Inventory Control Games with Prepayments

The cost game arises when a group of retailers who observe demand for a common good decide to cooperate and make join orders following the EOQ policy. In this paper we present a new class of inventory games that is strategically equivalent to that class of inventory cost games: inventory games with advance payments. This model extends the traditional inventory model to the situation where advance payments of retailers are required. We propose a core distribution, which is based on a proportional allocation, as well as a population monotonic allocation scheme, for inventory games with advance payments. Then, we examine the stability of grand coalition from both a myopic and farsighted perspective, and conclude that it is always stable from both points of view. To complete our study, we develop a sensitivity analysis for the model and evaluate the changes produced on the proposed core distribution.