Quotation Feinstein, Zachary, Rudloff, Birgit, Zhang, Jianfeng. 2021. Dynamic Set Values for Nonzero Sum Games with Multiple Equilibriums. Mathematics of Operations Research.


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Abstract

Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and unlike the zero sum case, they may have different values at different equilibriums. Instead of focusing on the existence of individual equilibriums, we study the set of values over all equilibriums, which we call the set value of the game. The set value is unique by nature and always exists (with possible value ∅). Similar to the standard value function in control literature, it enjoys many nice properties such as regularity, stability, and more importantly the dynamic programming principle. There are two main features in order to obtain the dynamic programming principle: (i) we must use closed-loop controls (instead of open-loop controls); (ii) we must allow for path dependent controls, even if the problem is in a state dependent (Markovian) setting. We shall consider both discrete and continuous time models with finite time horizon. For the latter we will also provide a duality approach through certain standard PDE (or path dependent PDE), which is quite efficient for numerically computing the set value of the game.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Mathematics of Operations Research
Citation Index SCI
WU Journalrating 2009 A
WU-Journal-Rating new FIN-A, INF-A, STRAT-A, VW-D, WH-A
Language English
Title Dynamic Set Values for Nonzero Sum Games with Multiple Equilibriums
Year 2021
Reviewed? Y
DOI https://doi.org/10.1287/moor.2021.1143
Open Access N

Associations

People
Rudloff, Birgit (Details)
External
Feinstein, Zachary (Stevens Institute of Technology, United States/USA)
Zhang, Jianfeng (University of Southern California, United States/USA)
Organization
Institute for Statistics and Mathematics IN (Details)
Research areas (ÖSTAT Classification 'Statistik Austria')
1118 Probability theory (Details)
1137 Financial mathematics (Details)
5361 Financial management (Details)
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