LEMAS: Learning Enabled Multi-Agent Systems (EE 290-4)

University of California, Berkeley | Spring 2026

Lecturers: Prof. Shankar Sastry and Pan-Yang Su

GSI: Maria Gabriela Mendoza

Lecture time and location: TuTh 2:00-3:30 pm, Cory 521

Office Hours (OH):

Prof. Shankar Sastry (Wed 2-3, Fri 11-12), Cory 333C
Pan-Yang Su (Tue 4-5, Thu 11-12), Cory 337A
Maria Gabriela Mendoza (Mon 11-12, Tu 10-11), Cory 337A

LEMAS Seminar Information (Starting February 13)

About

AI/ML are transforming societal systems: Opportunities abound for the transformation of multi-agent social systems using new technologies and business models to address some of the most pressing problems in diverse sectors such as energy, transportation, health care, manufacturing, and financial systems. Indeed, as a consequence, the term “digital transformation of societal scale systems” has become a favorite boardroom buzzword.

Issues of economic models for transformation, privacy, cybersecurity, and fairness considerations accompany the issues of transforming societal systems. Indeed, the area of “mechanism and incentive design” for societal-scale systems is a key feature in transitioning the newest technologies and providing new services. Crucially, human beings interact with automation and change their behavior in response to incentives offered to them. Training, Learning, and Adaptation in Human-AI Teams (HAT) is one of the most pressing problems in Human-AI/ML systems today.

In this course, we will present a few vignettes: how to align societal objectives with Nash equilibria using suitable incentive design, and proofs of stability of decentralized decision making while learning preferences. The application of the techniques to multi-agent problems in real-time tolling, Advanced Air Traffic Management for Air Taxis and High Value Package Delivery, Multi-Car Racing and Pursuit Evasion Games, and other societal-scale systems will be presented. This is a graduate-level class. We will need to cover materials from an array of disciplines and analytical techniques, and a fair amount of self-study will be needed.

Schedule

Date	Topic
Tuesday: 01/20	Course Introduction
Thursday: 01/22	Game Theory Basics, Solution Concepts, and Existence of equilibrium Drew Fudenberg and Jean Tirole. Game Theory. MIT Press, 1991. Chapters 1-2. Nash Jr, John F. “Equilibrium points in n-person games.” Proceedings of the national academy of sciences 36.1 (1950): 48-49. Glicksberg, Irving L. “A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points.” Proceedings of the American Mathematical Society 3.1 (1952): 170-174.
Tuesday: 01/27	Computation of equilibrium: Zero-sum and concave games Martin J. Osborne and Ariel Rubinstein. A Course in Game Theory. MIT press, 1994. Chapter 2.5. Mangasarian, Olvi L., and H. Stone. “Two-person nonzero-sum games and quadratic programming.” Journal of Mathematical Analysis and Applications 9.3 (1964): 348-355. Rosen, J. Ben. “Existence and uniqueness of equilibrium points for concave n-person games.” Econometrica: Journal of the Econometric Society (1965): 520-534. Mertikopoulos, Panayotis, and Zhengyuan Zhou. “Learning in games with continuous action sets and unknown payoff functions.” Mathematical Programming 173.1 (2019): 465-507.
Thursday: 01/29	Computation of equilibrium continued: Potential and near-potential games Monderer, Dov, and Lloyd S. Shapley. “Potential games.” Games and economic behavior 14.1 (1996): 124-143. Candogan, Ozan, Asuman Ozdaglar, and Pablo A. Parrilo. “Near-potential games: Geometry and dynamics.” ACM Transactions on Economics and Computation (TEAC) 1.2 (2013): 1-32.
Tuesday: 02/03	A brief introduction to auction theory (and a game played in class) Krishna, Vijay. Auction theory. Academic press, 2009. Chapter 1.
Thursday: 02/05	Sequential games and Markov games Martin J. Osborne and Ariel Rubinstein. A Course in Game Theory. MIT press, 1994. Chapter 6. Drew Fudenberg and Jean Tirole. Game Theory. MIT Press, 1991.
Tuesday: 02/10	Markov games continued Maheshwari, Chinmay, et al. “Independent and decentralized learning in Markov potential games.” IEEE Transactions on Automatic Control (2025). Guo, Xin, et al. “Markov α-Potential Games.” IEEE Transactions on Automatic Control (2025).
Thursday: 02/12	Markov games continued Maheshwari, Chinmay, et al. “Independent and decentralized learning in Markov potential games.” IEEE Transactions on Automatic Control (2025). Guo, Xin, et al. “Markov α-Potential Games.” IEEE Transactions on Automatic Control (2025).
Tuesday: 02/17	Student Presentation 1: Computational Game Theory
Thursday: 02/19	Student Presentation 2: Computational Game Theory
Tuesday: 02/24	Mathematical Preliminaries on Dynamical Systems and Stochastic Approximation Shankar Sastry. Nonlinear Systems: Analysis, Stability and Control. Springer, 2013. Vivek Borkar. Stochastic Approximation: A Dynamical Systems Viewpoint. Cambridge University Press, 2008.
Thursday: 02/26	Guest Lecture 1: Online Learning for Equilibrium Pricing in Markets Under Incomplete Information Presenter: Devansh Jalota Links to Papers: Online Learning for Equilibrium Pricing in Markets under Incomplete Information Stochastic Online Fisher Markets: Static Pricing Limits and Adaptive Enhancements
Tuesday: 03/03	Student Presentation 3: Learning in Games
Thursday: 03/05	Student Presentation 4: Learning in Games
Tuesday: 03/10	Student Presentation 5: Learning in Games
Thursday: 03/12	Student Presentation 6: Learning in Games
Tuesday: 03/17	Lecture: RESCUE: Resilient Exploration and Search Coordination of UAVs in Unknown Environments Presenter: Gaby Mendoza
Thursday: 03/19	Guest Lecture 2: Behavioral Economics as a Foundation for Principled Multi-Agent Reinforcement Learning: Tractability, Robustness, and Other Free Lunches Presenter: Eric Mazumdar
03/23 – 03/27	Spring break
Tuesday: 03/31	Convergence of Learning Dynamics: Best-Response Dynamics, Fictitious Play, and Gradient-Based Dynamics Monderer, Dov, and Lloyd S. Shapley. “Potential games.” Games and economic behavior 14.1 (1996): 124-143. Harris, Christopher. “On the rate of convergence of continuous-time fictitious play.” Games and Economic Behavior 22.2 (1998): 238-259. Hofbauer, Josef, and Sylvain Sorin. “Best response dynamics for continuous zero-sum games.” Discrete and Continuous Dynamical Systems Series B 6.1 (2006): 215. Benaïm, Michel, Josef Hofbauer, and Sylvain Sorin. “Stochastic approximations and differential inclusions.” SIAM Journal on Control and Optimization 44.1 (2005): 328-348. Population Games and Evolutionary Dynamics William H. Sandholm. Population games and evolutionary dynamics. MIT press, 2010.
Thursday: 04/02	Decentralized Learning in Markov games Maheshwari, Chinmay, et al. “Independent and decentralized learning in Markov potential games.” IEEE Transactions on Automatic Control (2025). Maheshwari, Chinmay, Manxi Wu, and Shankar Sastry. “Convergence of Decentralized Actor-Critic Algorithm in General–Sum Markov Games.” IEEE Control Systems Letters 8 (2024): 2643-2648.
Tuesday: 04/07	Efficiency and Fairness in Routing Games: Price of Anarchy and Unfairness Measures Su, Pan-Yang, et al. “Average Unfairness in Routing Games.” The 25th International Conference on Autonomous Agents and Multi-Agent Systems. Tim Roughgarden. Twenty Lectures on Algorithmic Game Theory. Cambridge University Press, 2016. Roughgarden, Tim, and Éva Tardos. “How bad is selfish routing?” Journal of the ACM (JACM) 49.2 (2002): 236-259. Roughgarden, Tim. “How unfair is optimal routing?” Symposium on Discrete Algorithms: Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete Algorithms. Vol. 6. No. 08. 2002. Stackelberg Games and Adaptive Incentive Design C. Maheshwari, K. Kulkarni, M. Wu and S. Sastry, “Adaptive Incentive Design With Learning Agents,” in IEEE Transactions on Automatic Control, doi: 10.1109/TAC.2025.3643351.
Thursday: 04/09	Guest Lecture 3: Congestion Pricing for Efficiency and Equity Presenter: Manxi Wu Links to Papers: Maheshwari, Chinmay, et al. “Congestion pricing for efficiency and equity: Theory and applications to the san francisco bay area.” arXiv preprint arXiv:2401.16844 (2024).
Tuesday: 04/14	Student Presentation 7: Learning in Stackelberg Games
Thursday: 04/16	Student Presentation 8: Learning in Stackelberg Games
Tuesday: 04/21	Student Presentation 9: Learning in Stackelberg Games
Thursday: 04/23	Mechanism Design: VCG Auctions and Optimal Auctions Nisan, Noam, Tim Roughgarden, Eva Tardos, and Vijay V. Vazirani, eds. Algorithmic Game Theory. Cambridge University Press, 2007.
Tuesday: 04/28	Guest Lecture 4: TBD Presenter: Chinmay Maheshwari
Thursday: 04/30	Mechanism Design: Applications in Advanced Air Mobility and Energy Systems Chao, Hung-po, and Robert Wilson. “Priority service: Pricing, investment, and market organization.” The American Economic Review (1987): 899-916. Su, Pan-Yang, et al. “Incentive-compatible vertiport reservation in advanced air mobility: An auction-based approach.” 2024 IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2024. Su, Pan-Yang, et al. “Two-stage mechanism design for electric vehicle charging with day-ahead reservations.” 2025 IEEE 64th Conference on Decision and Control (CDC). IEEE, 2025.
Tuesday: 05/06	Final Presentations
Thursday: 05/08	Final Presentations