Comparative scholarship in constitutional law and political science suggests that the power of courts to exercise judicial review depends partly on the judges’ strategic behaviour; judges can build this power only if they are mindful of how other actors are likely to react to their decisions. Arguably, compliance is the most immediate measure of judicial power.  An assertive court is not much good to anyone if its decisions are routinely ignored or defied.  Using an original agent-based model (a type of computer simulation) this paper explores the performance of several stylized judicial strategies in an environment where there are multiple compliers/non-compliers and compliance/noncompliance is a function of, among other things, prior acts of compliance/noncompliance. This simulation is intended to have some relevance for newly established constitutional courts, as well as supranational courts (eg the European Court of Human Rights) where judicial power cannot be taken for granted.