On the estimation of the initial stock in the problem of resource extraction

We consider a differential game of non-renewable resource extraction, in which the players do not know the precise value of the resource stock and, thus, have to make an estimate. We define the value of information about the initial stock and give recommendations for the choice of the estimate depending on the parameters of the problem. Further, we consider the situation where the players only know the bounds for the stock of the resource and solve the problem of computing the optimal estimate, such that it minimizes the players’ losses in the worst-case scenario. The analysis allows us to give a simple rule for the choice of the optimal estimate of the resource stock.