Optimality and consistency in a differential game with non-renewable resources

Imperfect competition amongst buyers for a non-renewable resource is modeled as a Stackelberg differential game. The buyers may act as a cartel or behave non-cooperatively in setting tariffs, which the sellers take as given. The buyer's optimal policy is not consistent when extraction costs depend on the stock level. Both optimal and consistent, unit and ad valorem tariff's are analyzed. When a buyers' cartel uses a consistent tariff, the sellers may prefer to behave as perfect competitors or a monopolist, depending on the functional form of demand and cost. Non-cooperative buyers who are constrained to act consistently are unable to extract any rent from competitive sellers.