Hardy-Weinberg Equilibrium and Mixed Strategy Equilibrium in Game Theory

ABSTRACT

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.

Cite this paper

H. Horaguchi, "Hardy-Weinberg Equilibrium and Mixed Strategy Equilibrium in Game Theory,"*Theoretical Economics Letters*, Vol. 3 No. 2, 2013, pp. 85-89. doi: 10.4236/tel.2013.32014.

H. Horaguchi, "Hardy-Weinberg Equilibrium and Mixed Strategy Equilibrium in Game Theory,"

References

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[1] G. H. Hardy, “Mendelian Proportions in a Mixed Population,” Science, Vol. 28, No. 706, 1908, pp. 49-50. doi:10.1126/science.28.706.49

[2] C. Stern, “The Hardy-Weinberg Law,” Science, Vol. 97, No. 2510, 1943, pp. 137-138. doi:10.1126/science.97.2510.137

[3] C. Stern, “Mendel and Human Genetics,” Proceedings of the American Philosophical Society, Vol. 109, No. 4, 1965, pp. 216-226.

[4] J. M. Smith, “Evolution and the Theory of Games,” Cambridge University Press, Cambridge, 1982. doi:10.1017/CBO9780511806292

[5] D. Fudenberg and J. Tirole, “Game Theory,” MIT Press, Cambridge, 1991.

[6] R. Gibbons, “Game Theory for Applied Economics,” Princeton University Press, Princeton, 1992.

[7] H. H. Horaguchi, “The Role of Information Processing Cost as the Foundation of Bounded Rationality in Game Theory,” Economics Letters, Vol. 51, No. 3, 1996, pp. 287-294. doi:10.1016/0165-1765(96)00828-2

[8] D. M. Kreps, “A Course in Microeconomic Theory,” Princeton University Press, Princeton, 1990.

[9] K. H. Weiss, and J. A. Kurland, “Going on an Antedate: A Strange History of Imperfect Perfect Proportions,” Evolutionary Anthropology, Vol. 16, No. 6, 2007, pp. 204-209. doi:10.1002/evan.20151

[10] J. Relethford, “Human Population Genetics,” Wiley-Blackwell, Hoboken, 2012.