|
Best response dynamics for continuous games
Author(s):
E.
N.
Barron;
R.
Goebel;
R.
R.
Jensen
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1069-1083.
MSC (2010):
Primary 91A25, 49J35;
Secondary 37B25, 34D20, 26B25
Posted:
November 2, 2009
MathSciNet review:
2566572
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  . 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.
|
