Game Theory for Controlling Autonomous Systems

Course title: Game Theory for Controlling Autonomous Systems
Instructor: Paolo Scarabaggio (ti.ab1732402233ilop@1732402233oigga1732402233barac1732402233s.olo1732402233ap1732402233)
Hours of instruction: 10 hours
ECTS: 1

Goal

This course is designed to provide PhD students with the necessary modeling and methodological tools for analyzing and designing algorithms to solve game equilibrium problems. It will include lectures, numerical examples, simulations, and case study analysis.

Schedule

• 17/06/2025 14:00-16:30
• 19/06/2025 14:00-16:30
• 24/06/2025 14:00-16:30
• 26/06/2025 14:00-16:30

The course will be held in online. Further information will be provided soon.

Enrollment

Please use the following link to enroll in the course. In case of problems with the link, please contact the instructor directly by email at ti.ab1732402233ilop@1732402233oigga1732402233barac1732402233s.olo1732402233ap1732402233

Syllabus

1. Introduction and motivation
2. Background
   • Convex Optimization: Convex sets and functions. Set-valued mappings. Normal cone and tangent cone operators. Projection and proximal operators. Lagrangian duality and KKT conditions.
   • Monotone Operator Theory: Fixed points, zeros, and contraction mappings. Averaged and nonexpansive mappings. Fixed point theorems and algorithms.
3. Nash equilibrium
   • Nash equilibrium problem and best response mapping.
   • Applications and models: Linear complementarity problems and variational inequalities.
   • Existence and uniqueness of equilibria.
   • Algorithms.
4. Generalized Nash equilibrium
   • Generalized Nash equilibrium problem.
   • Applications and models: Quasi-variational inequalities and mixed complementarity problems.
   • Existence and uniqueness of equilibria.
   • Algorithms.

Lecture notes

To be uploaded

Bibliography References:

• [1] Boyd, Stephen P., and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.
• [2] Bauschke, Heinz H., and Patrick L. Combettes. Convex analysis and monotone operator theory in Hilbert spaces. Vol. 408. Springer, 2011.
• [3] Facchinei, Francisco, and Jong-Shi Pang, eds. Finite-dimensional variational inequalities and complementarity problems. Springer , 2003.
• [4] Osborne, Martin J. An introduction to game theory. Vol. 3. No. 3. New York: Oxford university press, 2004.
• [5] Basar, Tamer, and Georges Zaccour, eds. Handbook of dynamic game theory. Berlin: Springer, 2018.
• Slides and supporting material from lecturer.

Examination method

• End-course examination based on a final written test or a project work, which involves applying the learned concepts and techniques to a real-world problem.
• Evaluation of class participation, including active engagement in lectures, discussions, and case study analysis.