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, 2002) and contains the class of inventory cost games (Meca et al. 2003). It is shown that every p-additive game and its corresponding subgames have a nonempty core. We also focus on studying the character concave or convex and monotone of 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.

翻译：我们引入了一类新的全平衡合作TU对策，即p-可加对策。该类对策受临时折扣库存情形（Toledo, 2002）中产生的库存对策启发，并包含库存成本对策类（Meca等, 2003）。研究表明，每个p-可加对策及其对应的子对策均具有非空核心。我们还重点研究了p-可加对策的凹性、凸性及单调性特征。此外，提出了改进的SOC-规则作为p-可加对策的一个解。该解适用于p-可加对策，因为它是一种可以通过群体单调分配方案实现的核心分配。同时，给出了改进SOC-规则的两种特征刻画。