Nonzero-Sum Stochastic Games and Mean-Field Games with Impulse Controls

Matteo Basei (), Haoyang Cao () and Xin Guo ()
Additional contact information
Matteo Basei: Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720-1777; EDF R&D, 75008 Paris, France
Haoyang Cao: Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720-1777; The Alan Turing Institute, British Library, NW1 2DB London, United Kingdom
Xin Guo: Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720-1777

Mathematics of Operations Research, 2022, vol. 47, issue 1, 341-366

Abstract: We consider a general class of nonzero-sum N -player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a veri?cation approach and provide su?cient conditions for the Nash equilibria (NEs) of the game. We then consider the limiting situation when N goes to in?nity, that is, a suitable mean-?eld game (MFG) with impulse controls. We show that under appropriate technical conditions, there exists a unique NE solution to the MFG, which is an ϵ-NE approximation to the N -player game, with ϵ = O 1 N . As an example, we analyze in detail a class of two-player stochastic games which extends the classical cash management problem to the game setting. In particular, we present numerical analysis for the cases of the single player, the two-player game, and the MFG, showing the impact of competition on the player’s optimal strategy, with sensitivity analysis of the model parameters.

Keywords: Primary: 91A15; secondary: 91A05; 91A06; 91A16; 49N25; stochastic games; impulse controls; quasi-variational inequalities; mean-field games; cash management (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2021.1131 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:1:p:341-366

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().