While originally developed to model socio-economic phenomena, Game Theory has recently emerged as a powerful framework to efficiently solve optimisation and multi-agent decision problems in engineering and computer science. After presenting the basic concepts and notation from classical competitive game theory, the course will focus on network games and learning dynamics and their convergence properties. Particular emphasis will be on mechanism design. Starting from problems such as constraint satisfaction, resource allocation, Bayesian inference, the course will show how to design a game and a learning mechanism to solve them in an efficient and distributed fashion.

Good knowledge of basic math is assumed (calculus, linear algebra, graphs, elementary probability and Markov chains). All remaining concepts will be built within the course.

1. Non-cooperative strategic games. Historical remarks. Basic examples. Fundamental concepts: Best Response, Dominated strategy, Nash equilibrium, Price of anarchy, price of stability. Correlated Equilibria. Examples. 2.Existence of Nash equilibria. Nash's Theorem for mixed strategies. Existence and Uniqueness results of Nash Equilibria in Continuous Games. Minimax Theorem. 3. Potential games. Finite improvement property. Congestion games. Potential network games: network coordination, anti-coordination, coloring, public good games. 4. Best response and noisy best response (logit) dynamics. Asymptotic behavior for potential games and weakly-acyclic games. 5. Super-modular games. Lattice structure of Nash equilibria set. Asymptotic behavior of the best response dynamics. Comparative statics. 6. Population games and evolutionary dynamics. Evolutionary stable strategies. Replicator dynamics and other imitation rules. Logit dynamics. 8. Learning in games. Fictitious play. Stochastic fictitious play. Convergence properties. 9. Learning Algorithms and (Conditional) No-Regret Learning 10. Network intervention, mechanism design, information design.

In presenza

Presentazione orale

P.D.1-1 - Novembre

10 3-hour lectures from the beginning of November, 2025