## Summary

### Presenter: Elias Fernández Domingos

Classical game theory typically analyzes interactions between two (or a few) players and aims to answer how each individual can maximize their utility. Such a question, from a mathematical perspective, becomes very intricate and complex as a player must consider the utilities of all other players and any possible set of beliefs. Thus, following the famous work of Nash, it is often assumed that all players act in a way that maximizes their utility and believe that others will do the same. This simplifies the analysis and transforms it into a search for the points of equilibrium at which no player has any incentive to change its strategy (Nash equilibrium). This assumption requires that players have perfect knowledge about the game/environment and is referred to as rationality. Yet, it is often cumbersome to assume that individuals are rational in many social and biological systems, even in simple pairwise interactions. Moreover, whenever the problem requires a proper understanding of conflicts occurring in large populations, it becomes necessary to characterize the choices and strategies of many individuals throughout time, and not only at equilibrium. As such, in many real-world multi-agent systems, the goal is shifted towards the understanding of the complex ecologies of behaviors emerging from a given dilemma (or "game"). This is where evolutionary game theory (EGT) shines as a theoretical and computational framework.

In this tutorial, we aim to introduce the students to the main models used in EGT and offer an overview of the research in the field, with an emphasis on its applicability to characterize hybrid human-AI multi-agent systems both when considering unstructured (well-mixed) populations, as well as structured populations, whose interaction structure is organized into a Complex Network4. Moreover, we will pay special attention to the computational approaches to EGT, by summarizing the practical challenges of implementing the numerical and agent-based simulations required to model large-scale systems.