Ing Ind - Inf (Mag.)(ord. 270) - BV (479) MANAGEMENT ENGINEERING - INGEGNERIA GESTIONALE
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088976 - GAME THEORY
Ing Ind - Inf (Mag.)(ord. 270) - MI (474) TELECOMMUNICATION ENGINEERING - INGEGNERIA DELLE TELECOMUNICAZIONI
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088976 - GAME THEORY
Ing Ind - Inf (Mag.)(ord. 270) - MI (481) COMPUTER SCIENCE AND ENGINEERING - INGEGNERIA INFORMATICA
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088976 - GAME THEORY
Obiettivi dell'insegnamento
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.
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.
Making judgements
1) To be able to state translate a problem in a game and analyze it.
Communication skills
1) To be able to explain and illustrate (in written form) a definition, the text of a theorem, its proof.
Argomenti trattati
1) The main assumptions of the theory. Main differences between the decision theory and the interactive decision theory.
2) Non cooperative games. Games in estensive form. Games with perfect information, backward induction. Combinatorial games.
3) Zero sum games. Conservative values. The case of equilibrium in pure strategies. Extending the finite game to mixed strategies. The von Neumann theorem. Finding optimal strategies and the value of a finite game by means of Linear Programming.
4) 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. Correlated equilibria.
5) Cooperative games, definitions, examples. Core, nucleolus, the Shapley value and power indices.
Prerequisiti
Some mathematical analysis and linear algebra and the basics of probability
Modalità di valutazione
1) Exam is written: it consists of some (usually three) exercises, and two theoretical questions
2) Each exercise is worth a fixed, known, number of points, the same with each theoretical question. 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.
Bibliografia
R. Lucchetti, A primer in game theory, Editore: Esculapio, Anno edizione: 2011
Maschler, Solan, Zamir, Game Theory, Editore: cambridge University Press, Anno edizione: 2013
Software utilizzato
Nessun software richiesto
Forme didattiche
Tipo Forma Didattica
Ore di attività svolte in aula
(hh:mm)
Ore di studio autonome
(hh:mm)
Lezione
32:30
48:45
Esercitazione
17:30
26:15
Laboratorio Informatico
0:00
0:00
Laboratorio Sperimentale
0:00
0:00
Laboratorio Di Progetto
0:00
0:00
Totale
50:00
75:00
Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua
Inglese
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
Disponibilità di supporto didattico in lingua inglese
Inglese