Stable partial cooperation in managing systems with tipping points

Tipping of a natural system, entailing a loss of ecosystem services, may be prevented by stable partial cooperation. The presence of tipping points reverses the grim story that a high level of cooperation is hard to achieve and leaves large possible gains of cooperation. We investigate a tipping game with constant emissions and a piecewise linear response, and the well-known lake system with concave-convex dynamics and time-dependent emissions. Tipping back, leading to a gain in services, can also be induced by stable partial cooperation, but is harder to achieve. A physically reversible natural system may prove to be socially irreversible.