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We introduce a nonlinear degenerate parabolic equation containing a nonlocalterm. The equation serves as a replicator dynamics model where the set ofstrategies is a continuum. In our model the payoff operator (which is thecontinuous analog of the payoff matrix) is nonsymmetric and, also, evolves withtime. We are interested in solutions $u(t, x)$ of our equation which arepositive and their integral (with respect to $x$) over the whole space is $1$,for any $t > 0$. These solutions, being probability densities, can serve astime-evolving mixed strategies of a player. We show that for our model there isan one-parameter family of self-similar such solutions $u(t, x)$, allapproaching the Dirac delta function $\delta(x)$ as $t \to 0^+$.

Similarity Solutions of a Replicator Dynamics Equation Associated to a Continuum of Pure Strategies