20290 - GAME THEORY: ANALYSIS OF STRATEGIC THINKING
CLMG - M - IM - MM - AFC - CLEFIN-FINANCE - CLELI - ACME - DES-ESS - EMIT - GIO
Course taught in English
Go to class group/s: 31
Game theory (GT) is the formal mathematical analysis of strategic interaction. GT now pervades most non-elementary models in microeconomic theory and many models in other branches of economics. Understanding GT is therefore necessary to study economic theory at an advanced level. Furthermore, GT provides a general theoretical language for the analysis of interaction in other social sciences as well. Indeed, although GT relies on some structural assumptions, it nonetheless provides something close to a neutral theoretical framework to develop models of interaction. For example, unlike traditional economic theory, game theory does not rest on the assumption that agents are selfish. The course introduces the necessary analytical tools which allow the students to understand how game theory is used, and illustrates such tools with some economic applications.
- Introduction to interactive decision theory, terminology, notation.
- Rationality, dominance, and rationalizability.
- Pure strategy Nash equilibrium, interpretation, existence.
- Mixed strategy Nash equilibrium, interpretation, existence.
- Other probabilistic equilibrium concepts: correlated and self-confirming equilibrium.
- Games with incomplete information: rationalizability, Bayesian and self-confirming equilibrium.
- Dynamic games: strategic form, dynamic programming, backward and forward induction.
- Subgame perfect equilibrium.
- Repeated games and multiplicity of subgame perfect equilibria.
- Bargaining games and uniqueness of subgame perfect equilibrium.
- Dynamic games with asymmetric or incomplete information.
- System of beliefs and perfect Bayesian equilibrium.
- Signaling games, pooling and separating equilibria, intuitive criterion.
Problem sets are regularly distributed and graded. Solving these problem sets is essential to prepare for the exams.
Grading system: The final grade is based on the best four problem sets (20%) and on the written exam -or exams- (80%).
The following graduate textbook is quite close to the approach of the course, but more advanced
- M.J. OSBORNE, A. RUBISTEIN, A Course in Game Theory, Cambridge MA, MIT Press, 1994, Freely downloadable.
- G. BONANNO, Game Theory, University of California, Davis, 2015, freely downloadable athttp://faculty.econ.ucdavis.edu/faculty/bonanno/
- Elementary set theory: sets, Cartesian products, functions.
- Elementary analysis: open, closed and bounded subsets of Euclidean spaces; limits, continuity, derivatives, maximization of real-valued functions.
- Linear algebra: vectors and operations on vectors, convexity, graphical representation on the Cartesian plane.
- Probability theory: probabilities on finite state spaces, conditional probabilities, Bayes rule.
- Decision theory: expected utility.