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The Tipping Game.

Florian Wagener and Aart de Zeeuw. 2018.


This paper shows that in the presence of a tipping point in a natural system, stable partial cooperation may prevent tipping and if this is not possible, the remaining gains of cooperation are small. This is good news, because the big loss of ecosystem services from tipping can often be avoided. Moreover, the usual grim story that a high level of cooperation is hard to achieve and usually leaves large possible gains of cooperation, does not hold in the presence of a tipping point. These results are shown for a simple tipping game, with constant inputs and piecewise linear dynamics, and for the well-known lake game, with time- dependent inputs and convex-concave dynamics. Tipping back to good conditions can also be induced by stable partial cooperation, but this paper shows that this is more vulnerable to free-riding. Therefore, a natural system that is physically reversible may prove to be socially irreversible.

Keywords: Tipping points, multiple Nash equilibria, partial cooperation, stability, ecological systems

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