L'insegnamento prevede 1.0 CFU erogati con Didattica Innovativa come segue:
Blended Learning & Flipped Classroom
Corso di Studi
Codice Piano di Studio preventivamente approvato
Da (compreso)
A (escluso)
Insegnamento
Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA
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A
ZZZZ
052503 - 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.
The course offers one cfu of innovative teaching. The form is flipped classroom. Within the topics of Nash equilibria and Social choice, some videos will be made available to students. They will watch them by themselves. Subsequently, in the class we propose some discussion on the topics, simple exercises, and we stimulate discussion on the results presented in the videos.
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. Games with a continuous of players and Wardrup equilibrium. Price of stability and of anarchy. Correlated equilibria.
5) Cooperative games, definitions, examples. Core, nucleolus, the Shapley value and power indices.
6) The bargaining problem: the Nash and the Rosenthal approaches.
7) Problems of matching.
8) Basic of Social choice and Arrow’s theorem.
9) Games with incomplete information: model and the Nash-Bayes equilibrium.
1 cfu with topics taken from items 4) and 8) will be offered as innovative teaching (some videos to see individually and flipped class room)
Prerequisiti
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
4) A brief oral examination is possible upon agreement between the student and the teacher
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
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
52:00
78:00
Esercitazione
28:00
42:00
Laboratorio Informatico
0:00
0:00
Laboratorio Sperimentale
0:00
0:00
Laboratorio Di Progetto
0:00
0:00
Totale
80:00
120:00
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