Dynamic stability of the Shapley value in the differential resource extraction game

The problem of limited resource extraction by two firms often occurs in practice. Both firms try to maximize their income. This issue has been thoroughly investigated in [2]. The difficulty lies in the fact that the model uses a system of differential equations, which do not have analytic solution. In this paper, an attempt was made to improve the model in order to the obtained systems with analytic solution, which could be analyzed.