Game Theory for Controlling Autonomous Systems

Academic year: 2025-26
Course title: Game Theory for Controlling Autonomous Systems
Instructor: Paolo Scarabaggio (ti.ab1763508865ilop@1763508865oigga1763508865barac1763508865s.olo1763508865ap1763508865)
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.

Schedule

• 24/06/2026: 10.00-12:30
• 24/06/2026: 13.30-16:00
• 25/06/2026: 10.00-12:30
• 25/06/2026: 13.30-16:00

Enrollment

Please use the following link to enroll in the course. In case of problems with the link, please get in touch with the instructor directly by email at ti.ab1763508865ilop@1763508865oigga1763508865barac1763508865s.olo1763508865ap1763508865

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.

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 the 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.