Evolutionary Game Theory: Mathematical Approaches to Understanding Cooperation

Many social and environmental problems today, such as climate change, require cooperation to solve. However, cooperation can be difficult to achieve when it conflicts with our short-term self-interest. This course will use mathematical models to explore the challenges and potential solutions to cooperation problems. We will delve into non-cooperative game theory, evolutionary game theory, and replicator dynamics to understand how cooperation can evolve in populations. We will also explore the role of kin selection and the Wright’s Infinite Islands model, with an example of conserving natural resources for future generations. Finally, social learning models will be presented as a means of understanding how individuals acquire knowledge and behaviours from others. By the end of the course, participants will gain insights into why cooperation can be difficult, but also how evolution has furnished us humans with a unique ability to cooperate, which can help us solve some of the most pressing challenges we face as a society.

Topics

1. Non-cooperative game theory.
2. Introduction to evolutionary game theory and replicator dynamics.
3. Iterated games and reciprocity as a solution to cooperative dilemmas.
4. Public goods games and games with nonlinear benefits.
5. Kin selection and the Wright’s Infinite Islands model, with an example of conserving natural resources for future generations.
6. Social learning models.

Pre-requisites

Participants will benefit from some familiarity with systems of ordinary differential equations, stability concepts, and numerical methods for solving ODEs. However, a refresher on these topics will be included.
Tutorials will include some use of the Python programming language. However, the emphasis will be on exploring the models, rather than coding, and templates will be provided.

Relevance

Many modern social and environmental problems (e.g., climate change) are not challenging because we lack the understanding or technology to solve them, they are challenging because solving them requires cooperation, and cooperating is difficult when it conflicts with our short-term self-interest. This course will introduce participants to how cooperation problems can be explored mathematically. We will explore why cooperation can be difficult to achieve, but also how evolution can sometimes favour cooperative behaviour, which can give us insights into how problems can be solved, and insights into ourselves as humans, a uniquely cooperative species.