GAMES AND NETWORKS

GAMES AND NETWORKS

Marco Scarsini

Instructional goals

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.

Intended learning outcomes

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.

Course Contents

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).

Reference Books

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.

Teaching Methods

The whole course will be taught in an interactive way.

Assessment Method

Weekly quizzes, a project, participation, a final exam.

Thesis assignment criteria

An interview with the student

Week 1 Contenuto sessioni on line e on campus

On campus: Games in normal form. Iterative elimination of dominated strategies. Pure Nash equilibria. Online: Examples of games in normal form and coding.

Week 2 Contenuto sessioni on line e on campus

On campus: Mixed strategies. Existence of Nash equilibria. Online: Examples of mixed equilibria and coding.

Week 3 Contenuto sessioni on line e on campus

On campus: Correlated equilibria. Online: Examples of correlated equilibria and coding.

Week 4 Contenuto sessioni on line e on campus

On campus: Games in extensive form. Subgame perfect equilibria. Online: Examples of games in extensive form and coding.

Week 5 Contenuto sessioni on line e on campus

On campus: Behavior strategies. Online: Examples of behavior strategies and coding.

Week 6 Contenuto sessioni on line e on campus

On campus: Games with incomplete information. Online: Examples of games with incomplete information and coding.

Week 7 Contenuto sessioni on line e on campus

On campus: Graphs: basic concepts. Online: Examples of graphs and coding.

Week 8 Contenuto sessioni on line e on campus

On campus: Graph representation of games. Best response dynamics. Online: Examples of best response dynamics and coding.

Week 9 Contenuto sessioni on line e on campus

On campus: Random graphs: various models. Online: Examples of random graphs and coding.

Week 10 Contenuto sessioni on line e on campus

On campus: Strategic network formation. Online: Examples of strategic network formation and coding.

Week 11 Contenuto sessioni on line e on campus

On campus: Games on networks. Online: Examples of games on networks and coding.

Week 12 Contenuto sessioni on line e on campus

On campus: Routing games. Online: Examples of routing games and coding.