A Rigorous Mathematical Analysis of Carbon Market Mechanisms for Nigeria’s Net-Zero Transition Under the Paris Agreement

Nigeria's commitment to achieving net-zero greenhouse gas emissions by 2060 under the updated Nationally Determined Contribution requires the design and implementation of effective carbon pricing and market mechanisms, yet the mathematical theory governing efficient carbon market design for a resource-dependent economy with Nigeria's structural characteristics remains underdeveloped. This dissertation develops a rigorous mathematical analysis of carbon market mechanisms suitable for Nigeria's net-zero transition, contributing original theoretical results across three domains. The first contribution analyses the optimal design of a cap-and-trade system for the Nigerian petroleum and gas sector, formulating the permit allocation and trading equilibrium as a complementarity problem and proving existence and uniqueness of competitive equilibrium under stated regularity conditions. The second contribution develops a stochastic control model for Nigeria's nationally determined carbon credit registry, characterising the optimal intertemporal management of Nature-based Solution credits under rainfall uncertainty and leakage risk, with application to the Nigerian REDD-plus programme in the Cross River and Ekiti forest zones. The third contribution analyses the game-theoretic equilibrium of carbon offset project developers competing to supply credits to the voluntary carbon market, proving conditions under which competitive supply achieves socially optimal credit volumes and identifying regulatory interventions required when competition fails. The framework is implemented using data from the Nigeria Carbon Market Activation Project and the Nigeria REDD+ Investment Programme for calibration. Keywords: carbon market design, cap-and-trade, stochastic control, game theory, Nigeria net-zero.