Incentive Design and Learning in Large Populations: A System-Theoretic Approach With Applications To Epidemic Mitigation

Abstract

We present a systematic approach to designing incentive mechanisms that guide large populations of strategic agents—human or synthetic—toward desirable outcomes. Our framework builds on population games and models agent behavior through simple learning rules. These adaptive responses evolve over time and are approximated using a deterministic evolutionary model. A key feature of our approach is the feedback loop between the incentive mechanism and the evolving population dynamics. This nonlinear system exhibits rich behavior and can often be analyzed with tools from control theory. Unlike prior work, our framework also accommodates an external subsystem influenced by the population’s strategic behavior—for instance, modeling the spread of an epidemic affected by individual choices. Our methodology, grounded in system-theoretic passivity, decouples the design process into two steps: first, selecting an optimal equilibrium under cost constraints; second, designing a controller to globally stabilize it. This approach offers strong robustness: agents need not understand the incentive mechanism, and the design does not rely on precise knowledge of their learning rules.

Biography

Nuno C. Martins graduated with a M.S. degree in Electrical Engineering from I.S.T., Portugal, in 1997, and a Ph.D. degree in Electrical Engineering and Computer Science with a minor in Mathematics from Massachusetts Institute of Technology (MIT), Cambridge, in 2004. He has also concluded a Financial Technology Option program at Sloan School of Management (MIT) in 2004. He is Professor of Electrical Engineering in the Electrical and Computer Engineering Department of the University of Maryland at College Park, where he also holds a joint appointment with the Institute for Systems Research. He was Director of the Maryland Robotics Center from 2012 until 2014. Prof. Martins received the 2006 American Automatic Control Council O. Hugo Schuck Award, a National Science Foundation CAREER Award in 2007, the 2008 IEEE CSS Axelby Award for the best paper in the IEEE Transactions on Automatic Control, the 2010 Outstanding ISR Faculty Award, the 2010 George Corcoran Award from the ECE Department/UMD and he was an UMD/ADVANCE Leadership Fellow in 2013. He is currently Associate Editor for the IEEE Transactions on Control of Network Systems. He served as Associate Editor for Systems and Control Letters (Elsevier), Automatica and the IEEE Control Systems Society Conference Editorial Board. He was also a program Vice-Chair for the IEEE Conference on Decision and Control in 2013 and 2014. His research interests are in learning in large populations, evolutionary dynamics, population games, distributed control, team decision, optimization and networked control.