Obiettivi Formativi

Comprensione del comportamento strategico di decisori razionali mediante l’illustrazione dei concetti di gioco in forma strategica e estesa, e quindi dei vari concetti di soluzione e di equilibrio per giochi di contrattazione e non cooperativi.

Learning Goals

Understanding of the strategic behavior of rational decision-makers through the illustration of the concepts of strategic and extensive form game, and then the various solution concepts and equilibrium to bargaining games and non-cooperative games.

Metodi didattici

Problem solving, lezione frontale, esercitazione.

Teaching Methods

Problem solving, lesson.

Prerequisiti

Elementi di analisi

Prerequisites

Elements of calculus

Verifiche dell'apprendimento

Esame scritto

Assessment

Written exam

Programma del Corso

Games in extensive form. Formal definition of games in extensive form: game with perfect information, with imperfect information, with imperfect information and chance moves. Backward induction. Kuhn's or Zermelo's Theorem. Definition of winning strategy and Von Neumann’s Theorem. The game of chess, David Gale's game, The Nim game. Games in strategic (or normal) form. From extensive-game form to strategic form game (without and with chance moves). Solution concepts of strategic-form games: strictly and weakly dominated strategies. Process of iterated elimination of strictly and weakly dominated strategies. Nash equilibrium. Stability property of Nash equilibrium. Best Replay map. Backward induction and Nash equilibria. The maxmin concept. Conservative value and conservative strategy. Games: Cournot duopoly competition; Chairman's Paradox Two-player zero-sum games: definition and examples. The maxmin value and the minmax value. Value of the game and optimal strategy. Saddle point and optimal strategy. Mixed strategies and mixed extension of a game in strategic form. Equilibrium in mixed strategies. Von Neumann's Minmax Theorem and Nash’s Theorem. Calculus of equilibrium in mixed strategies: The direct approach. The graphical procedure for two-player zero-sum game. Indifference principle. Dominance and equilibrium. First-price sealed-bid auctions. Second-price sealed-bid auction. Finitely-repeated games. The Prisoner Dilemma with the possibility of punishment. Infinitely-repeated game. Folk Theorem. Definition of Bayesian games. Bank Runs, Incomplete Information Cournot, Auction (first and second price)

Course Syllabus

Games in extensive form. Formal definition of games in extensive form: game with perfect information, with imperfect information, with imperfect information and chance moves. Backward induction. Kuhn's or Zermelo's Theorem. Definition of winning strategy and Von Neumann’s Theorem. The game of chess, David Gale's game, The Nim game. Games in strategic (or normal) form. From extensive-game form to strategic form game (without and with chance moves). Solution concepts of strategic-form games: strictly and weakly dominated strategies. Process of iterated elimination of strictly and weakly dominated strategies. Nash equilibrium. Stability property of Nash equilibrium. Best Replay map. Backward induction and Nash equilibria. The maxmin concept. Conservative value and conservative strategy. Games: Cournot duopoly competition; Chairman's Paradox Two-player zero-sum games: definition and examples. The maxmin value and the minmax value. Value of the game and optimal strategy. Saddle point and optimal strategy. Mixed strategies and mixed extension of a game in strategic form. Equilibrium in mixed strategies. Von Neumann's Minmax Theorem and Nash’s Theorem. Calculus of equilibrium in mixed strategies: The direct approach. The graphical procedure for two-player zero-sum game. Indifference principle. Dominance and equilibrium. First-price sealed-bid auctions. Second-price sealed-bid auction. Finitely-repeated games. The Prisoner Dilemma with the possibility of punishment. Infinitely-repeated game. Folk Theorem. Definition of Bayesian games. Bank Runs, Incomplete Information Cournot, Auction (first and second price)