Advanced Game Theory / Advanced Game Theory

Studyboard of Market and Management Anthropology, Economics, Mathematics-Economics, and Environmenta, Odense
Teaching activity id: 8032001.
Teaching language: English.ECTS / weighting: 10 ECTS / 0.167 full-time equivalent.
Examination language: English.
Exam activity id: 8032002.Approved: 03-10-17.
Period: Spring 2018.
Grading: Internal grading.
Assessment: 7-point scale.
Offered in: Odense.

Subject director:
Peter Sudhölter, Department of Business and Economics.

Prerequisites:
The prerequisites for this course are understanding of basic concepts of mathematics, in particular of Calculus and Linear Algebra. Moreover, the students should have some knowledge about utility maximization and they should be familiar with the Nash equilibrium concept and some refinements like subgame perfect Nash equilibrium.

The necessary skills may be obtained in the bachelors' courses Mikroøkonomi (course no. 9115501) and Matematik (8811401 and 9105701) or literature equivalent to “Perloff: Microeconomics. Theory and applications with calculus. Pearson Addison Wesley, 2010, 2nd edition” and “Sydsaeter and Hammond: Essential mathematics for economic analysis. Pearson Education, 2008, 3rd edition”.

Purpose:
A good knowledge of game theory is necessary in order to analyze and model a wide array of economic phenomena, namely multi-personal decision problems, including auctions, bargaining problems, fair division, oligopolistic competition, social network formation, and voting systems.
The course is therefore designed to provide knowledge of the main models and results of the theory of non-cooperative games as well as the theory of cooperative games that are used in economics and in the social sciences in general. Game theoretic problems described in the literature will be discussed and suitable models will be formulated and solved.
Furthermore, it is the aim of the course to give the students the competence to decide which game theoretic model is appropriate for a multi-personal decision problem and to provide them with skills that are necessary to apply the theoretical models to economic phenomena by themselves.
In order to control the necessary methods and results better, students will be encouraged to solve explicit exercises that may be discussed in a subsequent lesson. An independent reading and investigations based on the textbooks or other sources will occasionally be required, and the students will be encouraged to present some of their solutions.

Content - Key areas:
Classes of Games:
  • Strategic games (with perfect information)
  • Bayesian games (strategic games with imperfect information)
  • Extensive games with perfect information
  • Extensive games with imperfect information
  • Cooperative transferable utility games
  • Cooperative non-transferable utility games
  • Bargaining games

Solutions:
  • Games with perfect information: Nash equilibrium (pure or mixed), iterated elimination of dominated actions, correlated equilibrium, existence theorems
  • Bayesian games: Bayesian equilibrium
  • Extensive games: Subgame perfect equilibrium, sequential equilibrium, perfect Bayesian equilibrium
  • Cooperative games: Core, Shapley (NTU) value
  • Bargaining games: Nash solution

Goals description (SOLO taxonomy):
To fulfill the purposes of the course the student must be able to:

Demonstrate knowledge about the course’s focus areas enabling the student to:
  • Describe fundamental concepts of the theory of non-cooperative game theory like strategies and Nash equilibrium
  • Reflect on von Neumann’s minimax theorem and the properties of Nash equilibria in the constant-sum case.
  • Explain and describe Bayesian games and Bayesian equilibria
  • Describe and compare various refinements of Nash equilibrium like subgame perfect equilibrium, perfect Bayesian equilibrium, and sequential equilibrium, for various kinds of games in extensive form
  • Describe, explain, and identify games in cooperative form
  • Explain and model cost sharing problems by means of suitable transferable utility (TU) games
  • Explain and describe various solution concepts for TU games
  • Explain the axiomatic approach on the Shapley value

Demonstrate skills, such that the student is able to:
  • Analyze and compare finite non-cooperative games of various types
  • Apply various non-cooperative game theoretical models to simple microeconomic problems
  • Compute distinct types of Nash equilibria of explicitly given non-cooperative games
  • Analyze and relate game theoretical problems
  • Compare and relate various solutions for TU  
  • Criticize and compare underlying assumptions regarding all topics

Demonstrate competence, such that the student is able to:
  • Independently apply models and theories related to non-cooperative game theory
  • Formulate and solve game theoretical models by suitable mathematical methods in a range of appropriate and important economic problems
  • Identify a need for further development of the models and theories related to both, the non-cooperative as well as cooperative Game Theory
  • Use the above knowledge and skills to participate in team work to obtain and expand the competence in collaboration and communication
  • Discuss and understand theoretical articles in the mentioned areas and their importance with respect to economics

Literature:
Examples
(1) Osborne, M. J, and A. Rubinstein (1994): A Course in Game Theory, MIT Press, Cambridge, Massachusetts.
(2) Some selected articles might be distributed within the course.

Time of classes:
Spring.

Scheduled classes:
3 (2+1) hours weekly in 15 weeks (or another suitable partition of 44 hours).        

Form of instruction:
The students' workload is expected to be distributed as follows:
Lectures - 44 hours
Preparation, lectures - 113 hours
Assignments - 113 hours
Total 270 hours.

Time of examination:
Ordinary examination will be held during lectures. Re-examination in August.

Registration for the course is automatically a registration for the ordinary examination in the course. Cancellation is not possible. If the student does not participate in the examination, the student will use an examination attempt.
The university may grant an exemption from the rules in case of exceptional circumstances.
The student is responsible for registering for 2nd and 3rd examination attempt.

Examination form at the re-exam may be changed.

Examination conditions:
None.

Form of examination for the certificate:
6 Assignments, individually written.
One grade is given.

Supplemental information for the form of examination:
Duration: Dates for submission will be published on Blackboard.
Location: Home assignment.
Internet Access: Necessary.
Hand Out: Course page in Blackboard.
Hand In: Via SDUassignment in the course page in Blackboard.
Extent: No limitations.
Exam Aids: All exam aids allowed.

With some regularity students will be asked to hand in or to present their homework on exercises announced one week before. Some of the exercises will be taken from the textbook.

Comments:
Joint lecture with Mathematical Microeconomics

Programmes:
cand.oecon. Microeconomics
Spring Semester, elective subject. Offered in: Odense