Game dynamics, mixed strategies, and gradient systems

Game dynamics, as a branch of frequency-dependent population genetics, leads to replicator equations. If phenotypes correspond to mixed strategies, evolution will affect the frequencies of the phenotypes and of the strategies and thus lead to two dynamical models. Some examples of this, including the sex ratio, will be discussed with the help of a non-Euclidean metric leading to a gradient system. Some other examples from population genetics and chemical kinetics confirm the usefulness of such gradients in describing evolutionary optimization.

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