Linear-Quadratic-Singular Stochastic Differential Games and Applications

Jodi Dianetti
Additional contact information
Jodi Dianetti: Center for Mathematical Economics, Bielefeld University

No 678, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We consider a class of non-cooperative N -player non-zero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is quadratic in the state and linear in the control. We call these games linear-quadratic-singular stochastic differential games. Under natural assumptions, we show the existence of open-loop Nash equilibria, which are characterized through a linear system of forward-backward stochastic differential equations. The proof is based on an approximation via a sequence of games in which players are restricted to play Lipschitz continuous strategies. We then discuss an application of these results to a model of capacity expansion in oligopoly markets.

Keywords: Singular stochastic control; linear quadratic games; stochastic maximum principle; Nash equilibrium (search for similar items in EconPapers)
Pages: 22
Date: 2023-04-24
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://pub.uni-bielefeld.de/download/2978677/2978678 First Version, 2023 (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:bie:wpaper:678

Access Statistics for this paper

More papers in Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University Contact information at EDIRC.
Bibliographic data for series maintained by Bettina Weingarten ().