Optimization and game theory

General data

Course ID:	1000-715OTG
Erasmus code / ISCED:	(unknown) / (unknown)
Course title:	Optimization and game theory
Name in Polish:	Optymalizacja i teoria gier
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Type of course:	obligatory courses
Short description:	The lecture encompasses elements of differential and integral calculus of functions of many variables, optimization in multidimensional spaces and noncooperative game theory
Full description:	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).
Bibliography:	(in Polish) M. Malawski, A. Wieczorek, H. Sosnowska. Konkurencja i kooperacja. Teoria gier w ekonomii i naukach społecznych. Wydawnictwa Naukowe PWN, 2012; P.D. Straffin, Teoria gier, Scholar, 2004; J. Palczewski, Skrypt Optymalizacja II, http://mst.mimuw.edu.pl/lecture.php?lecture=op2; F. Leja. Rachunek różniczkowy i całkowy, PWN; D. A MC Quarrie, Matematyka dla przyrodników i inżynierów, Wydawnictwa Naukowe PWN 2005; M. Gewert, Z. Skoczylas, Analiza Matematyczna 2, Definicje, twierdzenia, wzory, Oficyna Wydawnicza GiS 2006; M. Gewert, Z. Skoczylas, Analiza Matematyczna 2, Przykłady i zadania, Oficyna Wydawnicza GiS 2006.
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 methods and assessment criteria:	final exam

This course is not currently offered.

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Copyright by University of Warsaw.