A cartel-fringe model in a nonrenewable resource economy with many fringe firms extracting from a common deposit

We study a model of a nonrenewable resource market, e.g. crude oil market. This market consists of a cartel with market power and a fringe consisting of many small firms, whose deposits are interrelated. In addition, the firms face constraints on extraction. Besides the nonrenewable resource, there is also its sustainable substitute, which constrains the price. We fully characterize the resulting Stackelberg equilibrium. Besides typical solution, in which initially the cartel and fringe extract simultaneously, we find that for some model parameters and initial capacities, the cartel may also deter the fringe from extraction, or it may refrain from extraction until the fringe depletes their deposit. We conduct sensitivity analysis and study the conditions when one of those counterintuitive solutions is optimal.