Strongly subgame consistent core in stochastic games

Stochastic games defined on finite tree graphs are investigated in the paper. Each node of the graph is defined by a given $n$-person normal form game. Transition to the next vertex of the tree is random and depends on the strategy profile realised in the current game. To determine cooperative solution of the game, the problem of maximization of players' joint total expected payoff is solved. The core is considered as the solution of the cooperative game. The definition of the strong subgame consistency (strong dynamic consistency) of the core is introduced. Method for constructing a cooperative distribution procedure of the imputation from the core which provides strong subgame consistency of the imputation is proposed.