1016286 - GAME THEORY
Expected Learning Outcomes
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.
Required Prerequisites
Basic knowlege of functions of one and two variables, analytic geometry and linear algebra.
Attendance of Lessons
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.
Textbook Information
[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.
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Representation of a game. | González-Díaz, chap. 2 |
| 2 | Dominated strategy and Nash equilibrium | González-Díaz, chap. 2, Osborne, chap. 2-3-4 |
| 3 | Zero-sum game | González-Díaz, chap. 2 |
| 4 | Extensive games | González-Díaz chap. 3, Gibbons chap. 2 |
| 5 | Games with incomplete information | González-Díaz chap. 4, Gibbons chap. 3 |
| 6 | Cooperative game | González-Díaz chap. 5 |
Learning Assessment
Learning Assessment Procedures
Oral exam and resolution of a numerical example.
Learning assessment may also be carried out on line, should the conditions require it.Examples of frequently asked questions and / or exercises
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