Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA
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052503 - GAME THEORY
Obiettivi dell'insegnamento
The course concerns the fundamentals of the mathematical theory of interactions between agents.
Starting from the main assumptions of the theory, it discusses both cooperative and non cooperative games, and it also provides an introduction to evolutionary game theory. The goal is to explain how rationality can explain and/or predict and/or suggest the behavior of interacting agents, where "agents" may refer not only to people, but also to computers, animals, microorganisms and so on.
The course offers 1 cfu of innovative teaching. The form is flipped classroom. Some videos will be made available to the students, to watch them by themselves. Then, in class we discuss the topics, solve simple exercises.
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.
4) To know some of the proofs of fundamental theorems in evolutionary 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) the importance or the meaning of a definition or a theorem.
2) To be able to explain the applications of the theory.
Argomenti trattati
1) Main assumptions of the theory. Main differences between decision theory and 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.
6) The bargaining problem: the Nash and the Rosenthal approaches.
7) Problems of matching.
8) The basics of Social choice and Arrow’s theorem.
9) The basics of evolutionary game theory.
1 cfu is 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) The exam is written: it consists of exercises and questions on the theory (both closed and open questions).
2) The points assigned to the questions/exercises add up to 35 points
3) Students getting at least 32 points are graded with 30 lode
The exam checks that the students:
1) are able to model simple interactive situations as games.
2) are able to explain and illustrate (in written form) a definition, a theorem, a proof.
3) are able to solve exercises.
Bibliografia
Maschler, Solan, Zamir, Game Theory, Editore: CUP, Anno edizione: 2013, ISBN: 9780511794216 Note:
Inglese