Brown–von Neumann–Nash Dynamics: The Continuous Strategy Case

Hofbauer J, Oechssler J, Riedel F (2009)
Games and Economic Behavior 65(2): 406-429.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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DOI
Autor*in
Hofbauer, J.; Oechssler, J.; Riedel, FrankUniBi
Einrichtung
Fakultät für Wirtschaftswissenschaften
Institut für mathematische Wirtschaftsforschung
Abstract / Bemerkung
Brown and von Neumann introduced a dynamical system that converges to saddle points of zero sum,carries with finitely many strategies. Nash used the mapping underlying these dynamics to prove existence of equilibria in general games. The resulting Brown-von Neumann-Nash dynamics are a benchmark example for myopic adjustment dynamics that, in contrast to replicator dynamics. allow for innovation, but require less rationality than the best response dynamics. This paper studies the BNN dynamics for games with infinitely many strategies. We establish Nash stationarity for continuous payoff functions. For negative semidefinite games (that include zero sum games), we generalize the results of Brown and von Neumann. In addition, we show that evolutionarily robust Nash equilibria are asymptotically stable. A complete stability analysis for doubly symmetric games is also obtained. (C) 2008 Elsevier Inc. All rights reserved.
Stichworte
Evolutionary stability; BNN; Learning in games
Erscheinungsjahr
2009
Zeitschriftentitel
Games and Economic Behavior
Band
65
Ausgabe
2
Seite(n)
406-429
ISSN
0899-8256
Page URI
https://pub.uni-bielefeld.de/record/1944377

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Hofbauer J, Oechssler J, Riedel F. Brown–von Neumann–Nash Dynamics: The Continuous Strategy Case. Games and Economic Behavior. 2009;65(2):406-429.
Hofbauer, J., Oechssler, J., & Riedel, F. (2009). Brown–von Neumann–Nash Dynamics: The Continuous Strategy Case. Games and Economic Behavior, 65(2), 406-429. https://doi.org/10.1016/j.geb.2008.03.006
Hofbauer, J., Oechssler, J., and Riedel, Frank. 2009. “Brown–von Neumann–Nash Dynamics: The Continuous Strategy Case”. Games and Economic Behavior 65 (2): 406-429.
Hofbauer, J., Oechssler, J., and Riedel, F. (2009). Brown–von Neumann–Nash Dynamics: The Continuous Strategy Case. Games and Economic Behavior 65, 406-429.
Hofbauer, J., Oechssler, J., & Riedel, F., 2009. Brown–von Neumann–Nash Dynamics: The Continuous Strategy Case. Games and Economic Behavior, 65(2), p 406-429.
J. Hofbauer, J. Oechssler, and F. Riedel, “Brown–von Neumann–Nash Dynamics: The Continuous Strategy Case”, Games and Economic Behavior, vol. 65, 2009, pp. 406-429.
Hofbauer, J., Oechssler, J., Riedel, F.: Brown–von Neumann–Nash Dynamics: The Continuous Strategy Case. Games and Economic Behavior. 65, 406-429 (2009).
Hofbauer, J., Oechssler, J., and Riedel, Frank. “Brown–von Neumann–Nash Dynamics: The Continuous Strategy Case”. Games and Economic Behavior 65.2 (2009): 406-429.
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