Topics in optimization include duality theorems in LP, branch and bound and cutting plane algorithms in IP, and Kuhn-Tucker conditions for NLP.
Topics in game theory and economics include computation of Nash equilibrium and refinements, selfish routing in networks and the price of anarchy, and non-emptiness of the core.
Doelstellingen van dit vak
This course provides a comprehensive overview of optimization techniques such as linear and integer programming, and non-linear programming, with applications in game theory and economics. Students learn optimization techniques from mathematics and operations research, and how to apply them in models from game theory and economic theory.
Only Master students can take this course. Exchange students need to have obtained a BSc degree in Economics, International Business, Econometrics, or a related topic. Familiarity with the basic concepts of optimization and linear programming will be helpful. A solid basis in mathematics and calculus is also recommendable.
The course will be based on chapters from standard textbooks plus additional readers.
Recommended literature for background reading :
- Hans Peters : Game Theory : A Multi-Leveled Approach. Springer-Verlag.
- David Luenberger and Yinyu Ye : Linear and Nonlinear Programming.
- Stephen Boyd and Lieven Vandenberghe : Convex optimization. Cambridge University Press.
- Christos H. Papadimitriou and Kenneth Steiglitz : Combinatorial Optimization: Algorithms and Complexity.
- Laurence A. Wolsey and George L. Nemhauser : Integer and Combinatorial Optimization, John Wiley & Sons.
- Sebastian Bubeck (2015) : Algorithms and complexity. Foundations and trends in machine learning 8 (231-358).
- Roger Myerson : Game Theory : Analysis of Conflict. Harvard University Press.