We provide an analysis of institutional dynamics under uncertainty by means of a stochastic di erential game of lobbying with two main ingredients. The first one is uncertainty inherent in the institutional process itself. The second one has to do with the crucial role of resource windfalls in economic and political outcomes, shaping lobbying power and adding a second source of uncertainty. We show that the main consequence of the first source of uncertainty is the existence of multiple equilibria with very distinct features. First, we obtain symmetric equilibria that allow the economy to reach almost surely a stable pointwise institutional steady state, which is exactly at the center of the political spectrum. Second, there exist asymmetric equilibria that only show up under uncertainty and do no allow for stochastic convergence to a steady state, meaning that any political position may be reached asymptotically with nonzero probability. With resource revenue-dependent lobbying power, the economy converges to a conservative position in the absence of uncertainty. When accounting for the two sources of uncertainty, we obtain that revenue volatility tends to stabilize institutional dynamics compared to the deterministic counterpart, which weakens the case for Friedman's first law of petropolitics.