine's Working Paper Archive 502, David K. Levine.
  9. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, Econometric Society, vol. 52(4), pages 1007-28, July.
  10. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, Elsevier, vol. 13(1), pages 111-124, March.
  11. Nikolai S. Kukushkin & Satoru Takahashi & Tetsuo Yamamori, 2005. "Improvement dynamics in games with strategic complementarities," International Journal of Game Theory, Springer, Springer, vol. 33(2), pages 229-238, 06.
  12. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, Elsevier, vol. 4(2), pages 284-313, April.
  13. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, Elsevier, vol. 48(1), pages 94-110, July.
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