The Replicator Dynamics for Games in Metric Spaces: a Finite‐Dimensional Approximation

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We study the replicator dynamics for asymmetric and symmetric games when the strategy sets are metric spaces. In this case the replicator dynamics evolves in a Banach space. We provide conditions, under which finite‐dimensional dynamicalsystems approximatesthisreplicator dynamics. These Approximations are studied in weak topology using the Kantorovich‐Rubinstein and, also, in the strong topology using the normal of total variation. Some numerical examples illustrate our results.

Saúl Mendoza Palacios Centro de Estudios Económicos del Colegio de México, Mexico