## Evolutionary Game Theory

http://www.webofstories.com/play/7295?o=R

In this video interview, biologist John Maynard Smith introduces the concept of applying ideas and notations from Classical Game Theory to the evolution of populations. Classical Game Theory considers the possible outcomes of contest situations in which each of the participants plays a certain strategy. The payoffs to each contestant depend on his/her strategy as well as those of all other contestants. In Smith’s words (I paraphrase), Classical Game Theory asks: “What would a reasonable man do in a contest situation if he can assume his opponent is a reasonable man as well?” This question, in Smith’s opinion, does not quite apply to the evolution of populations since animals cannot be evaluated as ‘reasonable’ or ‘rational’. However, the notions of contestants, strategies, and payoff matrices that are developed from Classical Game Theory lead to a very simple and powerful technique for analyzing population evolution.

In this biological adaption of Game Theory, the contestants are members of a population, the strategies are genetic traits inherited by the contestants, and the payoffs are measured in terms of Fitness – an individual’s ability to survive and reproduce. The Hawk Dove game (Anti-Coordination game) mentioned in lecture (September 2, 2011) and in the textbook is possibly the most well known and influential of Smith’s models. This game considers the possible outcomes of two animals fighting over a food resource. The two contestants in this game can choose between one of two strategies: behaving passively (Dove) and behaving aggressively (Hawk). If both contestants choose to be passive, the food is divided equally between them. If both behave aggressively, the food is destroyed. If one contestant is aggressive while the opponent is passive, he/she gets the majority of the food [Klineberg and Easley]. By factoring in the probability of hawks and doves meeting each other (a measure of the population distribution of both birds), Smith originated the concept of an Evolutionary Stable Strategy (ESS). Paraphrasing Smith’s definition, “An ESS is a behavior with the property that if every/almost every member of a population does it, then any mutant doing anything else doesn’t do as well against the members of the populations as the members of the population themselves do against each other.” Smith’s discovery of an ESS explained what biologists and anthropologists had observed in many animal populations: the instinct to preserve one’s own genes (and those of close relations) in order to maximize Fitness.

John Maynard Smith’s claim that he only had to read the “first chapter” of a Game Theory book in order to develop his theoretical models of population evolution left a profound impression on me. He used the simplest notions of classical game theory (developed by and for mathematicians and economists) to formulate a powerful tool for studying a complex biological phenomenon. In fact, much to Maynard’s dismay, his ideas are being “re-borrowed” by economists to explain phenomena outside the realm of biology! This is an inspiring example of the power of multidisciplinary work.

Klineberg and Easley: *Networks, Crowds and Markets: Reasoning in a Highly Connected World, 2010*