Equilibrium in Functional Stochastic Games with Mean-Field Interaction

Eduardo Abi Jaber (), Eyal Neuman and Moritz Voss
Additional contact information
Eduardo Abi Jaber: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Eyal Neuman: Imperial College London
Moritz Voss: UCLA Vision Lab - UCLA - University of California [Los Angeles] - UC - University of California

Working Papers from HAL

Abstract: We consider a general class of nite-player stochastic games with mean-eld interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in L2. We propose a novel approach for deriving the Nash equilibrium of the game explicitly in terms of operator resolvents, by reducing the associated rst order conditions to a system of stochastic Fredholm equations of the second kind and deriving their closed form solution. Furthermore, by proving stability results for the system of stochastic Fredholm equations we derive the convergence of the equilibrium of the N-player game to the corresponding mean-eld equilibrium. As a by-product we also derive an ε-Nash equilibrium for the mean-eld game, which is valuable in this setting as we show that the conditions for existence of an equilibrium in the meaneld limit are less restrictive than in the nite-player game. Finally we apply our general framework to solve various examples, such as stochastic Volterra linear-quadratic games, models of systemic risk and advertising with delay, and optimal liquidation games with transient price impact.

Keywords: mean-field games; Nash equilibrium; Volterra stochastic control; optimal portfolio liquidation; systemic risk; price impact (search for similar items in EconPapers)
Date: 2023-06-06
New Economics Papers: this item is included in nep-gth
Note: View the original document on HAL open archive server: https://hal.science/hal-04119787v1
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://hal.science/hal-04119787v1/document (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:hal:wpaper:hal-04119787

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().