# Evolutionary Stable Strategy

Instructor: Kristina Dougherty

Kris has taught science, math, and conservation to high school, college and graduate students, and she has a Ph.D. in wildlife ecology and a J.D.

This lesson describes an evolutionary stable strategy (ESS). It briefly introduces game theory, explains the features of an ESS, gives a simple game that predicts the possibility of ESS, then looks at some real examples of ESS in nature.

## What Is Game Theory?

Have you ever stood at the back of a long line at your favorite fast food restaurant, wondering why no one just runs to the front of the line to order first? Or why some animals eat peacefully, side-by-side in a field, while others stop eating to chase off any other animal that gets close? One reason is that the payoff of a strategy, for example, to stay in line vs. dash to the front, has benefits (get food first) and costs (yelling and maybe a few punches from others who are waiting). The payoff to each person in the line is frequency dependent, which means it depends on how everyone else reacts to what you do. If you run up front and everyone else stays in line, you get your fries first. But if you run, and then everybody runs, you might not be first, and you might end up with a few bruises, too. Game theory is a way to model and understand interactions between individuals. Strategies represented in a game theory model could include fight, run, or fight then run; depending on the payoffs, we could predict that individuals will be antagonistic toward each, cooperative, or even altruistic. Even though natural selection favors the fittest individuals (the individuals with the highest survival and reproduction), game theory models can help us understand why the fittest animals can sometimes be those who cooperate.

## The Features of an ESS

An evolutionary stable strategy is a special case where all individuals in a population use the same rule when interacting with each other. Stable means that the strategy cannot be 'invaded' by any alternative strategy, which is initially rare. So, going back to our restaurant, even if a person in the line occasionally chooses to run to the front, the payoff is not big enough such that the person will survive longer or reproduce more, on average, than the others. Evolutionary means we are talking about a heritable trait that is subject to the forces of natural selection. Animals using a particular strategy survive longer and produce more offspring... who inherit their parents' strategy.

## A Simple Model: Hawk vs. Dove

The hawk vs. dove game theory model is a great example of an ESS. In this game, there are two possible strategies: (1) a hawk will fight any other bird it encounters, and keep fighting until it is injured and forced to share a resource or the other bird retreats; (2) a dove will share a resource with other doves but retreat if the other bird fights (i.e., if the other bird is a hawk.) A payoff matrix is a good visual tool to represent a game theory model. Let's make sure we understand that this one shown here represents our hawk vs. dove game.

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