GAMES AND NETWORKS
Obiettivi formativi
The goal of the course is to expose the students to the basic concepts of strategic interactions, with a particular attention to situations that involve networks. The course will be mathematically formalized and rigorous.
Risultati di apprendimento attesi
At the end of this course the student will understand some fundamental concepts of game theory and network theory, and will be able to
1. formally model some real-life situations in terms of games and on networks,
2. find the suitable solution concepts,
3. draw conclusions from the above modeling.
Contenuti Del Corso
The course will cover the basic aspects of non-cooperative game theory, i.e., games in normal form, mixed strategies, and main solution concepts (iterated elimination of dominated strategies, Nash equilibrium, correlated equilibrium), games in extensive form, behavior strategies, and main solution concepts (subgame perfect equilibrium), games with incomplete information. It will then move to network theory, starting with a survey of the basic concepts in graph theory and then moving to network formation (stochastic and strategic).
Testi Di Riferimento
Jackson, M.O. (2008)
Social and Economic Networks. Princeton University Press, Princeton, NJ.
Maschler, M., Solan, E., Zamir, S. (2020) Game Theory.
Second edition. Cambridge University Press, Cambridge.
Pass, R. (2018) A Course in Networks and Markets: Game-Theoretic Models and Reasoning. MIT Press, Cambridge, MA.
Metodologie Didattiche
The whole course will be taught in an interactive way.
Modalità di verifica dell'apprendimento
Weekly quizzes, a project, participation, a final exam.
Criteri per l’assegnazione dell’elaborato finale
An interview with the student
Settimana 1
On campus: Games in normal form. Iterative elimination of dominated strategies. Pure Nash equilibria.
Online: Examples of games in normal form and coding.
Settimana 2
On campus: Mixed strategies. Existence of Nash equilibria.
Online: Examples of mixed equilibria and coding.
Settimana 3
On campus: Correlated equilibria.
Online: Examples of correlated equilibria and coding.
Settimana 4
On campus: Games in extensive form. Subgame perfect equilibria.
Online: Examples of games in extensive form and coding.
Settimana 5
On campus: Behavior strategies.
Online: Examples of behavior strategies and coding.
Settimana 6
On campus: Games with incomplete information.
Online: Examples of games with incomplete information and coding.
Settimana 7
On campus: Graphs: basic concepts.
Online: Examples of graphs and coding.
Settimana 8
On campus: Graph representation of games. Best response dynamics.
Online: Examples of best response dynamics and coding.
Settimana 9
On campus: Random graphs: various models.
Online: Examples of random graphs and coding.
Settimana 10
On campus: Strategic network formation.
Online: Examples of strategic network formation and coding.
Settimana 11
On campus: Games on networks.
Online: Examples of games on networks and coding.
Settimana 12
On campus: Routing games.
Online: Examples of routing games and coding.