Stable Shapley value in cooperative game of territorial environmental production

A game-theoretic model of territorial environmental production is studied. The process is modeled as a cooperative differential game. The stable mechanism of distribution of common cooperative benefit among players is proposed. We prove that the cooperative total stock of accumulated pollution is strictly less than the pollution under Nash equilibrium for the whole duration of the game. The perfect Nash equilibrium is found. We design a stable Shapley value as a cooperative solution, which is time-consistent. The Shapley value is also strategic stable and satisfies the irrational-behavior-proofness condition. The numerical example is given.