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# BAEcon Economics and Social Statistics / Course details

Year of entry: 2021

## Course unit details:Mathematical Economics II

Unit code ECON30290 20 Level 3 Full year Economics Yes

### Overview

The main theme of this course is game theory. Nowadays, game theory became the most important modelling tool in economic analysis, and this subject plays a key role in any modern economics curriculum. The objective of this course is to introduce students into this important field of mathematical economics.

We present a necessary minimum---a "critical mass"---of game-theoretic models and concepts that could be included into a 3rd year economics course. The main emphasis is on those aspects of game theory that have direct links to economic modelling. Although we have to introduce general game-theoretic notions and frameworks, we try to set reasonable limits on pursuing generalities. We attempt to explain the key ideas within the most simple settings and present every topic in the most simple way, retaining at the same time necessary key details.

Most of the material of the course deals with the classical topics in non-cooperative games and their economic applications, e.g., industrial organization and various aspects of competitive market behaviour. Among other themes, brief introductions to the basic models of evolutionary game theory and cooperative games are given. Less traditional topics are related to the analysis of determinacy, unbeatable/winning strategies and their applications. The course contains many examples and problems, most of which are presented in example classes, take-home tests and tutorials.

The whole 2nd semester part of the course is concerned with specialized game-theoretic models related to auctions and mechanism design, which have remarkable applications in economics.

This course uses only elementary mathematical techniques suitable for undergraduate economics students. However, it is of a genuinely mathematical nature: it involves rigorous reasoning -- theorems, assumptions, proofs, etc. It is addressed to students inclined to mathematics, who wish to enjoy the depth and elegance of the mathematical approach to economic modelling. This character of the course requires students’ intensive work and active learning.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Mathematical Economics I ECON20120 Pre-Requisite Compulsory
Pre-requisites: ECON20120

### Aims

The general aim of this course is to introduce students to the basic game-theoretic principles and techniques employed in economic modelling. The first semester part of the course reviews fundamental themes and concepts in game theory. The second semester part focuses on auctions and mechanism design.

### Learning outcomes

By the end of this course students should be able to:
• formalize real world situations in terms of either optimization problems or games;
• demonstrate the understanding of the main solution concepts in game theory;
• use in economic modelling various game-theoretic frameworks (static and dynamic games, games of complete information, Bayesian games, etc.);
• be familiar with the basic principles of evolutionary game theory and its applications in economics.

### Syllabus

Semester 1. The focus of the 1st semester part of the course is on general concepts and frameworks of game theory in the context of mathematical economics. Topics include:

• Simultaneous move games and dynamic games with perfect information. Nash equilibrium and subgame perfect Nash equilibrium. Games with communication. Contracts, implementable allocations and correlated equilibria. The economic models of Cournot, Stackelberg, Bertrand, Hotelling, Bertrand-Edgeworth, the "Monopoly Union" model, and Rubinstein's bargaining model. Unbeatable strategies and determinacy.
• Two stage games with imperfect information and repeated games. Economic models of bank runs. Infinitely repeated games. The Folk Theorem.
• Incomplete information. Static Bayesian games. Bayesian Nash equilibrium. Cournot and Bertrand models with asymmetric information. Simplest models of auctions. Dynamic Bayesian games. Perfect Bayesian Nash equilibrium. Signalling models.
• Learning and fictitious play. Evolutionary game theory. Evolutionary stable strategies. Replicator dynamics. Evolutionary stable steady states.

Semester 2. The second semester part focuses on game-theoretic models for auctions and mechanism design.

We follow the book "Auction Theory" by V. Krishna. We cover:

•      Auctions with Private Independent Values.

•      Mechanism Design

• Applications.

### Teaching and learning methods

Semester 1: 16 lectures, 4 exercise classes (within the lecture time slots) and 2 small-group tutorial/feedback meetings

Semester 2: Lectures and exercise classes.

### Employability skills

Other
Mathematical modelling and quantitative methods in economics underpin both advanced research and effective policy. To understand social dynamics, economic behaviour and the effects of social interventions researchers and practitioners have to be able to deploy a broad range of analytic skills. The course develops skills of this kind and thereby helps preparing the students for a future career in the realms of economics and finance.

### Assessment methods

Semester One

45% Exam

2.5% Take Home Test 1

2.5% Take Home Test 2

Semester Two

40% Exam

10% Assignments

### Feedback methods

Semester 1:

•     Students can get feedback and revision support at tutorial/feedback meetings and weekly office hours.

Semester 2:

•       Tutorial feedback.

•       Office hours.

•       Mock Exam

Semester 1:

•       R. Gibbons, “A Primer in Game Theory”, 1992.

•       M. Maschler, E. Solan, and S. Zamir, “Game Theory”, Cambridge University Press, 2013.

This reading is supplementary to the lectures and is optional. The 1st  Semester part of the module is self-contained, and no external texts or resources are required to fulfil its objectives. Electronic pdf copies of all course materials (lecture notes/slides, exercises and answers) will be posted to the web during the semester. They are sufficient for studying and revising the course.

Semester 2:

•       V Krishna, "Auction Theory" (2002). Textbook.

•       M. Maschler, E. Solan, and S. Zamir, “Game Theory”, Cambridge University Press, 2013.

•       K Sydsaeter et al, "Essential Mathematics for Economic Analysis" (FT Press, 2008).

•       K Sydsaeter et al, "Further Mathematics for Economic Analysis" (FT Press, 2008).

The textbook by V. Krishna is an essential reading material for the 2nd Semester part of the course. Short lecture summaries will be supplied after each lecture, but they shouldn’t and cannot replace thorough reading, preparation for class and self work. The other books on the list are recommended, and fully sufficient, for revising the course and preparing the examination.

### Study hours

Independent study hours
Independent study 0

### Teaching staff

Staff member Role
Igor Evstigneev Unit coordinator
Omer Idan Unit coordinator