## Mathematical Modelling 101 – Evolutionary Game Theory

Game Theory was fist applied to evolution by John Maynard-Smith and George Price in 1973. It differs from traditional game theory is that it focusses on dynamics of strategy change more than the properties of strategy equilibria, although equilibria still exist within EGT but are know as Evolutionary Stable Strategies as opposed to Nash Equilibria.

Dove-Hawk

Imagine a situation in which 2 members of a species come into conflict over a resource. Within this conflict each animal has the optional to ‘fight’, ‘display’ or ‘run away’. There are 2 strategies within this species, either the Dove strategy or the Hawk strategy. In the Dave strategy, upon meeting someone also adopting the Dove strategy both “Doves” display and share the resource or upon meeting a “Hawk” the Dove runs away. Adopting the Hawk strategy entails always fighting. So upon meeting a Dove the Hawk will fight and the Dove will run away and the Hawk will take all of the resource, and upon meeting another Hawk, both will fight and one will win out. On average across many interactions with other Hawks, the payoff gained ends up being (v/2)-c where v=value of resource and c=cost.

 Dove Hawk Dove v/2, v/2 v, 0 Hawk 0, v (v-c)/2, (v-c)/2

The question to ask of this game is, given values v and c, which strategy will evolutionarily win out?

## Mathematical Modelling 101 – Intro to Game Theory

This post is going to just be a very brief introduction to what Game Theory is, how it works and some basic terminology. In later posts I will get more advanced and cover how it can be applied to Cultural Evolution.

What is Game Theory?

Game theory is a branch of applied mathematics most commonly used in Economics. However, it can be very successfully applied to other social sciences as well as Evolutionary Biology. It gives both descriptive answers (what people do) and prescriptive answers (what people should do) in a given game.

Why is this relevant?

Game Theory is a very good tool in predicting outcomes, not only in the very simple games covered in this post, but also in predicting the outcomes of evolutionary strategies and of predicting outcomes for signalling games which can inform us on human and animal communicative strategies.  Running iterated games over populations can introduce interesting qualifications to these very simple ideas as well and explain some things which may, at first, appear maladaptive, as such is a very useful tool in bypassing our intuitions. It is of these things that the next few posts will explore.