Imagine a game where a coin sits on a vertex of a DAG. Players alternate moving the coin along edges. The player who cannot move loses. This is a classic game on DAGs. It is simpler than Cat and Mouse because there is only one token and no cycles.
Your task is to determine who wins at each starting position. Use backward induction starting at vertices with no outgoing edges. These are terminal positions where the current player loses because no move is available.