The following technical report is available from http://aib.informatik.rwth-aachen.de/:
Christof Löding and Philipp Rohde Solving the Sabotage Game is PSPACE-hard 2003-05
Abstract: We consider the sabotage game presented by van Benthem in an essay on the occasion of Jörg Siekmann's 60th birthday. In this game one player moves along the edges of a finite, directed or undirected multi-graph and the other player takes out a link after each step. There are several algorithmic tasks over graphs which can be considered as winning conditions for this game, for example reachability, Hamilton path or complete search. As the game definitely ends after at most the number of edges (counted with multiplicity) steps, it is easy to see that solving the sabotage game for the mentioned tasks takes at most PSPACE in the size of the graph. We will show that on the other hand solving this game in general is PSPACE-hard for all conditions. We extend this result to some variants of the game (removing more than one edge per round and removing vertices instead of edges). Finally we introduce a modal logic over changing models to express tasks corresponding to the sabotage games. We will show that model checking this logic is PSPACE-complete.
Regards, Volker