The two situations which lead to failure of Gromov’s Link Condition in multi-agent gridworlds

The two situations which lead to failure of Gromov’s Link Condition in multi-agent gridworlds: knight’s move (left) and two-step bishop’s move (right). Maroon arrows indicate admissible moves and blue squares indicate admissible ‘dances’ – a dance in a gridworld is composed of four moves in the shape of a 4-cell square. An agent can interrupt the other’s dance (left) or two dances can collide on the diagonal (right).