We study a game-theoretic model for energy markets. Our framework is an N-player stochastic dynamic Cournot game where one producer has a reserve (or stock) that depletes over time, while the others can produce indefinitely with no such quantity restriction. We think of the first player as producing energy from a fossil fuel such as oil, which is an exhaustible resource, while the others are producing from renewables. All players have costs of production that evolve over time, and the exhaustible player can choose to invest in R&D (research and development, including exploration) which may yield increases in stock probabilistically over time. The assumption that the players have heterogeneous and time-varying costs requires a reexamination and extension of previous literature which has typically considered homogeneous costs. We also study how this model may be applied to energy policy, comparing when it is optimal to consider taxing oil producers, opposed to subsidizing green energy, as a matter of public policy.
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