This tutorial shows how cooperation might evolve. It assumes that you have already completed the Conflict I and Stable Strategies tutorials and have a basic understanding of payoffs and symmetric games. If you have not yet done those tutorials, you should go through Conflict I before continuing here. If you work through all examples in detail, this tutorial should take about 20 minutes. This tutorial also refers to the tutorial on Relatedness (~10 minutes).

The Challenge

There are many examples of cooperation between individuals of the same species and even occasionally between individuals of different species. Yet, explaining the evolution of cooperation has always been a challenge. Let’s consider an abstract case to see why this is so. Suppose that two individuals can cooperate. One who receives cooperation gets a benefit, b, while one who cooperates bears a cost, c. There are two strategies, to cooperate or not to cooperate (called defect). This is the payoff matrix:


If both cooperate, then both get b-c, while if neither one cooperates, there is no cost or benefit. If one cooperates and the other defects, then the cooperator gets −c and the defector gets b.

What is the evolutionarily stable strategy (ESS) in this game, assuming b > 0 and c > 0?

  1. Wikipedia has articles on Hamilton and kin selection. Hamilton’s 1964 papers on “The genetical evolution of social behavior” can be found on PubMed (5875341 and 5875340).
  2. A spatial cooperation game simulator can be found at