Methods of Decision-Making
- To familiarize students with basic concepts, models and methods of decision making.
- 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
- IntroductionParticipants 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 gamesEquilibrium 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 participantsMethods 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.
- Interim assessment (2 module)0.5 * final exam + 0.1 * homework + 0.2 * test 1 + 0.2 * test 2
- Aleskerov F., Bouyssou D., Monjardet B. ‘Utility Maximization, Choice and Preference’, Springer Verlag, Berlin, 2007
- Osborne, M. J. (2009). An introduction to game theory / Martin J. Osborne. New York [u.a.]: Oxford Univ. Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edswao&AN=edswao.324093616