Department Colloquium - Jianfeng Zhang

Jianfeng Zhang, Department of Mathematics, University of Southern California

Set Values for Nonzero Sum Games With Multiple Equilibriums

Nonzero sum games typically have multiple Nash equilibriums (or no equilibriums), and unlike zero sum games, they may have different values at different equilibriums. While most works in the literature focus on the existence of individual equilibriums, we propose instead to study the value set over all possible equilibriums. It turns out that this value set has many nice properties such as regularity, stability, and more importantly the dynamic programming principle. There are two main features in order to obtain the DPP: (i) we must use closed-loop controls (instead of open-loop controls), and (ii) we must allow for path dependent controls and hence path dependent values, even if the problem is in a state dependent setting. We next impose an additional aggregated utility so as to choose an "optimal" equilibrium among the set we have analyzed, with social welfare as a possible application. This problem is typically time inconsistent when viewed dynamically. We shall propose a so called moving scalarization, a dynamic aggregated utility, to recover the time consistency. The talk is based on an ongoing work joint with Feinstein and Rudloff.
 

Friday, April 12 at 3:00pm to 4:00pm


Engineering Center, ECCR 265
1111 Engineering Drive, Boulder, CO 80309

Event Type

Colloquium/Seminar

Interests

Science & Technology, Research & Innovation

Audience

General Public

College, School & Unit

Engineering & Applied Science

Group
Applied Mathematics
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