1. SylabUZ
2. Faculty of Exact and Natural Sciences
3. winter term 2022/2023
4. WMIiE - oferta ERASMUS - Erasmus programme
5. Game Theory

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Game Theory - course description

Aim of the course

The purpose of the course is to get acquainted with basic theorems in game theory and present their meaning in modern economics.

Prerequisites

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Mathematical analysis, linear algebra, probability theory,

 

Scope

Lecture

I. Static noncooperative games:

1. Normal form game (1 hour)
2. Zero-sum game. Minimax von Neumann Theorem. (3 hours.)
3. n-person games and Nash equilibrium. Relationship between Nash equilibria and fixed point theory of continuous multifunctions. (6 hours.)
4. Noncooperative games in economics: Bertrand and Cournot models. (2 hours)
5. Nash bargaining. (3 hours.)

II. Extended form games (dynamic games):

1. Imperfect information games. Kuhn's existence Theorem. (2 hours).
2. Kuhn's Algorithm. (1 hour.)
3. Modeling of imperfect information games. (2 hours.)

III. Cooperative games:

1. Voting games and linearly productive games. (2 hours.)
2. The core of cooperative games. The non-emptiness of the core theorem. (2 hours.)
3. Shapley and Banzhaf values(axiomatic construction). (3 hours.)

IV. Elements of game theory with imperfect information:

1. Bayesian games. Auctions. (3 hours.)

Class

I. Non-cooperative static games:

1. Solving zero-sum games. (3 hours.)
2. n-person games and Nash equilibria. Examples. Prisoner dilemma. The best response mappings. (6 hours.)
3. Non-cooperative games in economics:  Bertrand and Cournot oligopoly. (2 hours.)
4. Nash bargaining model. Searching for the solutions. (3 hours.)

II. Extended form games (dynamic games):

1. Imperfect information. Application of Kuhn's algorithm for construction of Nash equilibria. (2 hours.)
2. Example of imperfect information games. (2 hours.)

III. Cooperative games:

1. Examples of voting and linearly-production games. (1 hour.)
2. The core of cooperative games, examples. (2 hours.)
3. Shapley and Banzhaf value (computing).  (3 hours.)

IV. Elements of game theory with imperfect information:

1. Bayesian games. Auctions. Examples of games (3 hours.)

V. Test and summary: (4 hours).

Teaching methods

Conventional lecture and discussion.

Class– solving mathematical problems, analysis of classical examples in game theory, and other applications.

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

Controlling the preparation degree of students and their activity during the class. 

Test with problems with differential degrees of difficulty. A positive result is a necessary condition for taking the exam.

The final mark encompasses the mark of the test (40%) and the mark of the exam (60%), provided both are positive.

Recommended reading

1. Fudenberg, D. Game theory. MIT Press, Boston, 1991.
2. Owen, G. Teoria gier. PWN, Warszawa, 1975.
3. Osborne, M.J. A course in game theory. MIT Press, Boston, 1994.
4. Płatkowski, T.  Wstęp do teorii gier. Uniwersytet Warszawski, Warszawa 2011.
5. Straffin, P.D. Teoria gier. Scholar, Warszawa, 2004.

Further reading

1. Myerson, R.B.  Game theory: an analysis of conflict. Harvard University Press, 1997.
2. Owen, G. Game theory. EG Publishing, New York, 1995.

Notes

Modified by dr Dorota Głazowska (last modification: 10-05-2022 18:13)