Multistage games with pairwise interactions on full graph

This paper is devoted to multi-stage 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 one stage game. A new approach for construction of characteristic function of multi-stage game is proposed, based on the use of values of characteristic functions of one 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 strongly time-consistency proved. The work is illustrated by an example.