This information is indicative and can be subject to change.
Cooperative games
Teacher: Michel GRABISCH
E-mail: [email protected]
ECTS: 2.5
Evaluation: written exam
Previsional Place and time:
Prerequisites: no prerequisite in game theory. Linear Programming is useful.
Aim of the course:
The course gives a complete description of cooperative game theory, which comes as a complement of the 1st semester course on game theory, which focuses on the noncooperative aspect. Cooperative game theory models situations where players have interest to cooperate in order to maximize the overall utility, either by increasing the total benefit of the society of players (e.g., a cartel of firms), or by diminishing the total cost of using a service (e.g., power plant, water distribution, etc.). The main question addressed is: supposing that the cooperation of all players increases the total benefit, how to share the surplus among the players in an equitable and rational way? The answer to this question (the solution of the game) reveals to be much more complex than it appears, and many concepts of solutions have been proposed: the core, the Shapley value, the nucleolus, etc.
Syllabus:
The course is divided as follows:
- Introduction, motivations, examples of application, TU-games and NTU-games, properties, simple games
- The concepts of imputation, core, balanced games, domination core, stable sets
- Convex games, vertices of the core, the Weber set
- The Shapley value, axiomatizations, the potential
- The nucleolus; properties, the Kohlberg criterion, implementation
- cooperative bargaining theory (Nash, Kalai-Smorodinsky)
- bankruptcy games
- various applications
- NTU-games
References:
G. Owen. Game theory. Academic Press, 1995.
B. Peleg and P. Sudholter. Introduction to the theory of cooperative games. Kluwer Academic Publisher, 2003
H. Peters. Game theory, a multileveled approach. Springer, 2008.
M. Maschler, E. Solan and S. Zamir. Game Theory (2nd Ed.). Cambridge University Press, 2013.
Cooperative games
Teacher: Michel GRABISCH
E-mail: [email protected]
ECTS: 2.5
Evaluation: written exam
Previsional Place and time:
Prerequisites: no prerequisite in game theory. Linear Programming is useful.
Aim of the course:
The course gives a complete description of cooperative game theory, which comes as a complement of the 1st semester course on game theory, which focuses on the noncooperative aspect. Cooperative game theory models situations where players have interest to cooperate in order to maximize the overall utility, either by increasing the total benefit of the society of players (e.g., a cartel of firms), or by diminishing the total cost of using a service (e.g., power plant, water distribution, etc.). The main question addressed is: supposing that the cooperation of all players increases the total benefit, how to share the surplus among the players in an equitable and rational way? The answer to this question (the solution of the game) reveals to be much more complex than it appears, and many concepts of solutions have been proposed: the core, the Shapley value, the nucleolus, etc.
Syllabus:
The course is divided as follows:
- Introduction, motivations, examples of application, TU-games and NTU-games, properties, simple games
- The concepts of imputation, core, balanced games, domination core, stable sets
- Convex games, vertices of the core, the Weber set
- The Shapley value, axiomatizations, the potential
- The nucleolus; properties, the Kohlberg criterion, implementation
- cooperative bargaining theory (Nash, Kalai-Smorodinsky)
- bankruptcy games
- various applications
- NTU-games
References:
G. Owen. Game theory. Academic Press, 1995.
B. Peleg and P. Sudholter. Introduction to the theory of cooperative games. Kluwer Academic Publisher, 2003
H. Peters. Game theory, a multileveled approach. Springer, 2008.
M. Maschler, E. Solan and S. Zamir. Game Theory (2nd Ed.). Cambridge University Press, 2013.
