Cooperation in the games with hypergraph communication structure is considered. As usual in cooperative game theory, to define the allocation rule, the characteristic function is used. The communication possibilities are described by the hypergraph in which the nodes are players and hyperlinks are the communicating subgroups of players. The payoff of each player is influenced by actions of other players dependent from a distance between them on hypergraph. The new approach for constructing the characteristic function in the game is proposed. This approach does not require the use of maxmin operations which substantially simplifies the calculations. It is proved that the constructed characteristic function satisfies the convexity property. The results are shown in an example.