The dynamic Nash bargaining solution for 2-stage cost sharing game

The problem of constructing the Dynamic Nash Bargaining Solution in a 2-stage game is studied. In each stage, a minimum cost spanning tree game is played, all players select strategy profiles to construct graphs in the stage game. At the second stage, players may change the graph using strategy profiles with transition probabilities, which decided by players in the first stage. The players' cooperative behavior is considered. As solution the Dynamic Nash Bargaining Solution is proposed. A theorem is proved to allow the Dynamic Nash Bargaining Solution to be time-consistent.