This paper is devoted to multistage games with pairwise interactions. The case of complete graph is considered, the vertices of which are players, and the edges are the connections between them. The characteristic function is introduced and its supermodularity is proved for single-stage game. A new approach for construction of characteristic function of multistage game is proposed, based on the use of values of characteristic functions of single-stage games. On the basis of the newly constructed characteristic function, the optimality principle is introduced, which is an analogue of the core, and its strong time-consistency proved. The work is illustrated by an example.

中文翻译：

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完整图上具有成对互动的多阶段游戏

本文致力于成对互动的多阶段游戏。考虑完全图的情况，其顶点是玩家，而边是它们之间的连接。介绍了特征函数，并证明了其对于单阶段游戏的超模块化。提出了一种基于单阶段游戏特征函数值的构造多阶段游戏特征函数的新方法。在新构建的特征函数的基础上，引入了与核心相似的最优原理，并证明了其较强的时间一致性。举例说明了这项工作。