Optimization and game theory 1000-715bOTG
The lecture consists of
– Elements of differential calculus for functions of many variables important for optimization: extended Sylvester theorem, convexity and concavity;
– Elements of multidimensional optimization both with and without constraints (including necessary Karush–Kuhn–Tucker conditions for various form of constraints and sufficient conditions), discrete time dynamic optimization and Bellman equation;
– 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, including subgame-perfect Nash equilibrium, minmaks and optimal/minimax,l strategies, pure and mixed strategies, evolutionary stable strategies, replicator dynamics.
Type of course
Prerequisites (description)
Course coordinators
Learning outcomes
Students know and understand methods of optimization, including nonlinear optimization and tools of noncooperative game theory within the scope of the lecture.
They can calculate 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
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:
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