  In many multi-agent spatiotemporal systems, the agents are under the
influence of shared, unobserved variables (e.g., the play a team is executing
in a game of basketball). As a result, the trajectories of the agents are often
statistically dependent at any given time step; however, almost universally,
multi-agent models implicitly assume the agents' trajectories are statistically
independent at each time step. In this paper, we introduce baller2vec++, a
multi-entity Transformer that can effectively model coordinated agents.
Specifically, baller2vec++ applies a specially designed self-attention mask to
a mixture of location and "look-ahead" trajectory sequences to learn the
distributions of statistically dependent agent trajectories. We show that,
unlike baller2vec (baller2vec++'s predecessor), baller2vec++ can learn to
emulate the behavior of perfectly coordinated agents in a simulated toy
dataset. Additionally, when modeling the trajectories of professional
basketball players, baller2vec++ outperforms baller2vec by a wide margin.
