2 semester

1.      

Title of the course

Game theory and operations research

2.      

Year and speciality

1, 1-31 81 06  Web-programming and the Internet technologies (MA course)

3.      

Semester

2

4.      

Number of credits

3

5.      

Lecturer

Bakhtin Victor Ivanovich

6.      

Objectives of the course

Acquaintance with basic ways for mathematical formalization of conflicts in economics and social sphere and principles for their settlement.

Teaching various efficient methods for the settlement of conflict situations subject to interests of the conflict parties.

Upgrade of the mathematical knowledge common level and enhancement the skills of usage of mathematical methods for solution of applied problems.

As a result of the course study a student have to know:

  • the definitions of games in extensive and strategic forms and their interaction;
  • games with complete and incomplete information, games with perfect recall;
  • dominant and undominated strategies;
  • cautious strategies;
  • Pareto optima;
  • matrix and bimatrix games;
  • mixed and behavioral strategies, their equivalence;
  • saddle points and Nash equilibria;
  • perfect and sequential equilibria;
  • properties of the equilibria in repeated games;

be able:

  • to formalize a game in the strategic and (or) extensive form;
  • to find the equilibria by means of sequential exclusion of dominated strategies;
  • to find the equilibria in games with complete information by means of the Zermelo–Kuhn algorithm;
  • to find the equilibria in mixed strategies for matrix and bimatrix games by means of the graph-analytic metod;
  • to find the perfect and sequential equilibria;
  • possess:
  • basic concepts of player’s rational behavior under conditions of common knowledge and incomplete information.

7.      

Prerequisites

Linear algebra.

Essentials of the probability theory.

Essentials of the calculus.

8.      

Contents of the course

Games in extensive and strategic forms. Information states. Games with perfect recall and with complete information. The Zermelo–Kuhn algorithm. Dominated and undominated strategies. Sequential exclusion of the dominated strategies. The ordering relation on the range of outcomes and the Pareto optima. Mixed and behavioral strategies, their equivalence. The canonical decision rules. Nash equilibia, their existence. Relations between the equilibria in pure and mixed strategies. Methods for finding Nash equilibria. Zero-sum games. The Von Neumann minmax theorem. Saddle points. Infinite games. Shortcomings of Nash equilibria. Perfect and sequential equilibria, their existence. Equilibria in repeated games.

9.      

Recommended literature

Basic

  1. Bakhtin, V.I.; Kovalenok, A.P.; Lebedev, A.V.; Lysyenko, Yu.V. Issledovanie operacii. – Minsk, BGU, 2003.
  2. Myerson, R. Game theory: analysis of conflict. 1997.

Supplementary

  1. Mulen, R. Teoriya igr i ekonomicheskie prilozhenia. 1979.
  2. Ouen, G. Teoria igr. 1971.
  3. Petrosyan, L.A.; Zenkyevich, N.A.; Semina, E.A. Teoriya igr. 1998.

10.   

Teaching methods

Lectures, exercises, supervised independent work

11.   

Language

Russian

12.   

Conditions (requirements),

running control

Tests

13.   

Form of assessment

Test