On the Value of the Preexisting Knowledge in an Optimal Control of Pollution Emissions

For a classical differential game of pollution control, we consider how the possession of specific information would impact the payoff of some players compared to cases in which the knowledge of information is incomplete. To measure the resulting discrepancy, we use the notion of value of information (VoI). Specifically, we study two scenarios, one in which the role of knowledge about the terminal cost is studied, and the other one, in which we analyze the influence of knowledge about the exact value of the upper bound on control. For each case, we obtain explicit analytical expressions for the payoff functions. These functions are used to quantify the exact value of information.