Syllabus
EN
IT
Learning Objectives
LEARNING OUTCOMES: the aim of this course is to introduce students to strategic reasoning through a formal training in game theory and a parallel set of lectures on applications to competition policy. Specifically, we will formally introduce the basic ingredients of non cooperative games and a number of equilibrium concepts used to solve them. These will be applied to studying strategic interaction among firms and to design incentive schemes to achieve a number of basic public policy goals.
KNOWLEDGE AND UNDERSTANDING:
At the end of the Course students should be able to understand and apply the logical approach of game theory to analyse the strategic environment that firms face in regime of oligopoly. In particular, we will study anti-competitive conducts put forth by firms and public policies to address them.
APPLYING KNOWLEDGE AND UNDERSTANDING:
At the end of the Course students should be able to apply the knowledge to identify potential anti-competitive practices.
MAKING JUDGEMENTS:
Given a firm's conduct, the student should be able to (i) sketch its overall impact on economic surplus and its redistributive impact on the individual surplus of the parties involved and (ii) suggest potential interventions.
COMMUNICATION SKILLS:
At the end of the course students should be able to analyse market practices and prepare presentations to discuss their effects on competition.
KNOWLEDGE AND UNDERSTANDING:
At the end of the Course students should be able to understand and apply the logical approach of game theory to analyse the strategic environment that firms face in regime of oligopoly. In particular, we will study anti-competitive conducts put forth by firms and public policies to address them.
APPLYING KNOWLEDGE AND UNDERSTANDING:
At the end of the Course students should be able to apply the knowledge to identify potential anti-competitive practices.
MAKING JUDGEMENTS:
Given a firm's conduct, the student should be able to (i) sketch its overall impact on economic surplus and its redistributive impact on the individual surplus of the parties involved and (ii) suggest potential interventions.
COMMUNICATION SKILLS:
At the end of the course students should be able to analyse market practices and prepare presentations to discuss their effects on competition.
Prerequisites
None
Program
First part: Complete Information
Static games of complete information. The Nash equilibrium in pure strategies. Nash equilibrium in mixed strategies. Cournot model. Bertrand model. Dynamic games of complete information. Extensive form games and backward induction. Subgame perfect Nash equilibrium. Stackelberg model of duopoly. Repeated games. The Prisoner’s dilemma and coordination. The Folk theorem.
Second part: Incomplete Information
Static Games of incomplete Information. Bayesian Nash equilibrium. An auction game. Harsanyi’ interpretation of mixed strategies. Dynamic games of incomplete information. Perfect Bayesian equilibrium. Basics of signalling.
The course is divided into 18 lessons of 2 hours each and 6 practice sessions of 2 hours each. Every week, students attend 3 lessons followed by a practice session to apply their knowledge to exercises. The topics covered in lessons is as follows.
Week 1:
Lessons 1-2-3: Introduction to Game Theory – Examples – Connections with other economic courses – Course goals – Informal introductory example – Normal-form representation –Dominant/Dominated strategies – Iterated Elimination of Strictly Dominated Strategies – Discussion on equilibrium concept – Best-response function - Nash equilibrium: definition and examples.
Week 2:
Lessons 4-5-6: Applications of Nash equilibrium: Cournot and Bertrand Duopoly – Mixed Strategy equilibrium – Introduction to dynamic games – Game trees – Nash equilibrium in dynamic games (1/2) – Extensive-form game – Strategies in dynamic games – Nash equilibrium in dynamic games (2/2) – Subgame-perfect Nash equilibrium (1/3).
Week 3:
Lessons 7-8-9: Subgame-perfect Nash equilibrium (2/3) – Subgames – Backward Induction – Comparison with Nash equilibrium/non-credible threats – Subgame-perfect Nash equilibrium (3/3) – Examples – Application of SPNE: Stackelberg Duopoly
Week 4:
Lessons 10-11-12: Repeated games– Presentation and definition – Folk Theorems and examples – Solutions and applications (Collusion in Bertrand), trigger strategies.
Week 5:
Lessons 13-14-15: Static games of incomplete information – Presentation, definition, types, beliefs and normal form representation – Strategies, expected payoffs and Bayesian Nash Equilibrium – Bayesian Cournot Nash, A bidding game and Harsanyi’s interpretation of mixed strategies.
Week 6:
Lessons 16-17-18: Dynamic games of incomplete information – Introduction to sequential rationality with incomplete information and new beliefs requirements – Perfect Bayesian Nash Equilibrium – Examples of Perfect Bayesian Nash Equilibrium, Signaling games.
Static games of complete information. The Nash equilibrium in pure strategies. Nash equilibrium in mixed strategies. Cournot model. Bertrand model. Dynamic games of complete information. Extensive form games and backward induction. Subgame perfect Nash equilibrium. Stackelberg model of duopoly. Repeated games. The Prisoner’s dilemma and coordination. The Folk theorem.
Second part: Incomplete Information
Static Games of incomplete Information. Bayesian Nash equilibrium. An auction game. Harsanyi’ interpretation of mixed strategies. Dynamic games of incomplete information. Perfect Bayesian equilibrium. Basics of signalling.
The course is divided into 18 lessons of 2 hours each and 6 practice sessions of 2 hours each. Every week, students attend 3 lessons followed by a practice session to apply their knowledge to exercises. The topics covered in lessons is as follows.
Week 1:
Lessons 1-2-3: Introduction to Game Theory – Examples – Connections with other economic courses – Course goals – Informal introductory example – Normal-form representation –Dominant/Dominated strategies – Iterated Elimination of Strictly Dominated Strategies – Discussion on equilibrium concept – Best-response function - Nash equilibrium: definition and examples.
Week 2:
Lessons 4-5-6: Applications of Nash equilibrium: Cournot and Bertrand Duopoly – Mixed Strategy equilibrium – Introduction to dynamic games – Game trees – Nash equilibrium in dynamic games (1/2) – Extensive-form game – Strategies in dynamic games – Nash equilibrium in dynamic games (2/2) – Subgame-perfect Nash equilibrium (1/3).
Week 3:
Lessons 7-8-9: Subgame-perfect Nash equilibrium (2/3) – Subgames – Backward Induction – Comparison with Nash equilibrium/non-credible threats – Subgame-perfect Nash equilibrium (3/3) – Examples – Application of SPNE: Stackelberg Duopoly
Week 4:
Lessons 10-11-12: Repeated games– Presentation and definition – Folk Theorems and examples – Solutions and applications (Collusion in Bertrand), trigger strategies.
Week 5:
Lessons 13-14-15: Static games of incomplete information – Presentation, definition, types, beliefs and normal form representation – Strategies, expected payoffs and Bayesian Nash Equilibrium – Bayesian Cournot Nash, A bidding game and Harsanyi’s interpretation of mixed strategies.
Week 6:
Lessons 16-17-18: Dynamic games of incomplete information – Introduction to sequential rationality with incomplete information and new beliefs requirements – Perfect Bayesian Nash Equilibrium – Examples of Perfect Bayesian Nash Equilibrium, Signaling games.
Books
Gibbons, R. (1992), Game theory for applied economists, Princeton University Press.
Bibliography
Belleflamme, Paul and Martin Peitz, (2015). Industrial
Organization Markets and Strategies, 2nd Edition, Cambridge University Press.
Motta Massimo (2014), Competition Policy: Theory and Practice, Cambridge University
Press.
website: slides ed esercizi
https://www.cambridge.org/it/academic/subjects/economics/industrial-economics/industrial-
organization-markets-and-strategies-2nd-edition?format=PB#resources
Organization Markets and Strategies, 2nd Edition, Cambridge University Press.
Motta Massimo (2014), Competition Policy: Theory and Practice, Cambridge University
Press.
website: slides ed esercizi
https://www.cambridge.org/it/academic/subjects/economics/industrial-economics/industrial-
organization-markets-and-strategies-2nd-edition?format=PB#resources
Teaching methods
Attendance is not mandatory, but highly recommended. Attending students are typically able to reap more benefits from the course and more easily meet the learning objectives.
Exam Rules
The assessment method is entirely based on a written exam. The exam is composed of two or three exercises, possibly including theoretical questions. It requires students to be able to solve games covered in the module.
The grade for the exam is expressed out of thirty points.
Exercises are divided into questions (regularly between 3 and 6 separate questions) and each question is worth between 1 and 3 points. If the answer to a question is only partially correct or incomplete, the student might receive no points or only a fraction of the question’s total points. The value of each question is indicated on the exam paper.
Grades will be communicated within a week after the exam takes place. They will be anonymized and available on the course webpage.
Since EEBL students take the exam at the same time as the exam in Industrial Organization, the grade obtained in each of the two modules will have a 50% weight in determining the final grade for the course. In particular:
Final Grade = 0.5 x (Grade in Game Theory Module) + 0.5 x (Grade in Industrial Organization Module).
Students will have to obtain at least 18/30 in each of the two modules to pass the exam.
The final exam grade reflects the student’s understanding and mastering of the course material according to the following scale.
<18: Insufficient. The student’s understanding of the core principles of the course is highly insufficient and/or superficial.
18-20: Basic understanding the course material barely sufficient to solve the simplest problems.
21-23: Basic understanding of the course material sufficient to solve the simplest problems.
24-26: Intermediate understanding of the course material and ability to solve most of the problems.
27-29: Good understanding of the course material, ability to solve most of the problems and to adapt to more challenging questions.
30-30L: Solid understanding of the course material, ability to autonomously manipulate the tools developed in the course and precise presentation of answers and concepts.
The grade for the exam is expressed out of thirty points.
Exercises are divided into questions (regularly between 3 and 6 separate questions) and each question is worth between 1 and 3 points. If the answer to a question is only partially correct or incomplete, the student might receive no points or only a fraction of the question’s total points. The value of each question is indicated on the exam paper.
Grades will be communicated within a week after the exam takes place. They will be anonymized and available on the course webpage.
Since EEBL students take the exam at the same time as the exam in Industrial Organization, the grade obtained in each of the two modules will have a 50% weight in determining the final grade for the course. In particular:
Final Grade = 0.5 x (Grade in Game Theory Module) + 0.5 x (Grade in Industrial Organization Module).
Students will have to obtain at least 18/30 in each of the two modules to pass the exam.
The final exam grade reflects the student’s understanding and mastering of the course material according to the following scale.
<18: Insufficient. The student’s understanding of the core principles of the course is highly insufficient and/or superficial.
18-20: Basic understanding the course material barely sufficient to solve the simplest problems.
21-23: Basic understanding of the course material sufficient to solve the simplest problems.
24-26: Intermediate understanding of the course material and ability to solve most of the problems.
27-29: Good understanding of the course material, ability to solve most of the problems and to adapt to more challenging questions.
30-30L: Solid understanding of the course material, ability to autonomously manipulate the tools developed in the course and precise presentation of answers and concepts.