# GAME THEORY

Academic Year 2021/2022 - 3° Year - Curriculum APPLICATIVO
Teaching Staff: Laura Rosa Maria SCRIMALI
Credit Value: 6
Scientific field: MAT/09 - Operational research
Taught classes: 42 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 and biology.

The goals of the course are:

Knowledge and understanding: to acquire base knowledge that allows students to understand strategic interaction problems.

Applying knowledge and understanding: to acquire knowledge useful to model real life game theory problems.

Making judgments: to implement correct solutions for complex decisional problems.

Communication skills: to acquire base communication skills using technical language.

Learning skills: to provide students with theoretical and practical methodologies in order to deal with several strategic problems that can meet during the study and the work activity; to acquire further knowledge on the problems related to game theory.

## Course Structure

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

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Learning assessment may also be carried out on line, should the conditions require it.

## Detailed Course Content

1. STATIC GAMES WITH COMPLETE INFORMATION (20 hours)

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 (8 hours)

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

3. STATIC GAMES WITH INCOMPLETE INFORMATION (8 hours)

Bayesian games. Correlated equilibria.

4. COOPERATIVE GAMES (6 hours)

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

Use of software to solve games

## Textbook Information

1. Erich Prisner, Game Theory Through Examples, The Mathematical Association of America, 2014

2. J. Aumann and Sergiu Hart, Handbook of game theory with economic applications, Elsevier, 2002

3. M.J. Osborne, A course in game theory, Cambridge, Mass., MIT Press, 1994.

4. R.B. Myerson, Game theory : analysis of conflict, Cambridge, Mass., Harvard University Press, 1991.