  We consider the following modification of annihilation game called node
blocking. Given a directed graph, each vertex can be occupied by at most one
token. There are two types of tokens, each player can move his type of tokens.
The players alternate their moves and the current player $i$ selects one token
of type $i$ and moves the token along a directed edge to an unoccupied vertex.
If a player cannot make a move then he loses. We consider the problem of
determining the complexity of the game: given an arbitrary configuration of
tokens in a directed acyclic graph, does the current player has a winning
strategy? We prove that the problem is PSPACE-complete.
