Course NCG: Noncooperative Games

Course description:
This course consists of 2 parts both of which focus on noncooperative games in the following order: matrix and bimatrix games, repeated games, specific models of stochastic (Markov) games, evolutionary games and generalized Nash games. We explore solution concepts like 'value' and 'optimal strategies' for zero sum games and 'equilibrium' for non-zero sum games as well as methods to calculate these. In these noncooperative games the players are strategic decision makers, who cannot make binding agreements to achieve their goals. Instead, threats may be applied to establish stable outcomes. This course will also emphasize connections between certain 'smooth games' with Monotone Inclusions and Variational Inequalities. This approach allows us to describe the fundamental role game theory plays in modern convex optimization and machine learning.
Topics to be covered:

• Solving two-player games using mathematical programming
• Equilibrium analysis for repeated games
• Behavioral equilibria for limiting average, infinite horizon, stochastic (Markov) games
• Nash equilibrium and Variational Inequalities (VI):
  • Convex and Monotone Functions
  • Variational Inequalities and Nash equilibria
• Saddle Point Problems and their role in Machine learning
  • Online Convex Optimization (OCO)
  • No-Regret Dynamics
  • Minimax Duality via no-regret
• Generalized Nash equilibrium
  • Definition and formulation as Monotone Inclusion
  • Splitting Methods
  • Mathematical Programming Formulations

Literature

• Lecture Notes
• For background literature on Variational Inequalities and Monotone Operators we will follow the very recent book Large-Scale Convex Optimization via Monotone Operators, by Ernest K. Ryu and Wotao Yin. The book can be downloaded from https://large-scale-book.mathopt.com.

Prerequisites:
Basic knowledge (bachelor level) of analysis (multivariate calculus) and linear algebra, as well as a first course in linear and nonlinear programming. Basic knowledge of Functional Analysis and Topology is also recommended.

Examination:
Take home exams. These assignments have to be completed in groups of at most two students.

Address for both lecturers:
Dr. M. Staudigl, Prof.dr. F. Thuijsman
Department of Knowledge Engineering, Maastricht University
P.O. Box 616, 6200 MD Maastricht
Phone : 043 - 3883489
E-mail : m.staudigl@maastrichtuniversity.nl, f.thuijsman@maastrichtuniversity.nl