20290 - GAME THEORY: ANALYSIS OF STRATEGIC THINKING
Course taught in English
Go to class group/s: 31
Class 31: PIERPAOLO BATTIGALLI
A preliminary knowledge on the following topics is suggested before attending the course: - 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.
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 to understand how game theory is used, and it 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, foward induction.
- Express strategic interaction and strategic reasoning with the language and tools of game theory.
- Define and describe the traditional solution concepts of game theory (Nash equilibrium and its main refinements), explain their limitations, and identify the applications where they are relevant.
- Define and describe new solution concepts like rationalizability and self-confirming equilibrium, and explain their theoretical foundation.
- Analyze situations of economic and social interaction as "games".
- Solve games and predict behavior using traditional as well as new solution concepts.
- Face-to-face lectures
- Exercises (exercises, database, software etc.)
Students are given home assignements in the form of problem sets. Such assignments are evaluated. The solutions are explained during office hours. Printouts of solutions are distributed.
|Continuous assessment||Partial exams||General exam|
- Students can either take two partial exams, one of the first part (intermediate partial exam, and one on the second part (final partial exam), or a general exam.
- Individual assignements of exercises are evalutated throughout the course and contribute 20% of the final grade.
Teaching material prepared by the instructor are distributed to the students. They include the updated versions of the following:
- Main body of lecture notes: GAME THEORY, Analysis of Strategic Thinking.
- Exercise book: GAME THEORY, Analysis of Strategic Thinking: Exercises.
- All the slides used in the lectures.