Time-consistency Problem Under Condition of a Random Game Duration in Resource Extraction

We consider time-consistency problem for cooperative differential $n$-person games with random duration. It is proved, that in many cases the solution (or optimality principle) for such games is time-inconsistent. For regularization of solution the special imputation distributed procedure (IDP) is introduced and the time-consistency of the new regularized optimality principle is proved. At last we consider one game-theoretical problem of non-renewable resource extraction under condition of a random game duration. The problem of time-consistency for the Shapley Value in this example is investigated.