# Equilibrium in Functional Stochastic Games with Mean-Field Interaction

arXiv: https://arxiv.org/abs/2306.05433 · HTML: https://mlsanity.com/paper/2306.05433/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2023.

## Built on by (most cited first, 1 of 1)

- [An Offline Learning Approach to Propagator Models](https://mlsanity.com/paper/2309.02994/) (2023)

## Abstract (arXiv)

We consider a general class of finite-player stochastic games with mean-field 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 semi-explicitly in terms of operator resolvents, by reducing the associated first order conditions to a system of stochastic Fredholm equations of the second kind and deriving their solution in semi-explicit form. 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-field equilibrium. As a by-product, we also derive an varepsilon-Nash equilibrium for the mean-field game, which is valuable in this setting as we show that the conditions for existence of an equilibrium in the mean-field limit are less restrictive than in the finite-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.