Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Best response dynamics for continuous games

Author(s): E. N. Barron; R. Goebel; R. R. Jensen
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 91A25, 49J35; Secondary 37B25, 34D20, 26B25
Posted: November 2, 2009
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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.

References:

1.
F. Clarke, Y. Ledyaev, R. Stern, and P. Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, New York, 1998. MR 1488695 (99a:49001)

2.
I. Gilboa and A. Matsui, Social stability and equilibrium, Econometrica 59 (1991), 859-867. MR 1106514

3.
G.W. Brown, Iterative solutions of games by fictitious play, Activity Analysis of Production and Allocation (T.C. Koopmans, ed.), Wiley, New York, 1951. MR 0056265 (15:48e)

4.
J. Hofbauer and S. Sorin, Best response dynamics for continuous zero-sum games, Discrete and Continuous Dynamical Systems Ser. B 6 (2006), no. 1, 215-224. MR 2172204 (2007b:34027)

5.
J.-P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984. MR 755330 (85j:49010)

6.
L.S. Shapley, Some topics in two-person games, Advances in Game Theory (M. Drescher, L.S. Shapley, and A.W. Tucker, eds.), Princeton University Press, Princeton, N.J., 1964. MR 0198990 (33:7140)

7.
R.T. Rockafellar and R. Wets, Variational Analysis, Springer-Verlag, Berlin, 1998. MR 1491362 (98m:49001)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 91A25, 49J35, 37B25, 34D20, 26B25

Retrieve articles in all Journals with MSC (2010): 91A25, 49J35, 37B25, 34D20, 26B25

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: 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
Posted: November 2, 2009
Communicated by: Yingfei Yi
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google