Coalition formation interacted with transitional state of environment

In coalition formation game, given the payoffs obtained in each coalition, the coalition formation behavior of players has been analyzed. In general, the payoffs are affected by "state of environment", i.e, external factors of the game. Because formed coalition depends on the payoffs, the state affects the resultant coalition to be formed indirectly. However, in reality, the transition of state may often occur as a result of a coalition formation and the transition probability is different from the coalition. In this paper, we focus on the game with the interaction of coalition formation and the transition of state. How the coalition formation behavior depends on the payoff and transition probability is studied by use of stochastic game proposed by Shapley.