A stochastic game framework for patrolling a border

Matthew Darlington, Kevin D. Glazebrook, David S. Leslie, Rob Shone, Roberto Szechtman

Abstract: Highlights•We introduce a stochastic game model of border patrol.•Smugglers repeatedly attempt to send small illicit items at discrete locations.•A patroller tries to prevent the smuggling, but to move locations must pay a cost.•We derive properties of Nash equilibria and efficient algorithms to find them.•We characterize interesting equilibria under assumptions on model parameters