# GAME THEORY

Academic Year 2018/2019 - 3° Year - Curriculum APPLICATIVO
Teaching Staff: Laura Rosa Maria SCRIMALI
Credit Value: 6
Scientific field: MAT/09 - Operational research
Taught classes: 35 hours
Exercise: 12 hours
Term / Semester:

## Learning Objectives

The course aims at introducing basic concepts in static and dynamic games. The course provides students with analytic tools in order to model and foresee situations in which players (consumers, firms, governments, etc.) strategically interact. The interest focuses on applications in economics, engineering, and biology.

The goals of the course are:

1. Knowledge and understanding: the aim of the course is to acquire base knowledge that allows students to understand strategic interaction problems.
2. Applying knowledge and understanding: students will acquire knowledge useful to model real life game theory problems.
3. Making judgments: through real examples, the student will be able to implement correct solutions for complex decisional problems.
4. Communication skills: students will acquire base communication skills using technical language.
5. Learning skills: the course provides students with theoretical and practical methodologies in order to deal with several strategic problems that can meet during the study and the work activity.

## Course Structure

For this course, there will be 2 hours of teaching per lecture twice a week. The course includes classroom lessons, exercises, and seminars.

During the first week of December, a midterm examination will be proposed via a 2-hour written paper. It corresponds to half-part of the program (3CFU). It should be noted that this exam is not compulsory.

## Detailed Course Content

1. STATIC GAMES WITH COMPLETE INFORMATION

Representation of a game. Dominant solutions and iterated elimination of strictly dominated strategies. Pure and mixed strategies. Nash equilibrium. Cournot model. Zero sum games. MInimax solutions. Von Neumann' theorem.

2. DYNAMIC GAMES WITH COMPLETE INFORMATION

Backward induction. Stackelberg duopolistic model. Subgame perfect equilibrium. Repeated games.

3. STATIC GAMES WITH INCOMPLETE INFORMATION

Bayesian games. Correlated equilibria.

4. COOPERATIVE GAMES

Cooperative games with transferable and non transferable utility . Core and Shapley value.

## Textbook Information

1. F. Colombo, Introduzione alla Teoria dei giochi, Carocci, 2008
2. R. Gibbons, Teoria dei giochi, Il Mulino, 1992
3. F. Patrone, Decisori (razionali) interagenti, Edizioni Plus, 2006
4. M. Li Calzi, Teoria dei Giochi, Edizioni Etas, 2010
5. G. Gambarelli, Giochi competitivi e cooperativi per applicazione a problemi decisionali di natura industriale, economica, commerciale militare, politica, sportiva, Giappichelli, 2003