Ing Ind - Inf (Mag.)(ord. 270) - BV (479) MANAGEMENT ENGINEERING - INGEGNERIA GESTIONALE
088976 - GAME THEORY
The course is aimed at illustrating the fundamentals of the mathematical theory of interactions between agents. It starts with the discussion of the main assumptions underlying the theory, and it continues by considering the possible description of the games: the extensive and the strategic form. Both the cooperative and non cooperative theory will be considered. The goal is to explain how rationality can explain and/or predict and/or suggest the behavior of interacting agents. This is not limited to human being, it can also be applied to animals, networks of computers and so on.
The course fits into the overall program curriculum pursuing some of the defined general learning goals.In particular, the course contributes the development of the following capabilities:
Understand context, functions, processes in a business and industrial environment and the impact of those factors on business performance
Design solutions applying a scientific and engineering approach (Analysis, Learning, Reasoning, and Modeling capability deriving from a solid and rigorous multidisciplinary background) to face problems and opportunities in a business and industrial environment
Risultati di apprendimento attesi
Knowledge and understanding
1) To know the fundamentals of interactive decision theory.
2) To know some of the proofs of fundamental theorems in non cooperative game theory.
3) To know some of the proofs of fundamental theorems in cooperative game theory.
Ability in applying knowledge and understanding
1) To be able to modelize simple interactive situations as games.
2) To be able to state and explain the proofs of fundamental theorems in game theory.
3) To solve exercises.
1) To be able to state translate a problem in a game and analyze it.
1) To be able to explain and illustrate (in written form) a definition, the text of a theorem, its proof.
1) The main assumptions of the theory. Main differences between the decision theory and the interactive decision theory.
2) The Nash non cooperative model, Nash equilibrium and existence of (mixed) equilibria in finite games. Examples. Potential games, how to find a potential. Examples: congestion games, routing games, network games, location games. Price of stability and of anarchy. Zero sum games. Games in estensive form. Games with perfect information, backward induction. From the extensive to the strategic form. Combinatorial games.
5) Cooperative games, definitions, examples. Core, nucleolus, the Shapley value and power indices.
6) Problems of matching.
7) Mechanism design
8) Basic of Social choice and Arrow’s theorem.
9) The bargaining problem: the Nash and the Rosenthal approaches.
The last topics will be proposed if time suffices.
Some mathematical analysis and linear algebra and the basics of probability
Modalità di valutazione
1) Exam is written: it consists of exercises and theoretical questions
2) Each exercise and theoretical question is worth a fixed, known, number of points. The sum is usually 35 points
3) Students getting at least 32 points are graded with 30 lode
The exam is aimed at checking that the students:
1) are be able to modelize simple interactive situations as games.
2) are able to explain and illustrate (in written form) a definition, the text of a theorem, a proof.
3) are able to solve exercises.
M. Maschler, E. Solan, S. Zamir,, Game theory, Editore: Cambridge University Press, Anno edizione: 2013
Nessun software richiesto
Tipo Forma Didattica
Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Di Progetto
Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese