Ing Ind - Inf (Mag.)(ord. 270) - MI (474) TELECOMMUNICATION ENGINEERING - INGEGNERIA DELLE TELECOMUNICAZIONI
088976 - GAME THEORY
Ing Ind - Inf (Mag.)(ord. 270) - MI (481) COMPUTER SCIENCE AND ENGINEERING - INGEGNERIA INFORMATICA
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 descriptions of a game: the extensive form 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 model 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 statement of a theorem, its proof.
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 finite games 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.
Some mathematical analysis and linear algebra and the basics of probability.
Modalità di valutazione
1) The exam is written. It consists of some exercises, and two open questions on the theory.
2) Each exercise and each open question is assigned a certain number of points. The sum is 35.
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 model simple interactive situations as games.
2) are able to explain and illustrate (in written form) a definition, the statement of a theorem, its proof.
3) are able to solve exercises.
R. Lucchetti, A primer in game theory, Editore: Esculapio, Anno edizione: 2011
Maschler, Solan, Zamir, Game Theory, Editore: cambridge University Press, Anno edizione: 2013
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Tipo Forma Didattica
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Ore di studio autonome
Laboratorio Di Progetto
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