The Hardy-Weinberg Equilibrium (HWE) can be linked to game theory. This article shows that payoffs, or resources, in a game with alleles as players, determine the frequency of homozygotes. The frequency of aa homozygotes in the HWE is an increasing function of the multiplicative difference in own payoffs for each allele. Thus, Mendelian proportions are variable rather than fixed depending on the resources for the alleles. Whereas the concept of evolutionary stable strategy (ESS) is based on non-cooperative competitive settings such as a competition between doves and hawks, this article explores a game theoretic situation where the mating of two alleles is presupposed.