Collective Risk-Taking in the CommonsOlivier Bochet∗, Jeremy Laurent-Lucchetti†, Justin Leroux‡, Bernard Sinclair-Desgagné§April 7, 2019AbstractThe management of natural commons is typically subject to threshold effects.If individuals are risk-averse, some of the recent economic literature holds thatuncertainty on the threshold may have a positive impact by lowering incentivesto over-consume. By contrast, this intuitive result may unravel when uncertaintyis modeled as a discrete or multimodal distribution. Using a variant of the Nashdemand game with two thresholds, two types of Nash equilibria typically coexist:cautious (respectively, dangerous) equilibriain which agents coordinate on the lowthreshold (resp. the high threshold). When both types of equilibria coexist, thesymmetric dangerous equilibrium is always Pareto dominated by the symmetriccautious equilibrium, and the latter is always Pareto efficient. We use an experi-mental setting to assess the severity of the coordination and equilibrium selectionproblem. While cautious (resp. dangerous) play is decreasing (resp. increas-ing) in the probability that the threshold is high, coordination failures are salientfor intermediate probabilities where the likelihood of coexistence of both type ofequilibria is high. We find that there is a U-shaped relationship between overallcoordination and the probability that the threshold is high