GAME THEORY

The course aims to introduce fundamental 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 valuable knowledge 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 be met during the study and the work activity; to acquire further knowledge on the issues related to game theory.

 

Teaching Organization

credit value 6 - 42 hours

total study 150 hours

108 hours of individual study
42 hours of frontal lecture

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

Part of the programme (max 3CFU)  could be done by a visiting professor (Italian or not).

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.

Information for students with disabilities and/or SLD

To guarantee equal opportunities, in compliance with the laws in force, interested students can ask for a personal interview in order to plan any compensatory and/or dispensatory measures, based on the didactic objectives and specific needs. It is also possible to contact the referent teacher CInAP (Center for Active and Participated Integration - Services for Disabilities and/or SLD) of our Department.

 

Fundamental knowledge of functions of one and two variables, analytic geometry and linear algebra.

 

Course attendance is strongly recommended.

 

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. 

 

[1] J. González-Díaz, I. García-Jurado, M. G. Fiestras-Janeiro, An Introductory Course on Mathematical Game Theory American Mathematical Soc., 2010

[2] M.J. Osborne, A course in game theory, Cambridge, Mass., MIT Press, 1994. 

[3] R. Gibbons, Game Theory for Applied Rconomists, Princeton University Press, 1992.

 

The final exam consists of an oral test during which the candidate is also requested to solve a numerical exercise. The final grade is established on the basis of the answers given by the candidate and the solving of the numerical example.

Final grades will be assigned taking into account the following criteria:

Rejected: Basic knowledge has not been acquired. The student is not able to solve simple exercises.

18-23: Basic knowledge has been acquired. The student solves simple exercises, has sufficient communication skills, and makes judgements.

24-27: All the knowledge has been acquired. The student solves all the proposed exercises making few errors and has good communication skills and making judgements.

28-30 cum laude: All the knowledge has been completely acquired. The student applies knowledge and has excellent communication skills, learning skills and making judgements.

 

Learning assessment may also be carried out online if the conditions should require it.

 

Nash equilibrium definition. Minimax. Computation of Nash equilibrium with pure and mixed strategies. Dominated solutions. Zero-sum game. Nash theorem. Prisoner's dilemma. Cooperative games. Imputations and core.