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Game Theory

Recommended for the 3-4th year of Specialist’s program and Bachelor’s program.
Course Info

Game theory is the mathematical discipline aimed to model various interactions of living organisms in quantitative terms. Game theory, as the universal method for the analysis of social interactions, has wide applications in economics, in the theory of control and management, financial mathematics, evolutionary biology, sociology, psychology and politics, in modelling different social processes, in particular, the processes of democratic elections, processes of fair distributions of resource, processes of arms control, etc. The course is designed for all wishing to get acquainted with main ideas and methods of game theory.

Game theory is a mathematical discipline. Therefore, for the fully-fledged understanding one has to have at least basic knowledge of mathematical analysis, linear algebra, differential equations and probability theory. However, many ideas of game theory can be explained without the use of serious mathematics. In order to be more accessible to a wider auditorium, the first part of the course is designed specifically to the explanation of the basic ideas without any advanced mathematics. Here we also spend some time on historical aspects related to lives of the founders of the theory. The requirements to the mathematical education of the auditorium increase to the second part of the course.

The course is capacious and covers a wide circle of problems and notions. They include the Nash equilibrium, auctions, Braess paradox, selfish routing, method of backward induction, models of voting and fair distributions, evolutionary games, evolutionary stable strategies, dynamic programming, Hamilton-Jacobi-Bellman equation, infinite time games and computer tournaments. Also covered are the pricing of financial instruments (options and credit derivatives), Black-Scholes theory and game options, games with a large number of players in statistical limit, mean field games, models of cooperation and coalition building. Examples include the games of the arms race, exploitation of common resources, social dilemmas (battle of the sexes, sex ratio game, sacrifice game, models of inspection and corruption, modelling antiterrorist measures, as well as biological and genetic information transmission.