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Regular version of the site
Bachelor 2020/2021

## Methods of Decision-Making

Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
When: 3 year, 1, 2 module
Mode of studies: distance learning
Language: English
ECTS credits: 5

### Course Syllabus

#### Abstract

The course includes main notions and stages of decision making, relevant mathematical models and methods, namely, linear and nonlinear programming, multi-objective and dynamical optimization methods, game considerations and their use in applied problems. Дистанционное обучение производится на платформах MS Teams, Webinar и Zoom. Ссылка на конкретные занятия заранее высылается преподавателем по почте. #### Learning Objectives

• To familiarize students with basic concepts, models and methods of decision making. #### Expected Learning Outcomes

• Know principles of mathematical models construction in decision analysis
• Be able to choose rational options in practical decision-making problems
• Have skills in analysis of game-theoretic models #### Course Contents

• Introduction
Participants and stages of decision making (DM). Mathematical models and methods in DM
• Linear optimization models and Linear Programming (LP)
Examples. Geometry and Algebra of LP problems. Simplex method. Duality in LP. Integer LP.
• Nonlinear optimization models and Nonlinear Programming (NLP)
Classical optimization. Nonlinear programming. Khun-Tucker conditions in convex programming problem. Idea of numerical methods.
• Multicriterial Decision Making (MCDM)
Vectorial criteria, decision and criterial spaces, multicriterial preferences. Pareto optimality. Linear convolution method, the method of main criterion, goal programming and other methods to choose specific efficient decision. DM in condition of uncertainty
• Methods of dynamic system optimization (with discrete time)
State and control variables. Bellman function and Bellman principle, method of dynamical programming.
• Models of network planning
• Matrix games
Equilibrium solutions and their properties. Game as a model of conflict situations. Examples. Classification of games. Minimax and maximin strategies. Saddlle point. Nonzero sum games. Equilibrium points, their properties vs saddle points.
• Methods to calculate equilibrium solutions in conflict situation with finite strategy sets of participants
Methods to solve ((2x2), (2xn) and (mx2) matrix games. Solution of arbitrary (mxn) matrix game by reducing to a corresponding LP problem. Method of the best response to solve nonantagonistic two-player games. #### Assessment Elements

• homework
• test 1
• test 2
• final exam #### Interim Assessment

• Interim assessment (2 module)
0.5 * final exam + 0.1 * homework + 0.2 * test 1 + 0.2 * test 2 #### Recommended Core Bibliography

• Aleskerov F., Bouyssou D., Monjardet B. ‘Utility Maximization, Choice and Preference’, Springer Verlag, Berlin, 2007