  Game Logic with sabotage ($\mathsf{GL_s}$) is introduced as a simple and
natural extension of Parikh's game logic with a single additional primitive,
which allows players to lay traps for the opponent. $\mathsf{GL_s}$ can be used
to model infinite sabotage games, in which players can change the rules during
game play. In contrast to game logic, which is strictly less expressive,
$\mathsf{GL_s}$ is exactly as expressive as the modal $\mu$-calculus. This
reveals a close connection between the entangled nested recursion inherent in
modal fixpoint logics and adversarial dynamic rule changes characteristic for
sabotage games. A natural Hilbert-style proof calculus for $\mathsf{GL_s}$ is
presented and proved complete using syntactic equiexpressiveness reductions.
The completeness of a simple extension of Parikh's calculus for game logic
follows.
