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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Best response dynamics for continuous games


Authors: E. N. Barron, R. Goebel and R. R. Jensen
Journal: Proc. Amer. Math. Soc. 138 (2010), 1069-1083
MSC (2010): Primary 91A25, 49J35; Secondary 37B25, 34D20, 26B25
Published electronically: November 2, 2009
MathSciNet review: 2566572
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Abstract: We extend the convergence result of Hofbauer and Sorin for the best response differential inclusions coming from a nonconcave, nonconvex continuous payoff function $ U(x,y)$. A counterexample shows that convergence to a Nash equilibrium may not be true if we attempt to generalize the result to a three-person nonzero sum game.


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Additional Information

E. N. Barron
Affiliation: Department of Mathematics and Statistics, Loyola University Chicago, Chicago, Illinois 60626
Email: ebarron@luc.edu

R. Goebel
Affiliation: Department of Mathematics and Statistics, Loyola University Chicago, Chicago, Illinois 60626
Email: rgoebel@luc.edu

R. R. Jensen
Affiliation: Department of Mathematics and Statistics, Loyola University Chicago, Chicago, Illinois 60626
Email: rjensen@luc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10170-3
PII: S 0002-9939(09)10170-3
Keywords: Best response, quasiconcave, quasiconvex, Nash equilibrium
Received by editor(s): May 8, 2009
Received by editor(s) in revised form: August 18, 2009
Published electronically: November 2, 2009
Communicated by: Yingfei Yi
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.