The commons problem under uncertainty and precaution

We study a commons problem under uncertainty, where individual actions affect the risk of a future damage event. We show that for risk-averse agents, an extra risk on the amount of the damage induces more precautionary actions in Nash equilibrium. Similarly, for prudent agents an extra risk in all states of the world induces more precautionary actions in Nash equilibrium. We show that this may lead to the result that small extra risks may increase welfare in Nash equilibrium and derive a condition on the relationship between actions and damage probability and the opportunity costs of precaution for this result to occur. The model applies to climate change, where the actions are the countries' carbon dioxide emissions causing the threat of climate damage, as well as to the COVID-19 pandemic, where physical social contacts cause the risk of an infection with the coronavirus. Data from a representative panel survey in Germany provide evidence that the empirical results are in line with the theoretical predictions.