# John Maynard Smith: games animals play

October 9, 2013 3 Comments

Although this blog has recently been focused on static fitness landscapes and the algorithmic lens, it’s url and a big chunk of the content focuses of evolutionary game theory (EGT). Heck, I even run a G+ community on the topic. If you are a biologist and asked me to define EGT then I would say it is a general treatment of frequency-dependent selection. If you were a mathematician then I might say that it is classical game theory done backwards: instead of assuming fully rational decision makers, imagine simple agents whose behavior is determined by their genes, and instead of analyzing equilibrium, look at the dynamics. If you are a computer scientists, I might even say to look at chapter 29 of your Algorithmic Game Theory book: it’s just a special case of AGT. However, all of these answers would be historically inaccurate.

My explanations presuppose a dynamic theory, but Maynard Smith & Price (1973) introduced EGT in the same way as most of biology and economics is done: equilibrium analysis. They defined the idea of an evolutionary stable strategy and analyzed biological populations under the assumption that they could reach this equilibrium. It provided great insights into animal conflicts during mating and the sex ratio, but it wasn’t until Taylor and Jonker (1978), Hofbauer et al. (1979), and Zeeman (1980) that a dynamical theory was developed in the form of the replicator equation. So maybe you shouldn’t listen to my definitions of EGT, and instead watch a great video Jacob Scott found where John Maynard Smith introduces evolutionary game theory for the Londom Mathematical Society:

### References

Hofbauer, J., Schuster, P., & Sigmund, K. (1979). A note on evolutionary stable strategies and game dynamics. *Journal of Theoretical Biology*, 81:609-612.

Maynard Smith, J., & Price, G.R. (1973). The logic of animal conflict Nature, 246, 15-18 DOI: 10.1038/246015a0

Nisan, N., Roughgarden, T., & Tardos, E. (Ed.). (2007). *Algorithmic game theory*. Cambridge University Press.

Taylor, P.D. & Jonker, L. (1978). Evolutionary stable strategies and game dynamics. *Math. Biosci.*, 40: 145-156.

Zeeman, E.C. (1980). *Population dynamics from game theory*. In: Nitecki, A., Robinston, C. (Eds), *Proceedings of an International Conference of Global Theory of Dynamic Systems.*. Lecture Notes in Mathematics, 819. Springer, Berlin.

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