Game theory [ LINMA2345 ]

> https://icampus.uclouvain.be/claroline/course/index.php?cid=INMA2491

LFSAB1101, LFSAB1102.

Basic mathematics (bachelor level), applied math cursus is a plus.

Game theory is a rich and pluridisciplinary theory which aims at modeling and optimizing the way people take a decision in a concurrent environment (that is, if one's decision impacts each other's profit).  It is the legacy of some among the 20th century's greatest mathematicians, like Von Neumann, Nash,... It has ramifications in Sociology, Economy, Mathematics, Operations Research, etc.
The course will survey the main concepts of Game Theory, among which decision theory, Nash Equilibria, Games with communication, Repeated Games, Bargaining and Coalitional games, and applications diverse fields of engineering.

• AA1.1, AA1.2, AA1.3
• AA3.1
• AA5.1, AA5.2, AA5.3, AA5.4, AA5.5

At the end of the course, the student will be able to :

1. Understand and explain the framework of Decision Theory, its intrinsic limitations and broad goals, and how it leads to Game Theory.
2. Choose the particular tools in the game theorist's toolbox in order to properly model a 'real-life' situation.
3. Study and solve a problem in game theory by the computation of equilibria.
4. Criticize and analyze the results of these computations for practical implementations.

Transversal L.O.:

During the course, the student will learn how to detect, model, and analyze practical situations and, based on this mathematical model, propose a relevant solution.

Written exam.

The course will be given partly by the professor, and partly as a seminar with student presentations.  Regular exercise sessions will be delivered.

1. Decision Theory: axioms, fundamental theorems, bayesian models, significance.
2. Elementary Game theory:  strategic/extended form, Domination, Iterative deletion.
3. Nash equilibrium, Nash's theorem, 2 players zero-sum games.
4. Sequential equilibria, computation and significance.
5. Perfect, proper, robust equilibria.
6. Games with communication and correlated equilibria.
7. Repeated games.
8. Nash's bargaining theory.
9. Coalitional games: the core, Shapley's value,...
10. Applications to:  Finance, auctions, voting,'

Main:

• Myerson, Roger B. Game Theory: Analysis of Conflict, Harvard University, 1991.

Others:

• Osborne, Martin J. An introduction to game theory, Oxford University Press, 2004.
• Osborne, Martin J.; Rubinstein, Ariel.  A course in game theory, MIT Press, 1994.
• Nowak, Martin A. Evolutionary Dynamics: Exploring the Equations of Life.  Harvard University Press, 2006.