Optimization and game theory 1000-715OTG
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
polynomial);
– Elements of theory of Riemmann integral of functions od many variables;
– 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
Learning outcomes
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)
Assessment criteria
final exam
Additional information
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