Two-stage network games

In the paper, two-stage network games are studied. First stage of the game is a network formation stage, while on the second stage players choose their strategies according to the network realized on the first stage. Both noncooperative and cooperative settings are considered. In the noncooperative case the Nash equilibrium is used as a solution concept, whereas in the cooperative setting an allocation (the Shapley value) is considered as a solution concept. It is proved that the Shapley value does not satisfy the time-consistency property.