p-additive games: a class of totally balanced games arising from inventory situations with temporary discounts

We introduce a new class of totally balanced cooperative TU games, namely p-additive games. It is inspired by the class of inventory games that arises from inventory situations with temporary discounts (Toledo Ph.D. thesis, Universidad Miguel Hernández de Elche, 2002) and contains the class of inventory cost games (Meca et al. Math. Methods Oper. Res. 57:481–493, 2003). It is shown that every p-additive game and its corresponding subgames have a nonempty core. We also focus on studying the character of concave or convex and monotone p-additive games. In addition, the modified SOC-rule is proposed as a solution for p-additive games. This solution is suitable for p-additive games, since it is a core-allocation which can be reached through a population monotonic allocation scheme. Moreover, two characterizations of the modified SOC-rule are provided. This work was partially supported by the Spanish Ministry of Education and Science and Generalitat Valenciana (grants MTM2005-09184-C02-02, ACOMP06/040, CSD2006-00032). Authors acknowledge valuable comments made by the Editor and the referee.