Replicator Dynamics, MWU, and Their Evolutionary Motivation

This repository contains the materials for my seminar presentation in the course Seminar: Learning in Games at the Technical University of Munich.

The seminar focuses on the connection between evolutionary game theory, replicator dynamics, and the multiplicative weights update method. It explains how natural selection can be modeled as a continuous-time dynamical process, and how the same relative-performance principle appears in discrete-time learning algorithms such as MWU.

Repository Structure

.
├── README.md
├── handout/
│   ├── handout.tex
│   └── output/
│       └── handout.pdf
├── presentation/
│   ├── main.tex
│   ├── beamerthemeTUMclean.sty
│   ├── Slides/
│   ├── Figures/
│   ├── logos/
│   └── output/
│       └── presentation.pdf
├── quiz/
│   ├── quiz.tex
│   └── output/
│       └── quiz.pdf
└── references/
    ├── README.md
    └── bib/
        └── references.bib

Contents

• presentation/ contains the Beamer source files, custom theme, figures, logos, and the final presentation PDF.
• handout/ contains the LaTeX source and compiled PDF for the seminar handout.
• quiz/ contains the LaTeX source and compiled PDF for the audience mini quiz.
• references/ contains the BibTeX bibliography and reference information.

Main Materials

• presentation/output/presentation.pdf
• handout/output/handout.pdf
• quiz/output/quiz.pdf

Topic Overview

The seminar covers the following main ideas:

1. Evolutionary game theory reinterprets strategies as inherited traits and payoffs as fitness.
2. Replicator dynamics describe how types with above-average fitness increase in frequency.
3. The unilateral form of replicator dynamics has a logit representation.
4. This logit representation connects continuous-time replicator dynamics to exponential weights.
5. Multiplicative weights update can be viewed as a discrete-time analogue of replicator dynamics.
6. No-regret guarantees control average performance, but actual trajectories may still cycle.
7. Evolutionarily stable strategies strengthen the notion of stability by testing resistance against rare mutants.

Main References

The seminar mainly relies on the following references:

1. K. Sigmund and M. A. Nowak,
   “Evolutionary game theory,”
   Current Biology, 9(14): R503–R505, 1999.

2. P. Schuster and K. Sigmund,
   “Replicator dynamics,”
   Journal of Theoretical Biology, 100(3): 533–538, 1983.

3. S. Sorin,
   “Replicator dynamics: Old and new,”
   Journal of Dynamics and Games, 7(4): 365–386, 2020.

The BibTeX entries are available in references/bib/references.bib.

Notes

Generated PDFs are included for convenience. The LaTeX source files are kept in the corresponding directories so that the presentation, handout, and quiz can be modified and rebuilt if needed.