Stochastic Game Theoretic Models for Competitive Resource Extraction in the Nigerian Upstream Petroleum Sector

Competitive resource extraction in Nigeria's upstream petroleum sector involves strategic interactions among multiple exploration and production companies, the Nigerian National Petroleum Company Limited, and regulatory authorities, with outcomes that significantly affect national resource rents, environmental management, and long-term energy security. This dissertation develops stochastic game theoretic models to analyze and optimize competitive resource extraction dynamics in the Nigerian upstream petroleum sector. A systematic review of differential game theory, stochastic games, and natural resource economics literature establishes the theoretical foundations and identifies gaps in models accounting for multi-player extraction games under reserve uncertainty and regulatory intervention. An original stochastic differential game model is formulated in which each firm's extraction strategy is a feedback control policy, reserve dynamics evolve as a diffusion process, and regulatory royalty policy constitutes a government control variable. The existence and uniqueness of Markov perfect Nash equilibria are established under specified regularity conditions, representing an original theoretical result. Comparative statics derived from the model demonstrate how fiscal incentive structures shift extraction dynamics, providing a formal basis for evaluating Nigeria's Petroleum Industry Act fiscal provisions. Numerical solution methods exploiting the Hamilton-Jacobi-Bellman equations are developed and implemented for a stylized three-firm game calibrated on Nigerian field production data. Results identify conditions under which the Nash equilibrium generates aggregate extraction rates above the social optimum, quantifying the resource curse externality in game-theoretic terms. Keywords: stochastic game theory, resource extraction, petroleum sector, Nash equilibrium, Nigeria