Cooperation and competition in inventory games

Inventory cost games are introduced in Meca et al. (1999). These games arise when considering the possibility of joint ordering in n-person EOQ inventory situations. Moreover, the SOC-rule is introduced and analysed as a cost allocation rule for this type of situations. In the current paper it is seen that n-person EPQ situations with shortages lead to exactly the same class of cost games. Furthermore, an alternative characterization of the SOC-rule is offered, primarily based on a transfer property which constitutes a special form of additivity. Necessary input variables for the SOC-rule are the (optimal) individual average number of orders per time unit in case there is no cooperation. Assuming that these average numbers are observable but not verifiable, we allow the players to select them strategically, while knowing that the SOC-rule will be (consecutively) applied as the cost allocation principle. Necessary and sufficient conditions are provided for the existence (and uniqueness) of a so-called constructive equilibrium in which all players make joint orders.