# Module Overview

### Decision Theory and Games

This module introduces the student to decision making and games theory. It covers the areas of decision making under certainty and under risk. These concepts are then expanded to include competitive decision making and the strategy of game play. Case studies of all models will be presented, formulated and solved using appropriate software.

MATH 4814

##### ECTS Credits

5

*Curricular information is subject to change

How to make complex decisions under certainty: the Saaty scale and the analytic hierarchical process.

Decisions under strict uncertainty: Maximax, Maximin, Hurwicz, Savage and Laplace criteria. Axioms of decision under strict uncertainty.

Decisions under risk and expected return/utility.  Decision trees: Imperfect information and Bayes Theoem, the value of imperfect information. Sensitivity analysis, one-way and two-way analyses.  Threshold analysis. Concept of utility and utility theory. Lotteries, axioms of lotteries, reference gambles and assessing utilities using direct methods. Describing attitudes to risk – risk premium and risk aversion function.

Game theory and games: strategic form for two person games. Two person zero sum games: pure and mixed strategy solutions. The concept of domination. Solutions for 2x2, 2 x N, N x 2 and N x N games.
Formulation N x M games as a linear programming problem. Solution to N x M games using the simplex algorithm and interpretation of the results.

Some concepts concerning non-zero sum games and definition of Nash equilibria.

Lectures supported by problem-solving sessions and the use of software packages.

Module Content & Assessment
Assessment Breakdown %
Formal Examination100