  We consider the stable matching of two independent Poisson processes in
$\mathbb{R}^d$ under an asymmetric color restriction. Blue points can only
match to red points, while red points can match to points of either color. It
is unknown whether there exists a choice of intensities of the red and blue
processes under which all points are matched. We prove that for any fixed
intensities, there are unmatched blue points in sufficiently high dimension.
Indeed, if the ratio of red to blue intensities is $\rho$ then the intensity of
unmatched blue points converges to $e^{-\rho}/(1+\rho)$ as $d\to\infty$. We
also establish analogous results for certain multi-color variants. Our proof
uses stable matching on the Poisson-weighted infinite tree (PWIT), which can be
analyzed via differential equations. The PWIT has been used in many settings as
a scaling limit for models involving complete graphs with independent edge
weights, but we believe that this is the first rigorous application to
high-dimensional Euclidean space. Finally, we analyze the asymmetric matching
problem under a hierarchical metric, and show that there are unmatched points
for all intensities.
