Game Theory: An Introduction, 2nd Edition

CHAPTER SEVEN

Evolutionary Stable Strategies and Population Games

I was a young man with uninformed ideas. I threw out queries, suggestions, wondering all the time over everything; and to my astonishment the ideas took like wildfire. People made a religion of them.

—Charles Darwin

All the ills from which America suffers can be traced to the teaching of evolution.

—William Jennings Bryan

If automobiles had followed the same development cycle as the computer, a Rolls-Royce would today cost $100, get a million miles per gallon, and explode once a year, killing everyone inside.

—Robert Cringely

7.1 Evolution

A major application and extension of game theory to evolutionary theory was initiated by Maynard-Smith and Price.1 They had the idea that if you looked at interactions among players as a game, then better strategies would eventually evolve and dominate among the players. They introduced the concept of an evolutionary stable strategy (ESS) as a good strategy that would not be overcome by any mutants so that bad mutations would not overtake the population. These concepts naturally apply to biology but can be used to explain and predict many phenomena in economics, finance, and other areas in social and political arenas. These applications make finding an ESS an important way to distinguish among Nash equilibria. In this chapter, we present a brief introduction to this important concept.

Consider a population with many members. Whenever two players encounter each other, they play ...