Elementary Mathematics of Decision Making 1000-OG-EN-EMDM

The theory of decision making is an interdisciplinary subject involving mathematics, economics and beyond (e.g., political sciences or evolutionary biology). The aim of this course is to present the language and methods from elementary mathematics which are relevant for the precise formulation and solution of a variety of classical decision making problems. In these type of problems an important role is played by computer simulations and counterexamples.

List of concepts and subjects:
1. Decision variables and feasible region; objective function (cost, payoff, utility).
2. Single criterion vs multicriteria decision making.
3. Basic optimization with single variable function: quadratic function.
4. Advanced optimization with single variable function: the method of calculus.
5. Basic optimization with multivariate function: linear programming.
6. Elementary probability: expected value and variance.
7. Games of chance.
8. Markov chains.
9. Zero sum games: von Neumann’s minimax.
10. Non-zero sum strategic games: Nash equilibrium, Pareto optimum, Cournot duopoly.
11. Voting and preferences.

Total student workload

Contact hours with teacher: - participation in lectures - 30 hrs - participation in tutorial - 30 hrs Self-study hours: - preparation for lectures - 15 hrs - preparation for tutorial - 15 hrs - reading literature - 20 hrs - writing project - 10 hrs - preparation for test - 15 hrs - preparation for examination - 15 hrs Altogether: 150 hrs (6 ECTS)

Learning outcomes - knowledge

Student W1: student is familiar with the basic distinction between single criterion and multicriteria decision making W2: knows the definitions of the following concepts: extremum, optimum, equilibrium, expected value, variance, Markov matrix, stationary distribution, strategic game, voting preference W3: is familiar with basic examples illustrating the concepts in W2

Learning outcomes - skills

Student U1: can find extrema of a simple function U2: is able to assess fair value and risk in a simple game of chance via expected value and variance U3: can find stationary distribution in a Markov chain with a small number of states U4: can analyze the competitive and collaborative aspects of a strategic game via Nash equilibria and Pareto optima U5: is capable of providing its own basic examples illustrating computational techniques related to the concepts introduced during lectures

Learning outcomes - social competencies

Student K1: understands that some social problems are the consequences of the logic of rules K2: is aware of the limitations of mathematical modeling

Teaching methods

Demonstration teaching methods: - display Expository teaching methods: - informative (conventional) lecture Exploratory teaching methods: - practical - classic problem-solving - project work

Observation/demonstration teaching methods

- display

Expository teaching methods

- informative (conventional) lecture

Exploratory teaching methods

- project work
- classic problem-solving

Prerequisites

School mathematics

Course coordinators

Krzysztof Leśniak

Assessment criteria

Assessment methods
Lectures - written examination - W1, W2, W3, K1, K2
Tutorial - test, project - U1, U2, U3, U4, U5, K1, K2

Assessment criteria

Lectures:
fail- 0-24 pts (0-49%)
satisfactory- 25-29 pts (50-59%)
satisfactory plus- 30-34 pts (60-69%)
good- 35-39 pts (70-79%)
good plus- 40-44 pts (80-89%)
very good- 45-50 pts (90-100%)

Tutorial:
fail- 0-24 pts (0-49%)
satisfactory- 25-29 pts (50-59%)
satisfactory plus- 30-34 pts (60-69%)
good- 35-39 pts (70-79%)
good plus- 40-44 pts (80-89%)
very good- 45-50 pts (90-100%)

Practical placement

not applicable

Notes

Term 2023/24L:

None

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 1000-OG-EN-EMDM in USOSweb