Unit GAMES AND DECISION THEORY
- Course
- Mathematics
- Study-unit Code
- 55A00081
- Curriculum
- Matematica per l'economia e la finanza
- Teacher
- Joseph Rinott
- Teachers
-
- Joseph Rinott
- Hours
- 42 ore - Joseph Rinott
- CFU
- 6
- Course Regulation
- Coorte 2019
- Offered
- 2020/21
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- MAT/06
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- English
- Contents
- Elements of decision theory
Elements of cooperative and not-cooperative games theory
Elements of social choice theory - Reference texts
- K. Leyton-Brown, Y. Shoham: Essentials of Game Theory, Morgan & Claypool Publishers, 2008.
D.M. Kreps: Notes On The Theory of Choice, Westview Press, 1988
W. Gaertner: A Primer in Social Choice Theory, Oxford University Press, 2009.
Presh Talwalkar : The Joy of Game Theory: An Introduction to Strategic Thinking Paperback – 2014
Additional material will be provided by the teachers during the course. - Educational objectives
- The aim of the course is to acquire the main theoretical and methodological tools for modeling rational choices (both in presence of a single agent or for more agents) and to recommend the best choices for achieving the goals set.
- Prerequisites
- The course requires basic knowledge of probability theory present in a first course of Probability and Statistics.
All other knowledge required is covered by the undergraduate degree in Computer Science. - Teaching methods
- Frontal lessons that provide solutions of problems and cases study and exercises, usually held with the use of IT tools.
- Learning verification modality
- The exam is a written test on all the topics taught in the course
- Extended program
- DECISION THEORY AND GAME THEORY
1. Introduction to the course. Binary relations and their properties. Decision problem under certainty. Preference relations.
2. Probability background as needed. Subjective probability (Savage). Some background in statistics, and Bayesian statistics.
3. Lotteries, decisions under uncertainty.
4. Introduction to expected utility according to von Neumann-Morgenstern. von Neumann-Morgenstern axioms.
5. von Neumann-Morgenstern representation theorem.
6. Introduction to game theory. Various classifications of models in game theory. Examples, e.g. Prisoner’s Dilemma, the Chicken game, and their
relation to current politics (Trump and North Korea?). Definition of non-cooperative strategic game.
7. Pareto optimality, best response, removal of dominate strategies, Nash equilibrium and its computation.
8. Nash equilibria in non-cooperative strategic games. Strictly competitive (or zero-sum) non-cooperative strategic games. Maxminimization, maxmin
theorem, the relation to Nash equilibrium, and value of a strictly competitive (or zero-sum) game. Some examples.
9. Mixed and pure strategies for a non-cooperative strategic games. Expected utility for mixed strategy profiles. Mixed strategy Nash equilibrium.
10. Approximate Nash equilibrium, regret, Evolutionarily Stable Strategies (ESS).
11. Correlated equilibrium
12. Cooperative games and computation of Shapley’s value.
13. Games with sequential actions.
14. Repeated and stochastic games.
15. Statistics as a game and implications. Some discussion of statistical decision rules.
16. Paradoxes, Arrow’s impossibility theorem.
17. Social choice: aggregation of preferences, Gibbard Satterthwaite theorem, manipulations, majority rules and individual rights.