Reducing shoplifting by investment in security

We consider a single retailer with a given potential revenue, who sells a product that is subject to shoplifting. In order to decrease losses due to shoplifting and to maximize his profit, the retailer can invest in security measures. In particular, we assume that the retailer purchases security services from a single security supplier. The security supplier decides which price to charge the retailer for these services, with the purpose of maximizing his own profit, and the retailer decides on the quantity of security services to purchase. We address this problem using a game theoretic approach, where the retailer competes with the supplier-the leader-who specifies first the service price. The retailer responds by deciding how much to invest in security. We study the conditions under which both players are profitable and the extent to which double marginalization affects the supply chain performance.