| Area of Mathematics: | Statistics-Probability-Operational Research (ESPOR) | ||
| Semester: | 7ο | ||
| Course ID: | 72302 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | |||
| Instructors: | |||
Description
- Games in extensive form (game tree, information sets, the notion of strategy and equilibrium point, Zermelo-Kuhn Theorem, dynamic programming solution for subgames perfect equilibrium).
- Normal form games (mixed extension, derivation of normal form from extensive form, equilibrium in mixed strategies, Nash Theorem).
- Matrix games (security levels of players, existence of common security level, Minimax Theorem, Linear Programming solution, simplification of strategies, symmetric matrix games, games against nature).
- Bimatrix games (best response, graphical solution of Nash equilibria for 2×2 games).
- Games with cooperation (characteristic function game, examples, transformation into normal form, 0-1 normalization, equivalence classes, alliances, set of feasible allocations and the core, graphical solution of core for games of 2 and 3 players, the core in special classes of games (e.g. voting systems), Shapley value (existence and uniqueness theorem), finding Shapley value for political and economical games via the characteristic function).
Bibliography
- Gibbons R., Game Theory for Applied Economists, Princeton Press, 1992
- Rasmusen E., Games and Information: An Introduction to Game Theory, 3rd ed., Blackwell, Oxford, 2001
