Abstract
We introduce a class of infinite dimensional replicator dynamics in the form of nonlinear and non local integrodifferential equations. We study the properties of the steady state of the equation and their connections with Nash equilibria of the game as well as the global stability of the steady state using techniques from the theory of variational inequalities and infinite dimensional dynamical systems.
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Acknowledgements
The authors wish to acknowledge the partial support of a National Technical University of Athens Caratheodory Research Grant.
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© 2011 Springer-Verlag Berlin Heidelberg
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Kravvaritis, D., Papanicolaou, V., Xepapadeas, T., Yannacopoulos, A.N. (2011). A Class of Infinite Dimensional Replicator Dynamics. In: Peixoto, M., Pinto, A., Rand, D. (eds) Dynamics, Games and Science I. Springer Proceedings in Mathematics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11456-4_33
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DOI: https://doi.org/10.1007/978-3-642-11456-4_33
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