Dynamic Shapley value for repeated network games with shock

Considering a repeated network formation game, we suppose that the player who has the largest set of neighbors in a network may leave the game with a positive probability. This effect is called a “shock”. The shock may appear only once, and the game round at which the shock is appeared is chosen at random. Dealing with a cooperative framework of the repeated game, we find the Shapley value, the cooperative solution, in an explicit form. It turns out that the Shapley value is subgame inconsistent for the considered model. The fact of subgame inconsistency may break the cooperative agreement. To prevent players from breaking the agreement, we design a mechanism of stage payments.