30418 - COMPUTATIONAL MICROECONOMICS - MODULE 1 (GAME THEORY)
Course taught in English
Go to class group/s: 25
Lezioni della classe erogate online
- Elementary set theory: sets, Cartesian products, functions. - Elementary analysis: open, closed and bounded subsets of Euclidean spaces; limits, continuity, derivatives, integrals, maximization of real-valued functions (of one or more variables). - Abstract linear algebra: vector spaces, operators, matrices. - Multivariable calculus - Probability theory: probabilities on finite state spaces, conditional probabilities, Bayes rule. - Principles of economics.
The analysis of decision making is at the heart of economics. Decision can be studied in isolation, taking as given the environment faced by the agent, or in interactive situations, where such environment comprises the decisions of other agents. Decision theory focuses on the study of a single agent. Game theory extends this analysis to the study of interacting agents. All economic theory relies on the methods of decision and game theory. A familiarity with these methods is thus necessary to achieve a thorough theoretical understanding of economic phenomena. The course provides a rigorous introduction to the mathematical tools and the conceptual aspects of the theory of decision and games, with a focus on algorithmic solution procedures.
- Preferences, utility, and rational choice.
- The consumer: choice and demand.
- Choice under risk and uncertainty.
- Exchange economies.
- Introduction to interactive decision theory. Static games.
- Rationalizability: the algorithm of iterated dominance.
- Pure strategy Nash equilibrium, interpretation, existence, derivation.
- Mixed strategy Nash equilibrium, interpretation, existence, algorithmic solution.
- Games with incomplete information: rationalizability and Bayesian equilibrium.
- Dynamic games: strategic form, rational planning.
- Iterated weak dominance, backward and forward induction algorithms.
- Subgame perfect equilibrium.
- Repeated games.
- Dynamic games with asymmetric or incomplete information.
- Perfect Bayesian equilibrium in signaling games: pooling and separation.
- Express a decision problem with the language and tool of decision theory.
- Express strategic interaction and strategic reasoning with the language and tools of game theory.
- Recognize the basic economic applications of the theory.
- Define and describe the different solution procedures provided by the theory.
- Identify their limitations and applicability.
- Analyze economic situations as decision problems and games.
- Predict behavior in economic situations by solving the game and decision problems that represent them.
- Online lectures
- Exercises (exercises, database, software etc.)
- Individual assignments
Students are regularly given exercises that illustrate the contents of the course.
|Continuous assessment||Partial exams||General exam|
The written exam aims at verifying whether:
- The student understood the theoretical concepts taught in the course.
- They are able use them to prove theoretical results covered in the program (or minor variations thereof), and to solve specific decision problems and games.
Specifically, the exam comprises three parts:
- Questions about the definition of theoretical concepts and true/false questions, the former verify whether the student studied the concepts taught in the course, the latter verify the understanding of such concepts.
- Proof of one of the theoretical results (theorem) covered in the program, or a minor variation of such results to verify the ability to proceed logically from assumptions to conclusions.
- Solution of some decision problems or games according to the concepts and procedures taught in the course.
2. Textbook: Models of Microeconomic Theory by Martin J. Osborne and Ariel Rubinstein, 2020 (free pdf version available online).
3. Strategy: An Introduction to Game Theory (Third Edition) by Joel Watson, 2013.
4. Other materials will be posted during the semester.