Centralized and competitive extraction of distributed renewable resources on networks with nonlinear aggregate growth

We study the optimal and strategic extraction of a renewable resource that is spatially distributed over a network, migrates across nodes (with no loss of biomass during transit), and evolves according to a nonlinear (concave) aggregate growth function. A subset of nodes hosts extractors, while the remaining ones serve as reserves. We analyze a centralized planner's problem and a non-cooperative game with stationary Markov strategies. For three canonical growth families (logistic, power, and log-type saturating laws) paired with corresponding utilities, we derive closed-form value functions and feedback rules for the planner, and we construct a symmetric Markov equilibrium for the game on strongly connected networks.