A Game Theoretic Approach to Collections and Disbursements

Many firms use lock boxes serviced by local depository banks in an attempt to reduce collection float. Likewise, an increasing number of large firms use controlled disbursing to pay their bills, in order to increase and control their disbursement float. Almost all the literature treats the lock box location problem and the disbursement bank location problem separately. The purpose of this paper is to examine simultaneously the optimal collection strategies of sellers and the optimal payment strategies of buyers. Our analysis involves multiple periods where the decisions of each party take into consideration the potential strategies of the other. That is, the collection-payment problem is analyzed both as a two-party and a multiple-party game. The rationale for casting the problem in a game theoretic framework is quite simple: When a seller selects lock boxes and depository banks he takes into consideration the fact that his buyers may use controlled disbursing banks. Likewise, when buyers select disbursing banks or branches they realize that the seller may shift the location of the designated lock boxes in response. Obviously, our analysis is relevant primarily for firms that manage large amounts of payments and collections and use sophisticated cash management techniques.