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.

Authors and Affiliations

1. Center of Operations Research, Miguel Hernández University, Edificio Torretamarit, Avda. Ferrocarril s. n., 03202 Elche (Alicante), Spain (e-mail: ana.meca@umh.es), , , , , , ES

   Ana Meca

2. Department of Statistics and OR, Faculty of Mathematics, Santiago de Compostela University, 15782 Santiago de Compostela, Spain (e-mail: ignacio@zmat.usc.es), , , , , , ES

   Ignacio García-Jurado

3. Department of Econometrics, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands (e-mail: P.E.M.Borm@kub.nl), , , , , , NL

   Peter Borm

Manuscript received: July 2002/Final version received: September 2002

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ID="*" This work was partially supported by the Spanish Ministry for Education and Culture (grant PB98-0613-C02-02). Peter Borm and Ignacio García-Jurado gratefully acknowledge the support by the Center of Operations Research (CIO) of the Miguel Hernández University. Authors thank Fioravante Patrone for his comments.

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