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L13619 Advanced Mathematical Economics

Module description & content | Aims & objectives | Module downloads | Lectures & tutorials | Assessment | Module texts

Pre-requisite: L12302 Microeconomic Theory
Credits: 15

Lecturers

Dr V Anesi

t: +44 (0)115 84 66156

e: vincent.anesi@nottingham.ac.uk

Module description & content

The prerequisite for this module is Microeconomic Theory (L12302). The module is intended to provide an introduction to some applications of mathematical techniques in economics. In particular, examples of economic issues that can be analyzed using mathematical models are discussed in detail. Applications are from a variety of economic topics including: Public Economics, Industrial Organization, Natural Resource Economics, and Political Economy. Particular attention will be given to providing an intuitive understanding of the logic behind the formal results presented. Students who wish to pursue a higher degree in economics will find the module particularly useful.

 

PART I: INTRODUCTION

Chapter 0: General Introduction

Chapter 1: Basic Preliminaries of Game-Theoretic Analysis

1. Sets
2. Functions
3. Noncooperative Games
4. Nash Equilibrium
5. Sequential Rationality, and Subgame Perfection

PART II: LONG-RUN RELATIONSHIPS

Chapter 2: Repeated Games 

1. Introduction
2. The Stage Game
3. The Repeated Game
4. Subgame Perfect Equilibria and the One-Shot Deviation Principle
5. Application 1: Group Size and Public Good Provision
6. Application 2: Price Wars (Oligopolistic competition)

Chapter 3: Dynamic Games

1. Introduction
2. The Game
3. Stationary Markov Equilibrium
4. Application: Extraction of a Common Resource
5. Stochastic Games

PART III: COALITIONS

Chapter 4: Coalitional Refinements

1. Introduction
2. Games and Coalitions
3. Pareto Dominance
4. Strong Nash Equilibrium
5. Coalition-Proof Nash Equilibrium
6. Application: Income Redistribution

Chapter 5: Cooperative Game Theory

1. Basic Elements of Cooperative Games
2. The Core
3. Application: Income Redistribution
4. Coalition Formation

PART IV: INCOMPLETE INFORMATION AND MECHANISM DESIGN

Chapter 6: Games of Incomplete Information

1. Bayesian Games
2. Bayesian Nash Equilibrium
3. Application 1: Cournot Competition with Incomplete Information
4. Application 2: Research and Development

Chapter 7: The Mechanism Design Problem

1. Introduction to the Mechanism Design Problem
2. Examples: Social Choice, Pure Exchange Economies, Public Projects, Auctions
3. Mechanisms and Implementation

Chapter 8: The Principal Agent Problem with Hidden Information

1. Introduction
2. The Basic Model
3. The Complete Information Contract
4. Incentive Feasible Menu of Contracts
5. The Revelation Principle
6. Optimization Programme of the Principal
7. The Rent Extraction-Efficiency Trade-Off
8. Application 1: Marginal Cost Pricing
9. Application 2: Quantity and Price Discrimination
10. Application 3: Financial Contracts

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Aims and objectives

There are three main aims for this module and they are:

• To provide a rigorous grounding in certain mathematical tools and methods of argumentation used in microeconomic theory.
• To develop a clear perception of the role of mathematical tools and logical methods in the construction of the formal theory of individual decision-making.
• To inculcate the ability to analyze economic problems through rigorous applications of the formal theory of individual decision-making.

On completing this module, the learning outcomes are such that students will be able to:

Knowledge and Understanding:

• A1 Demonstrate a broad knowledge of core areas of economics
• A3 Show understanding of analytical methods, both theory- and model-based.
• A4 Demonstrate understanding of verbal, graphical, mathematical and econometric representation of economic ideas and analysis, including the relationship between them.
• A5 Show understanding of relevant mathematical and statistical techniques.
• A7BSc Demonstrate more in depth knowledge and skills of quantitative or theoretical modelling areas of economics and/or econometrics

Intellectual Skills:

• B1 apply complex ideas to solve problems
• B3 reason logically and work analytically
• B4 perform with high levels of accuracy

Professional / Practical Skills:

• C2 select and apply appropriate techniques to solve problems
• C3 justify conclusions using economic arguments with appropriate rigour

Transferable Skills:

• D1 apply mathematical, statistical and graphical techniques in an appropriate manner
• D2 communicate effectively and clearly in written and oral formats

Emphasised learning outcomes from the study of this module are A7BSc, B1, C2, D1.

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Module downloads

Lecture slides and other material for this module can be found on WEBCT at http://webct.nottingham.ac.uk/webct/entryPage.dowebct - restricted to registered students only.

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Lectures and tutorials

Economics lecture timetables are available online in the Portal.

There will be 18 1-hour lectures; supplemented by 3 1-hour tutorials. The tutorials will be devoted to problem solving. Students are to sign up to tutorial groups using Nexus.

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Module Assessment

One 2.5-hour examination (100%) at the end of the Semester.

Previous Examination Papers and Feedback for all modules can be viewed online in the Portal but are restricted to registered students only. A password may be required to access this material.

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Module Texts

• Osborne, M.J., Rubinstein, A., 1994. A Course in Game Theory. MIT Press.
• Osborne, M.J., 2004. An Introduction to Game Theory. Oxford University Press.
• Mas-Colell, A., Whinston, M.D., Green, J.R., 1995. Microeconomic Theory. Oxford University Press.
• Mailath, G.J., Samuelson, L., 2006. Repeated Games and Reputations. Long-Run Relationships. Oxford University Press.
• Fudenberg, D., Tirole, J., 1991. Game Theory. MIT Press.
• Ordeshook, P.C., 1986. Game Theory and Political Theory: An Introduction. Cambridge University Press.
• Ray, D., 2007. A Game-Theoretic Perspective on Coalition Formation. Oxford University Press.

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Further information

If you have any questions regarding this module please feel free to contact the lecturer. At the end of this semester, we would welcome your views on the organisation and content of this module.

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