Natural vs anthropogenic risk reduction: Facing invasion risks involving multi-stable outcomes

Natural resources important to economic systems are managed in the presence of event uncertainty, marking the transition from a more desirable ex ante state to a less desirable ex post state. The risks of this transition are endogenous and depend on state of the natural resource system and human behavior. In designing least cost policies of risk reduction, policy makers should consider the optimal mix of natural and human risk reduction. Decisions about the best risk reduction mix matter most for systems vulnerable to ex post multi-stability, in which the natural resource system has the potential to begin in one of multiple, locally optimal basins of attraction. This is because ex ante decisions can affect the initial conditions for the ex post system, thereby determining the ex post basin of attraction and the optimal ex post state. In this paper, we find that an ex ante system that is convex and uniquely stable without risk may become non-convex and multi-stable in the presence of endogenous risks and ex post multi-stability. This result arises because ex post non-convexities, and the uncertainties associated with the invasion and its magnitude, can create ex ante non-convexities that generate multiple optimality candidates.