On the comparison principle for a nonlocal infinity Laplacian

In this article, we prove the uniqueness of viscosity solutions to ${\mathcal{L}}_{\mathrm{\infty }}u=f$ in $\mathrm{\Omega }$, where ${\mathcal{L}}_{\mathrm{\infty }}$ denotes the nonlocal infinity Laplace operator, $\mathrm{\Omega }$ a bounded domain, and $f$ a continuous functions such that $f\le 0$. Uniqueness is established through a comparison principle.