Abstract

Perhaps the most challenging aspect of research on multi-agent dynamical systems, formulated as non-cooperative stochastic differential/dynamic games (SDGs) with asymmetric dynamic information structures is the presence of strategic interactions among agents, with each one developing beliefs on others in the absence of shared information. This belief generation process involves what is known as second-guessing phenomenon, which generally entails infinite recursions, thus compounding the difficulty of obtaining (and arriving at) an equilibrium. This difficulty is somewhat alleviated when there is a high population of agents (players), in which case strategic interactions at the level of each agent become much less pronounced. This leads, under some structural constraints, to what is known as mean field games (MFGs), which have been the subject of intense research activity during the last ten years or so.

MFGs constitute a class of non-cooperative stochastic differential games where there is a large number of players or agents who interact with each other through a mean field coupling term—also known as the mass behavior or the macroscopic behavior in statistical physics—included in the individual cost functions and/or each agent’s dynamics generated by a controlled stochastic differential equation, capturing the average behavior of all agents. One of the main research issues in MFGs with no hierarchy in decision making is to study the existence, uniqueness and characterization of Nash equilibria with an infinite population of players under specified information structures and further to study finite-population approximations, that is to explore to what extent an infinite-population Nash equilibrium provides an approximate Nash equilibrium for the finite-population game, and what the relationship is between the level of approximation and the size of the population.

Following a general overview of the difficulties brought about by strategic interactions in finite-population SDGs, the talk will dwell on two classes of MFGs: those characterized by risk sensitive (that is, exponentiated) objective functions (known as risk-sensitive MFGs) and those that have risk-neutral (RN) objective functions but with an additional adversarial driving term in the dynamics (known as robust MFGs). In stochastic optimal control, it is known that risk-sensitive (RS) cost functions lead to a behavior akin to robustness, leading to establishment of a connection between RS control problems and RN minimax ones. The talk will explore to what extent a similar connection holds between RS MFGs and robust MFGs, particularly in the context of linear-quadratic problems, which will allow for closed-form solutions and explicit comparisons between the two in both infinite- and finite-population regimes and with respect to the approximation of Nash equilibria in going from the former to the latter. The talk will conclude with a brief discussion of several extensions of the framework, such as to hierarchical decision structures with a small number of players at the top of the hierarchy (leaders) and an infinite population of agents at the bottom (followers) as well as to games where players make noisy observations.

Biography

Tamer Başar has been with the University of Illinois at Urbana-Champaign since 1981, where he holds the academic positions of Swanlund Endowed Chair; Center for Advanced Study (CAS) Professor of Electrical and Computer Engineering; Professor, Coordinated Science Laboratory; Professor, Information Trust Institute; and Affiliate Professor, Mechanical Science and Engineering. He is also the Director of the Center for Advanced Study. At Illinois, he has also served as Interim Dean of Engineering and Interim Director of the Beckman Institute for Advanced Science and Technology. He is a member of the US National Academy of Engineering; Fellow of IEEE, IFAC, and SIAM; a past president of the IEEE Control Systems Society (CSS), the founding president of the International Society of Dynamic Games (ISDG), and a past president of the American Automatic Control Council (AACC). He has received several awards and recognitions over the years, including the highest awards of IEEE CSS, IFAC, AACC, and ISDG, the IEEE Control Systems Technical Field Award, and a number of international honorary doctorates and professorships, most recently an honorary doctorate from KTH, Sweden. He has over 900 publications in systems, control, communications, optimization, networks, and dynamic games, including books on non-cooperative dynamic game theory, robust control, network security, wireless and communication networks, and stochastic networks. He was Editor-in-Chief of the IFAC Journal Automatica between 2004 and 2014, and is currently editor of several book series. His current research interests include stochastic teams, games, and networks; multi-agent systems and learning; data-driven distributed optimization; epidemics modeling and control over networks; security and trust; energy systems; and cyber-physical systems.