Outline
The project aims to investigate how regularization in receding-horizon linear-quadratic games can guide strategies toward a chosen infinite-horizon Nash equilibrium, and validate the approach on a real-world-inspired case study.
Motivation
Many games in the real world, such as those arising in energy markets or multi-robot coordination [1], are naturally modeled over an infinite time horizon. However, solving such infinite-horizon games is often analytically and computationally intractable. A common workaround is to adopt a receding horizon approach: at each time step, a finite-horizon game is solved, and only the first control action is applied [2]. In linear-quadratic games, this truncation introduces a noteworthy side effect: while the infinite-horizon game may admit multiple Nash equilibria, the corresponding finite-horizon game typically yields a unique equilibrium [3]. Since different equilibria can have different properties (for example, in terms of social welfare or fairness) it may be desirable to steer the system toward a particular infinite-horizon equilibrium. In this project, we investigate how adding a regularization term to the finite-horizon cost function can help guide the solution of the receding horizon game toward a desired infinite-horizon Nash equilibrium. This approach preserves the tractability and flexibility of receding horizon control while enabling greater control over the long-term strategic behavior of the system.
Milestones
- M1 (Weeks 1-2): Conduct a literature review on linear-quadratic games and receding-horizon (model predictive) games;
- M2 (Weeks 3-9): Develop and analyze candidate regularization terms that can steer the solution of the finite-horizon game toward a selected infinite-horizon Nash equilibrium;
- M3 (Weeks 9-12): Implement the proposed approach in a simulation environment (e.g., control of autonomous vehicles);
- M4 (Weeks 12-14): Evaluate the results and finalize the report.
Requirements
We are looking for motivated students with a strong background in control theory. If you are interested, please send an email containing your BS and MS transcripts to [email protected] .
References
[1] Ren, Kai, et al. “Chance-constrained Linear Quadratic Gaussian Games for Multi-robot Interaction under Uncertainty.” arXiv preprint arXiv:2503.06776 (2025).
[2] Hall, Sophie, et al. “Receding horizon games with coupling constraints for demand-side management.” 2022 IEEE 61st Conference on Decision and Control (CDC). IEEE, 2022.
[3] Başar, Tamer, and Geert Jan Olsder. Dynamic noncooperative game theory. Society for Industrial and Applied Mathematics, 1998.