  Algorithms for computing game-theoretic solutions have recently been applied
to a number of security domains. However, many of the techniques developed for
compact representations of security games do not extend to {\em Bayesian}
security games, which allow us to model uncertainty about the attacker's type.
In this paper, we introduce a general framework of {\em catcher-evader} games
that can capture Bayesian security games as well as other game families of
interest. We show that computing Stackelberg strategies is NP-hard, but give an
algorithm for computing a Nash equilibrium that performs well in experiments.
We also prove that the Nash equilibria of these games satisfy the {\em
interchangeability} property, so that equilibrium selection is not an issue.
