GAME THEORY
The aim is to introduce notions of game theory with reference to non-cooperative games.
At the end of the course the students will have acquired the basic theoretical and cognitive tools related to the analysis of the behavior and strategic decisions of the economic agents.
• Part One: Static games with complete information
1.1. Representation of games in normal form; 1.2. Iterated elimination of strictly dominated strategies; 1.3. Motivation and definition of Nash equilibrium; 2.1. The Cournot duopoly model; 2.2. Bertrand's duopoly model (for b = 1); 3.1. Mixed strategies; 3.2. Existence of Nash equilibrium.
• Second part: Dynamic games with complete information
1.1. Theory: "backward induction"; 1.2. Stackelberg's duopoly model; 2.1. Theory: perfection in subgames; 2.2. The bank run; 3.1. Theory: Two-stage repeated games; 3.2. Theory: Infinitely repeated games; 3.3. Collusion between oligopolysts in the model of Cournot; 4.1. Representation of games in extended form; 4.2. Perfect Nash equilibrium in subgames.
• Third part: Static games with incomplete information
Outline: representation in normal form, Bayesian Nash equilibrium, Cournot duopoly with incomplete information, bank run with incomplete information.
• Part Four: Dynamic games with incomplete information
Outline: perfect Bayesian Nash equilibrium, signaling games.
• Part One: Static games with complete information
1.1. Representation of games in normal form; 1.2. Iterated elimination of strictly dominated strategies; 1.3. Motivation and definition of Nash equilibrium; 2.1. The Cournot duopoly model; 2.2. Bertrand's duopoly model (for b = 1); 3.1. Mixed strategies; 3.2. Existence of Nash equilibrium.
• Second part: Dynamic games with complete information
1.1. Theory: "backward induction"; 1.2. Stackelberg's duopoly model; 2.1. Theory: perfection in subgames; 2.2. The bank run; 3.1. Theory: Two-stage repeated games; 3.2. Theory: Infinitely repeated games; 3.3. Collusion between oligopolysts in the model of Cournot; 4.1. Representation of games in extended form; 4.2. Perfect Nash equilibrium in subgames.
• Third part: Static games with incomplete information
Outline: representation in normal form, Bayesian Nash equilibrium, Cournot duopoly with incomplete information, bank run with incomplete information.
• Part Four: Dynamic games with incomplete information
Outline: perfect Bayesian Nash equilibrium, signaling games.
[1] R. Gibbons, Game Theory, Ed. Il Mulino (1994).
[2] exercises / notes, downloadable from the CLEII website.
Lectures and excercises
Written test.
Partial tests .
The evaluation is the sum of the grades reported in the every exercises carried out in the test.