Allelic polymorphism is well known in cases where the heterozygote is fitter than either homozygote (Fisher, 1958, p. 114ff). By contrast, we consider a model where the tactics of a predator and its prey are both controlled by genetic factors which exhibit pure Mendelian dominance. Using a deterministic, differential-equation approximation we prove that, under suitable conditions, the system has a unique equilibrium point where each species is dimorphic at the locus controlling its behavior. At the equilibrium, each species, taken as a whole, uses its tactics in the proportions of the game-theoretic optimal mixed strategy. The equilibrium is strongly stable in the sense that oscillations about it are damped out exponentially. Interestingly, the corresponding haploid model does not exhibit this type of damping. Our object is to give a detailed mathematical analysis of a model which makes explicit one possible form of interspecific interaction. This example illustrates very clearly the genetic feedback mechanism discussed by Pimentel (1961, 1965) and exhibits a form of competitive selection quite different from that considered by Nei (to appear).