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Wiley InterScience | ||||||||
  International Journal of Economic TheoryVolume 2 Issue 1, Pages 41 - 53 Published Online: 2 Mar 2006 © 2009 The International Association for Economic Theory
Abstract | References | Full Text: PDF (Size: 152K) | Related Articles | Citation Tracking  Stability and instability of the unbeatable strategy in dynamic processes I thank Drew Fudenberg for instruction and guidance. I am also grateful to Attila Ambrus, Ulrich Berger, Eric Budish, William H. Sandholm, Satoru Takahashi, an anonymous referee, and seminar participants at Harvard University and Tokyo University for helpful comments and suggestions, to Satoshi Takahashi for his help with the simulations presented in Section 3.3, and to Josef Hofbauer for, among other things, introducing me to his results on best response dynamics discussed in Section 3.2 Copyright IAET KEYWORDS unbeatable strategy • ESS • replicator dynamics • best response dynamics • smoothed best response dynamics KEYWORDS C72 • C73 ABSTRACTA strategy is unbeatable if it is immune to any entrant strategy of any size. This paper investigates static and dynamic properties of unbeatable strategies. We give equivalent conditions for a strategy to be unbeatable and compare it with related equilibrium concepts. An unbeatable strategy is globally stable under replicator dynamics. In contrast, an unbeatable strategy can fail to be globally stable under best response dynamics even if it is also a unique and strict Nash equilibrium. | 
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