## GAME THEORY

## Syllabus

### Updated A.Y. 2022-2023

### Updated A.Y. 2020-2021

### Updated A.Y. 2020-2021

**Presentation**

Game Theory proposes a way to model strategic interactions among rational agents using logico-mathematical approach. Relevant economic examples are competition among strategic firms, conflicts among nations, trading behavior in stock markets, among others. The course presents the fundamental introductory tools to game theoretic analysis. A variety of examples will be discussed to illustrate the main concepts, with a specific reference to classical economic applications.

**Programme for Game Theory**

**Strategic games of complete information**

Dominant strategies and Nash equilibrium.

Applications: Cournot Oligopoly, Bertrand duopoly, Hotelling model of political competition, public good provision.

Mixed strategies. Existence of a Nash equilibrium in finite games.**Extensive games with perfect information**

Extensive form, backward induction.

Subgame Perfect Nash Equilibrium.

Applications: Stackelberg duopoly, entry games, ultimatum games.

Some example of bargaining.

**Extensive games with imperfect information: preliminaries.**

**Pre-requisites:** Basic notions of Mathematics and Probability. Microeconomics, in particular individual decision under uncertainty.

**Main reference: **M.J. Osborne, *An Introduction to Game Theory*, Oxford University Press

**Knowledge and Understanding**

The course provides the fundamental instruments to analyse strategic interactions that often appear in the contemporary economic debate. Students will be exposed to logico-mathematical thinking and rigorous development of line of thoughts, via the use of assumptions, statements and proofs. At the end of the course, students will have a clear understainding of the bacics of game theory.

### Updated A.Y. 2019-2020

### Updated A.Y. 2019-2020

**Presentation**

Game Theory proposes a way to model strategic interactions among rational agents using logico-mathematical approach. Relevant economic examples of such interactions concern competition among firms, conflicts among nations, trading behavior in stock markets. The course presents the fundamental introductory tools to game theoretic analysis. A variety of examples will be discussed to illustrate the main concepts, with a specific reference to classical economic applications.

**Programme for Game Theory**

**Strategic games of complete information**

Dominant strategies and Nash equilibrium.

Applications: Cournot Oligopoly, Bertrand duopoly, public good provision.

Mixed strategies. Existence of a Nash equilibrium in finite games.**Extensive games with perfect information**

Extensive form, backward induction.

Subgame Perfect Nash Equilibrium.

Applications: entry games.

**Pre-requisites:** Basic notions of Mathematics and Probability. Microeconomics, in particular individual decision under uncertainty.

**Main reference: **M.J. Osborne, *An Introduction to Game Theory*, Oxford University Press

**Knowledge and Understanding**

The course provides the fundamental instruments to analyse strategic interactions that often appear in the contemporary economic debate. Students will be exposed to logico-mathematical thinking and rigorous development of line of thoughts, via the use of assumptions, statements and proofs. At the end of the course, students will have a clear understainding of the bacics of game theory.

### Updated A.Y. 2018-2019

### Updated A.Y. 2018-2019

**Presentation**

Game Theory proposes a way to model strategic interactions among rational agents using logico-mathematical approach. Relevant economic examples of such interactions concern competition among firms, conflicts among nations, trading behavior in stock markets. The course presents the fundamental introductory tools to game theoretic analysis. A variety of examples will be discussed to illustrate the main concepts, with a specific reference to classical economic applications.

**Programme for Game Theory**

**Strategic games of complete information**

Dominant strategies and Nash equilibrium.

Applications: Cournot Oligopoly, Bertrand duopoly, Hotelling model of political competition, public good provision.

Mixed strategies. Existence of a Nash equilibrium in finite games.

**Extensive games with perfect information**

Extensive form, backward induction.

Subgame Perfect Nash Equilibrium.

Applications: Stackelberg duopoly, entry games, ultimatum games.

Some example of bargaining.

**Extensive games with imperfect information: preliminaries.**

**Pre-requisites:** Basic notions of Mathematics and Probability. Microeconomics, in particular individual decision under uncertainty.

**Main reference: **M.J. Osborne, *An Introduction to Game Theory*, Oxford University Press

**Knowledge and Understanding**

The course provides the fundamental instruments to analyse strategic interactions that often appear in the contemporary economic debate. Students will be exposed to logico-mathematical thinking and rigorous development of line of thoughts, via the use of assumptions, statements and proofs. At the end of the course, students will have a clear understainding of the bacics of game theory.

### Updated A.Y. 2017-2018

### Updated A.Y. 2017-2018

**Presentation**

Game Theory is the mathematical modeling of strategic interactions among rational agents. Relevant economic examples of such interactions concern competition among firms, conflicts among nations, trading behavior in stock markets. The course presents the fundamental introductory tools to game theoretic analysis. A variety of examples will be discussed to illustrate the main concepts, with a specific reference to classical economic applications.

**Programme for Game Theory**

• Strategic games of complete information

Dominant strategies and Nash equilibrium.

Applications: Cournot Oligopoly, Bertrand duopoly.

Mixed strategy equilibria. Existence of a Nash equilibrium.

• Extensive games with perfect information

Extensive form, backward induction. Subgame Perfect Nash Equilibrium. Applications: Stackelberg duopoly, entry games, ultimatum games. Extention to game with simultaneous moves.

**Pre-requisites:** Basic notions of Mathematics and Probability. Microeconomics, in particular individual decision under uncertainty.

**Main reference: **M.J. Osborne, *An Introduction to Game Theory*, Oxford University Press

***********************

**Detailed syllabus for Game Theory a.y. 2017-2018**

(based on M.J. Osborne, An Introduction to Game Theory, Oxford University Press 2009, International edition)

1. Introduction

2. Nash Equilibrium: Theory

All chapter, except section 2.9.

3. Nash Equilibrium: Illustrations

Only the sections 3.1, 3.2, 3.3.

4. Mixed Strategy Equilibrium

All chapter, except sections 4.4, 4.6, 4.8, 4.9, 4.10, 4.11.

5. Extensive Games with Perfect Information

6. Extensive Games with Perfect Information: Illustrations

Only sections 6.1, 6.2

7. Extensive Games with Perfect Information: Extensions and discussions

Only Section 7.1

***********************************

**Knowledge and Understanding**

The course provides the fundamental instruments to analyse strategic interactions that often appear in the contemporary economic debate. Students will be exposed to logico-mathematical thinking and rigorous development of line of thoughts, via the use of assumptions, statements and proofs. At the end of the course, students will have a clear understainding of the bacics of game theory.