  We prove distributional convergence for a family of random processes on
$\mathbb{Z}$, which we call asymmetric cooperative motions. The model
generalizes the "totally asymmetric hipster random walk" introduced in
[Addario-Berry, Cairns, Devroye, Kerriou and Mitchell, 2020]. We present a
novel approach based on connecting a temporal recurrence relation satisfied by
the cumulative distribution functions of the process to the theory of finite
difference schemes for Hamilton-Jacobi equations [Crandall and Lyons, 1984]. We
also point out some surprising lattice effects that can persist in the
distributional limit, and propose several generalizations and directions for
future research.
