  In this paper, we formulate a finite population variation of the Fisher-KPP
equation using the fact that the reaction term can be generated from the
replicator dynamic using a two-player two-strategy skew-symmetric game. We use
prior results from Ablowitz and Zeppetella to show that the resulting system of
partial differential equations admits a travelling wave solution, and that
there are closed form solutions for this travelling wave. Interestingly, the
closed form solution is constructed from a sign-reversal of the known closed
form solution of the classic Fisher equation. We also construct a closed form
solution approximation for the corresponding equilibrium problem on a finite
interval with Dirichlet and Neumann boundary conditions. Two conjectures on
these corresponding equilibrium problems are presented and analysed
numerically.
