In this work, we propose a model for the extraction of a nonrenewable resource in an economy where, initially, only one agent is enabled to perform extraction tasks. However, at certain nonpredictable (random) times, more companies receive the government’s approval for extracting the country’s resources. We provide a setup suitable for the use of standard dynamic programming results for both, the competitive and cooperative schemes; we develop the corresponding HJB equations, prove a verification theorem, and give an example. Our framework is inspired by the trends that oil industries are experiencing in countries like Mexico and Russia.
This work presents a two-player extraction game where the random terminal times follow (different) heavy-tailed distributions which are not necessarily compactly supported. Besides, we delve into the implications of working with logarithmic utility/terminal payoff functions. To this end, we use standard actuarial results and notation, and state a connection between the so-called actuarial equivalence principle, and the feedback controllers found by means of the Dynamic Programming technique. Our conclusions include a conjecture on the form of the optimal premia for insuring the extraction tasks; and a comparison for the intensities of the extraction for each player under different phases of the lifetimes of their respective machineries.
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