Pirates and fishermen: Is less patrolling always bad?

Motivated by the Somali fishermen–pirates, I explore the time allocation decision of potential pirates between piracy and an alternative non-violent occupation, fishing, when the returns of both piracy and fishing are sensitive to patrolling intensity. For a range of parameters, the static model yields multiple equilibria, an “efficient” one with no patrolling and low piracy, a less efficient equilibrium with intermediate levels of both piracy and patrolling and a highly inefficient high-patrolling high-piracy equilibrium. Analyzing the dynamic analogue, I obtain the surprising result that sufficiently low patrolling can be a good strategy.