Tipping points and business-as-usual in a global commons

This paper analyzes a dynamic strategic model of resource extraction from a global commons. Countries derive benefits from both direct extraction and aggregate conservation of an open access resource. Each period, a country's output depends both on its resource usage and on the global stock of the resource stored within the ecosystem. Leading examples are ocean fisheries, habitat preservation, forestry, and land carbon biomass. The production coefficients on these inputs vary across countries and evolve stochastically over time. A Business-as-usual (BAU) equilibrium characterizes each country's resource usage in the absence of an effective international agreement. Under non-concave resource dynamics, depletion of the resource in a BAU equilibrium may reach a tipping point below which the stock spirals downward toward a steady state of marginal sustainability. Under the assumptions of the model, the tipping points emerge endogenously. If the number of extractors exceeds some fixed, finite bound, the commons always tips regardless of the initial stock. We find that countries will accelerate their rates of extraction the closer they are to reaching the low-end steady state. By contrast, in the socially efficient plan the commons never tips if the initial stock is large.