Abstract: Game theory is a rich mathematical framework to model and analyze the interactions of multiple decision makers with possibly conflicting objectives. Finite games in strategic form (i.e., those with a finite number of players, each with finitely many possible actions, that simultaneously and independently choose their action) are particularly important and well-studied.
In this talk we discuss a novel flow representation for finite games in strategic form. Based on this representation, we develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. Besides its intrinsic interest, this decomposition facilitates the study of Nash and correlated equilibria as well as convergence properties of natural distributed game dynamics. We explain the background and basic ideas, and illustrate the implications of the decomposition for dynamic analysis, pricing schemes, efficiency loss, and network games.
Based on joint work with Ozan Candogan, Ishai Menache, and Asu Ozdaglar (MIT).
Biosketch: Pablo A. Parrilo is a Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology. He is currently an Associate Director of the Laboratory for Information and Decision Systems (LIDS), and is also affiliated with the Operations Research Center (ORC). Past appointments include Assistant Professor at the Automatic Control Laboratory of the Swiss Federal Institute of Technology (ETH Zurich), Visiting Associate Professor at the California Institute of Technology, as well as short-term research visits at the University of California at Santa Barbara (Physics), Lund Institute of Technology (Automatic Control), and University of California at Berkeley (Mathematics). He received an Electronics Engineering undergraduate degree from the University of Buenos Aires, and a PhD in Control and Dynamical Systems from the California Institute of Technology.
His research interests include optimization methods for engineering applications, control and identification of uncertain complex systems, robustness analysis and synthesis, and the development and application of computational tools based on convex optimization and algorithmic algebra to practically relevant engineering problems.
Pablo Parrilo has received several distinctions, including a Finmeccanica Career Development Chair, the Donald P. Eckman Award of the American Automatic Control Council, the SIAM Activity Group on Control and Systems Theory (SIAG/CST) Prize, the IEEE Antonio Ruberti Young Researcher Prize, and the Farkas Prize of the INFORMS Optimization Society. He is currently on the Editorial Board of the MOS/SIAM Book Series on Optimization.