COURSE OUTLINE: MH4320

Course Title

Computational Economics

Course Code

MH4320

Offered Study Year 4, Semester 1
Course Coordinator Bei Xiaohui (Asst Prof) xhbei@ntu.edu.sg 6513 8655
Pre-requisites MH1200, MH2500
AU 4
Contact hours Lectures: 39, Tutorials: 12
Approved for delivery from AY 2019/20 semester 1
Last revised 21 Aug 2019, 17:28

Course Aims

This course aims to introduce you to the fundamental concepts of game theory and mechanism design. Game theory, besides being of fundamental mathematical interest, is a main tool to model economic and strategic situations and then study the behavior of rational agents in such situations. Mechanism design is the study of how to design games (such as auctions) so that agents have incentive to act in a desirable way, e.g. by telling the truth. This course will improve your ability to model and analyze economics situations in a mathematical way. We will study the way rational agents will play games, based on their assumptions about the rationality of other agents. We will learn about the concept of Nash equilibria, which are solutions to games that no rational agent has an incentive to deviate from, and learn how to compute these.

In the second part of the course we turn to the problem of social choice, namely choosing from a set of alternatives, given the preferences of a set of players. We will see that many desirable properties of social choice functions cannot be satisfied, and then turn to ways to deal with this issue. The first way is to introduce payments and money-valued preferences, which leads to auction theory and related topics. Here students will learn how to design auctions and other economic mechanisms so that players have no incentive to lie, and to learn how to compute expected revenues. Secondly, we will consider mechanisms that do not allow payments, and study the ways manipulations by the players can be limited in this case. In the second part of the course students will learn how to design economic mechanisms that have certain properties (if possible), and how to judge economic mechanisms, as well as to apply Bayesian reasoning to compute expected outcomes.

The course is aimed at 3rd and 4th year students interested in economics, mathematical modelling, and applied math in general.

Intended Learning Outcomes

Upon successfully completing this course, you should be able to:

  1. Model strategic situations as extensive-form and strategic-form games
  2. Compute equilibrium strategies for various forms of games
  3. Find Maxmin strategies for 0-sum games
  4. Analyze, which properties of social choice functions (such as elections) can be satisfied simultaneously
  5. Design incentive-compatible mechanism for welfare-maximizing social choice
  6. Evaluate different types of auction methods and their properties, and calculate revenues
  7. Compute stable matchings and other allocation problem solution, and understand the player’s abilities to manipulate the outcome of such mechanisms

Course Content

Extensive-form games

Strategic-form games and Domination

Nash Equilibria and Maxmin Strategies

Mixed Equilibria, Zero-sum Games

Computing Equilibria

Computing Equilibria and Nash’s Theorem

Social Choice Theory

Auctions

VCG-Mechanisms

Games of Incomplete Information

Bayesian Equilibria

Revenue Equivalence

Stable Matchings

Assessment

Component Course ILOs tested SPMS-MAS Graduate Attributes tested Weighting Team / Individual Assessment Rubrics
Continuous Assessment
Tutorials
Homework 1, 2, 3, 4, 5, 6, 7 1. a, b, c
2. a, c
3. b
5. a
15 team See Appendix for rubric
Presentation 1, 2, 3, 4, 5, 6, 7 1. a, c
2. a, c
3. a
4. a
5. a
15 individual See Appendix for rubric
Project 1, 2, 3, 4, 5, 6, 7 1. a, c
2. a, c
3. b
4. a
5. a
10 team See Appendix for rubric
Examination (2 hours)
Short Answer Questions 1, 2, 3, 4, 5, 6, 7 1. a, b
2. c
3. a
60 individual See Appendix for rubric
Total 100%

These are the relevant SPMS-MAS Graduate Attributes.

1. Competence

a. Independently process and interpret mathematical theories and methodologies, and apply them to solve problems

b. Formulate mathematical statements precisely using rigorous mathematical language

c. Discover patterns by abstraction from examples

2. Creativity

a. Critically assess the applicability of mathematical tools in the workplace

c. Develop new applications of existing techniques

3. Communication

a. Present mathematics ideas logically and coherently at the appropriate level for the intended audience

b. Work in teams on complicated projects that require applications of mathematics, and communicate the results verbally and in written form

4. Civic-mindedness

a. Develop and communicate mathematical ideas and concepts relevant in everyday life for the benefits of society

5. Character

a. Act in socially responsible and ethical ways in line with the societal expectations of a mathematics professional, particularly in relation to analysis of data, computer security, numerical computations and algorithms

Formative Feedback

You will receive formative feedback through written responses to your homework submissions and verbal feedback through in-class and tutorial discussion. You will receive verbal feedback on your final project presentation. You will receive summative group feedback on the final exam following the conclusion of the module.

Learning and Teaching Approach

Lectures
(39 hours)

Derivation and demonstration:
Helps you understand the motivation behind the mathematical notions and ideas presented in the course. Presents systematic ways to solve problems.

Modeling:
Develops your ability to model economic and strategic situations mathematically, and then reason about strategic issues.

Tutorials
(12 hours)

Modeling:
Develops your ability to model economic and strategic situations mathematically, and then reason about strategic issues.

Problem Solving:
Develops your ability to solve a variety of problems in game theory and mechanism design

Reading and References

M. Maschler, E. Solan, S. Zamir. Game Theory. Cambridge University Press, 2013.
ISBN: 978-1107005488

This book covers many, but not all topics in the course. Optional.

Course Policies and Student Responsibilities

Absence due to medical or other reasons

If you are sick and not able to attend a midterm or missed the deadlines for your assignments, you must:
1. Send an email to the instructor regarding the absence.
2. Submit the original Medical Certificate* to an administrator.
*The Medical Certificate mentioned above should be issued in Singapore by a medical
practitioner registered with the Singapore Medical Association.

In this case, the missed assessment component will not be counted towards the final grade. There will be no make-up midterm.

Homework Assignments

You are encouraged to collaborate on the assignments because peer-to-peer learning helps you understand the subject better and working in a team trains you to better communicate with others. There will be 3 homework assignments in this course which must be submitted for grading and feedback. These can be done by groups of any size between 1 and 4.

You have to submit group assignments, and hence, do take note of this collaboration
policy:

1) Every group has to write up and submit one solution
2) If a group has used other collaborators, these must be explicitly identified
3) If you obtained a solution through research (e.g., on the web), you must acknowledge the source, but write up the solution in your own words
4) It is a violation of the collaboration policy for you to permit anyone other than the lecturer and group members to see your written solutions. Ideas may be shared, but do not share your written solutions with other students outside your group
5) If you have any questions about the collaboration policy please talk to the lecturer.

Final Project

You will form into groups of size at most 4 to work on a final project. The idea is to allow you to take a more creative approach to the course material. There are no specific requirements in terms of the types of techniques that you use. For example, you can take a real-world scenario and try to model it using game theory. You can try to prove a theorem. You can try to solve a small game of imperfect information by computer. Or you can do a combination of the above. The project is deliberately open-ended, but it should have something to do with the course material.

The final product of your project should be a report, due by the end of week 12 and a class-presentation at the class/tutorial of the last two weeks. The report should explain clearly what you did (and why, i.e. what design decisions did you make along the way and why); it should also contain some evaluation of whether it worked well, and what could be done to improve it. The report should be at most 8 pages in single-column format.

Each group should also write a very brief (1-page) proposal in which you describe what you plan to do, what difficulties you will need to overcome to do it, and how you plan to evaluate what you did. This proposal is due by the end of week 7, i.e., before the recess week. If you are unsure about whether something is an appropriate project, please feel free to talk to the lecturer.

Grading Criteria: In the formula of calculating the project score, 20% will be evaluated based on the project’s overall merit, while 80% will be evaluated based on individual efforts.
All members of a group must contribute to the project. In the final report, each group needs to indicate explicitly the contribution of each member, e.g., “each member contributes equally in this project”, or “A, B, C contributed (part I, II, III) or (30%,20%,50%), respectively”.
At the presentation, all members should have a chance to speak. Individual efforts will also be examined at the Q&A session.

Academic Integrity

Good academic work depends on honesty and ethical behaviour. The quality of your work as a student relies on adhering to the principles of academic integrity and to the NTU Honour Code, a set of values shared by the whole university community. Truth, Trust and Justice are at the core of NTU’s shared values.

As a student, it is important that you recognize your responsibilities in understanding and applying the principles of academic integrity in all the work you do at NTU. Not knowing what is involved in maintaining academic integrity does not excuse academic dishonesty. You need to actively equip yourself with strategies to avoid all forms of academic dishonesty, including plagiarism, academic fraud, collusion and cheating. If you are uncertain of the definitions of any of these terms, you should go to the Academic Integrity website for more information. Consult your instructor(s) if you need any clarification about the requirements of academic integrity in the course.

Course Instructors

Instructor Office Location Phone Email
Bei Xiaohui (Asst Prof) MAS-05-46 6513 8655 xhbei@ntu.edu.sg

Planned Weekly Schedule

Week Topic Course ILO Readings/ Activities
1

Extensive-form games

1

Chapter 1,3

2

Strategic-form games and Domination

1

Chapter 4.1-4.6

3

Nash Equilibria and Maxmin Strategies

1, 2, 3

Chapter 4.8-4.10

4

Mixed Equilibria, Zero-sum Games

1, 2, 3

Chapter 4.12, 5.1

5

Computing Equilibria

2, 3

Chapter 5.2

6

Computing Equilibria and Nash’s Theorem

2, 3

Chapter 5.3

7

Social Choice Theory

4

Chapter 21

8

Auctions

5, 6

Chapter 12.1-12.4

9

VCG-Mechanisms

5, 6

Lecture Notes

10

Games of Incomplete Information

1, 6

Chapter 9.4

11

Bayesian Equilibria

1, 6

Chapter 12.4

12

Revenue Equivalence

6

Chapter 12.5

13

Stable Matchings

7

Chapter 22

Appendix 1: Assessment Rubrics

Rubric for Tutorials: Homework (15%)

There are 5 questions for each homework and 15 in total. They assess your ability to:

1) Model strategic situations as extensive-form and strategic-form games

2) Compute equilibrium strategies for various forms of games

3) Find Maxmin strategies for 0-sum games

4) Analyze, which properties of social choice functions (such as elections) can be satisfied simultaneously

5) Design incentive-compatible mechanism for welfare-maximizing social choice

6) Evaluate different types of auction methods and their properties, and calculate revenues

7) Compute stable matchings and other allocation problem solution, and understand the player’s abilities to manipulate the outcome of such mechanisms

Marks

Criteria

>= 90%

Solutions to the given questions satisfy the requirements and are within the set of possible correct answers in almost all instances.

75% to 89%

Solutions to the given questions satisfy the requirements and are within the set of possible correct answers in most instances. Some errors exist but they are not significant in most cases.

65% to 74%

Solutions to the given questions satisfy the requirements and are within the set of possible correct answers in most instances.

Some solutions are not quite correct or do not satisfy some of the requirements. Partial credits are awarded.

50% to 64%

Solutions to the given questions satisfy the requirements and are within the set of possible correct answers in many instances.

Some solutions are not quite correct or do not satisfy some of the requirements. Partial credits are awarded.

There appear to be major misconceptions for a few topics.

< 50%

Did not attempt most of the questions; OR

Solutions to the given problems and questions are incorrect and/or do not satisfy the requirements in most cases.

There appear to be major misconceptions for many topics.

Rubric for Tutorials: Presentation (15%)

The final project presentation will be given by all members of a team at class. They access your ability to:

1) Explain core economic terms, concepts, and theories.

2) Employ the “economics way of thinking”

3) Apply oral communication skills within the discipline.

Each student will be evaluated independently based on your performance in the presentation and Q&A session.

Marks

Criteria

>= 90%

Presentation: The presentation is creative, as well as informative and a lot of pictures, videos, sounds, etc are used. All economic components are accurate and appropriately applied.

Q&A: Answers to all questions are clear, accurate and complete with sufficient details to support the response.

75% to 89%

Presentation: The presentation is somewhat creative. It is mostly bullet points but does incorporate some visuals such as pictures, videos, etc. Almost all economic components are accurate and appropriately applied.

Q&A: Answers to questions are clear and relevant but insufficiently supported with details.

65% to 74%

Presentation: The presentation is mostly bullet points with very few other elements. Many economic components are accurate and appropriately applied.

Q&A: Answers are incomplete and key points are not clear. Short answers were given.

50% to 64%

Presentation: The presentation is not very creative, with only bullet points but no pictures, videos, etc. Some economic components are accurate according to the description provided, but there are some major inaccuracies or problems with the connections that are made.

Q&A: Answers are irrelevant. Questions are not understood.

< 50%

Presentation: Did not give the presentation; OR

The student lacks the competence to apply relevant scientific theories and methods. The objectives are neither clearly defined nor described. The planning and execution of the work are not acceptable. The presentation has significant deficiencies in terms of form, structure and language.

Q&A: No answer was given.

Rubric for Tutorials: Project (10%)

The final project report accesses your ability to:

1) Explain core economic terms, concepts, and theories.

2) Employ the “economics way of thinking”

3) Apply written communication skills within the discipline.

50% of the grade as group score will be evaluated based on the overall merit of the report.

50% of the grade as individual score will be evaluated based on individual efforts. In the final report, each group needs to indicate explicitly the contribution of each member, e.g., “each member contributes equally in this project”, or “A, B, C contributed (part I, II, III) or (30%,20%,50%), respectively”.

Marks

Criteria

>= 90%

The group understands and applies economic concepts and theories in a clear and effective manner. Mathematics are utilized to bear on the issue/topic at hand. The form, dissemination, structure and language of the report are at an extremely high level.

75% to 89%

The group is able to select and apply relevant scientific theories and methods at a very good level. Some mathematics is utilized to bear on the issue/topic at hand. The form, dissemination, structure and language of the report are at a very high level.

65% to 74%

The candidate is able to select and apply relevant scientific theories and methods at a good level. The form, dissemination, structure and language of the report are at a good level.

50% to 64%

The candidate is generally able to apply relevant scientific theories and methods. The form, dissemination, structure and language are at an acceptable level.

< 50%

Did not submit the report; OR

The group lacks the competence to apply relevant scientific theories and methods. The objectives are neither clearly defined nor described. The planning and execution of the work are not acceptable.

Rubric for Examination: Short Answer Questions (60%)

The examination will use point-based marking (not rubrics based).