*Note from June 29, 2020*

Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.

5 credits

30.0 h + 22.5 h

Q2

Teacher(s)

Jungers Raphaël;

Language

English

Prerequisites

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

Main themes

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.

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.

Aims

| |

1 | - AA1.1, AA1.2, AA1.3
- AA3.1
- AA5.1, AA5.2, AA5.3, AA5.4, AA5.5
- Understand and explain the framework of Decision Theory, its intrinsic limitations and broad goals, and how it leads to Game Theory.
- Choose the particular tools in the game theorist's toolbox in order to properly model a 'real-life' situation.
- Study and solve a problem in game theory by the computation of equilibria.
- Criticize and analyze the results of these computations for practical implementations.
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. |

*The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.*

Content

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

Teaching methods

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

Evaluation methods

Written or oral exam. A continuous evaluation could take place.

Online resources

Please see the Moodle website.

Bibliography

**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.

Teaching materials

- Game Theory. Course notes by R.J. et al. available online

Faculty or entity

**MAP**