Obiettivi Formativi

Lo scopo del corso è quello di introdurre lo studente agli aspetti principali della teoria dei giochi e le sue applicazioni. Verranno forniti gli strumenti analitici per modellizzare e analizzare situazioni in cui gli agenti interagiscono tra loro e, nel fare le proprio scelte, devono tenere in considerazione le scelte degli altri. Particolare enfasi verrà data alle applicazioni. Lo studente sarà in grado di distinguere i diversi concetti di equilibrio per giochi cooperativi e giochi non-cooperativi. Potrà modellizzare una situazione di interazione mediante un gioco e determinare le strategie in equilibrio.

Learning Goals

The aim of the course is to introduce the student to the main aspects of game theory. Moreover, applications will be given. The student will be able to distinguish the different concepts of equilibrium for cooperative games and non-cooperative games.

Metodi didattici

Lezioni frontali ed esercitazioni in aula.

Teaching Methods

Lessons

Prerequisiti

E richiesta la conoscenza degli elementi di base dellAnalisi matematica; in particolare il calcolo per funzioni di più variabili.

Prerequisites

Calculus

Verifiche dell'apprendimento

La verifica consiste in una prova scritta con esercizi e brevi domande teoriche a risposta aperta. Sono previste verifiche in itinere.

Assessment

Written exam

Programma del Corso

NON-COOPERATIVE GAMES Games in strategic form: formal definition and examples. Mixed strategies and mixed extension of a game in strategic form. Strictly and weakly dominated strategies; process of iterated elimination of dominated strategies. Nash equilibrium; stability property of Nash equilibrium. Calculus of equilibrium by using the Best Replay map and the indifference principle. The maxmin strategy and the conservative value. Relationship between different equilibria. Two-players zero-sum games. The graphical procedure for the calculus of equilibrium. Fair division. Routing games. Games in extensive form with perfect informations: definitions and examples. The backward induction. The game of chess, David Gale's game, The Nim game. Games with imperfect informations and chance moves. Examples. COOPERATIVE GAMES formal definition and examples. Solution concept; the Core and the Shapley value.

Course Syllabus

NON-COOPERATIVE GAMES Games in strategic form: formal definition and examples. Mixed strategies and mixed extension of a game in strategic form. Strictly and weakly dominated strategies; process of iterated elimination of dominated strategies. Nash equilibrium; stability property of Nash equilibrium. Calculus of equilibrium by using the Best Replay map and the indifference principle. The maxmin strategy and the conservative value. Relationship between different equilibria. Two-players zero-sum games. The graphical procedure for the calculus of equilibrium. Fair division. Routing games. Games in extensive form with perfect informations: definitions and examples. The backward induction. The game of chess, David Gale's game, The Nim game. Games with imperfect informations and chance moves. Examples. COOPERATIVE GAMES formal definition and examples. Solution concept; the Core and the Shapley value.