Evolutionary Games and Dynamical Models of Behavior: A Primer on Replicator Equations
Välkommen till föreläsningen i seminarieserien i matematik.
In this lecture, we comprehensively introduce the main concepts and tools of evolutionary game theory, with a focus on their applications in biology. The lecture covers the basics of Nash equilibria, evolutionarily stable strategies, and replicator dynamics. Replicator equations are a class of differential equations used to model evolutionary dynamics in populations. They capture how the frequencies of strategies in a population change over time based on the relative payoffs of those strategies. We explore how replicator equations extend to multiplayer games and games in structured populations. The lecture also discusses how these theoretical models provide insights into the evolution of social behaviors in animal and human populations. We start by defining key concepts in game theory and equilibrium, then introduce the concept of an evolutionarily stable strategy - a key concept in evolutionary game theory. We examine how evolutionary game dynamics like replicator dynamics can be applied to model the evolution of behaviors in a population. We discuss examples of how these tools have been applied to answer questions in evolutionary biology.