Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A reaction-diffusion system arising in game theory: Existence of solutions and spatial dominance
Pages: 3891 - 3901, Issue 10, December 2017

doi:10.3934/dcdsb.2017200      Abstract        References        Full text (371.0K)           Related Articles

Hideo Deguchi - Department of Mathematics, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan (email)

1 H. Deguchi, Existence, uniqueness and non-uniqueness of weak solutions of parabolic initial-value problems with discontinuous nonlinearities, Proc. Roy. Soc. Edinburgh Sect. A, 135 (2005), 1139-1167.       
2 H. Deguchi, On weak solutions of parabolic initial value problems with discontinuous nonlinearities, Nonlinear Anal., 63 (2005), e1107-e1117.
3 H. Deguchi, Existence, uniqueness and stability of weak solutions of parabolic systems with discontinuous nonlinearities, Monatsh. Math., 156 (2009), 211-231.       
4 H. Deguchi, Weak solutions of a parabolic system with a discontinuous nonlinearity, Nonlinear Anal., 71 (2009), e2902-e2911.       
5 I. Gilboa and A. Matsui, Social stability and equilibrium, Econometrica, 59 (1991), 859-867.       
6 J. C. Harsanyi and R. Selten, A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge, MA, 1988.       
7 J. Hofbauer, Stability for the best response dynamics, preprint, 1995.
8 J. Hofbauer, Equilibrium selection via travelling waves, in Game Theory, Experience, Rationality (eds. W. Leinfellner and E. K√∂hler), Kluwer Academic Publishers, Dordrecht, 5 (1998), 245-259.       
9 J. Hofbauer, The spatially dominant equilibrium of a game, Ann. Oper. Res., 89 (1999), 233-251.       
10 J. Hofbauer and P. L. Simon, An existence theorem for parabolic equations on $R^N$ with discontinuous nonlinearity, Electron. J. Qual. Theory Differ. Equ., 8 (2001), 1-9.       
11 H. P. McKean and V. Moll, Stabilization to the standing wave in a simple caricature of the nerve equation, Comm. Pure Appl. Math., 39 (1986), 485-529.       
12 S. Morris, R. Rob and H. S. Shin, p-dominance and belief potential, Econometrica, 63 (1995), 145-157.       
13 D. Oyama, S. Takahashi and J. Hofbauer, Monotone Methods for Equilibrium Selection Under Perfect Foresight Dynamics, Working paper No.0318, University of Vienna, 2003.
14 S. Takahashi, Perfect foresight dynamics in games with linear incentives and time symmetry, Internat. J. Game Theory, 37 (2008), 15-38.       
15 D. Terman, A free boundary problem arising from a bistable reaction-diffusion equation, SIAM J. Math. Anal., 14 (1983), 1107-1129.       

Go to top