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## Master’s Programme 'Applied Economics and Mathematical Methods'

2018/2019
ENG
Instruction in English
6
ECTS credits
Course type:
Compulsory course
When:
1 year, 3, 4 module

### Course Syllabus

#### Abstract

The course “Microeconomics 2” begins with the simplest game-theoretic models with two participants and then develops to more complicated n-person, dynamic and cooperative games. Another part of the course is devoted to social choice theory mainly to voting problems. The problems of existence optimal solutions and their finding are studied with the help of the modern mathematical methods.

#### Learning Objectives

• To develop the competence of students in Microeconomics, with especial attention to decision-making models including game theory and social choice theory.
• How to aggregate individual interests into the unique social or group one

#### Expected Learning Outcomes

• The student should know based competitive economics models.
• The student should know optimality concepts on conflict situations and their characterizations.
• The student should know methods of finding optimal behavior in some classes of strategic games.
• The student should know cost/profit sharing methods.
• The student should know voting models.

#### Course Contents

• The subject and methods of game theory. Conflicts and cooperation, their mathematical models.
• Matrix games. Saddle points. Mixed strategies. Minimax Theorem.
• Non-cooperative n-person games. Optimality concepts in non-cooperative games, equilibrium. Game-theoretic models of oligopolies. Auctions.
• The mixed extension of non-cooperative games. Nash’s Theorem on existence of equilibria in mixed strategies in finite n-person games.
• Refiniments of equilibria. Perfect equilibria, strong equilibria, correlated equilibria.
• Games with incomplete information. Bayesian equilibria.
• Games in extensive form. Zermelo's Theorem on the existence of pure equlibria in finite extensive games with perfect information. Behavioral strategies Kuhn's Theorem.
• Dynamic games. Stochastic and recursive games. Repeated games with complete information.
• Cooperative games with transferable utilities. Characteristic functions. Solutions of cooperative games. The core and its existence. The Shapley value.
• Cost and profit sharing rules. Egalitarian and utilitarian rules.
• Bargaining problems. Axiomatic characterizations of bargaining solutions.
• Social welfare functions. Arrow’s Theorem and its extensions.
• Voting theory. Manipulation of preferences.
• Infinite two-person zero-sum games. Existence theorems

#### Assessment Elements

• Class participation
• Home assignments
• Final exam

#### Interim Assessment

• Interim assessment (4 module)
0.2 * Class participation + 0.6 * Final exam + 0.2 * Home assignments

#### Recommended Core Bibliography

• Barron, E. N. (2013). Game Theory : An Introduction (Vol. Second edition). Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=565752
• Binmore, K. G. (2007). Game Theory: A Very Short Introduction. New York: OUP Oxford. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=209659
• Webster, T. J. (2014). Analyzing Strategic Behavior in Business and Economics : A Game Theory Primer. Lanham, MD: Lexington Books. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=748851