Optimization and game theory 1000-715bOTG
The lecture consists of
– Differential calculus for functions of many variables (differential, partial derivatives, gradient,
total differential, implicit function theorem, Sylverter theorem, convexity and concavity, Taylor
– Elements of multidimensional optimization both with and without constraints (including necessary Karush–Kuhn–Tucker conditions for various form of constraints and sufficient conditions);
– Elements of game theory (games in extensive and normal form, dominant and dominated strategies, reduction of the game for extensive and normal form, Nash equilibrium, minmaks and optimal strategies, pure and mixed strategies, evolutionary stable strategies, replicator dynamics).
Type of course
Students know and understand basic notions od multidimensional analysis, they know and understand methods of optimization, including nonlinear optimization and tools of noncooperative game theory within the scope of the lecture.
They can calculate derivatives of functions, Riemman integrals (K_W05), extrema of functions of many variables (with or without constraints) (K_U05), find Nash equilibria, dominant and dominated strategies, minimax and ESS (or to show that they do not exist)
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: