One way the government could intervene in the oil market is by providing information about the harmful effects of either the production or consumption of oil. This could involve sharing data or facts about how fossil fuels are non-renewable and about how burning them causes global warming.
Oil has both negative production externalities and negative consumption externalities, so the government could decide to focus on reducing the over-production of oil.
The diagram shows that oil is over-produced at q1 (where MPC meets MPB). This is because producers think about profits and ignore the harmful effects that the prodcution of oil has on third parties. If they were to consider these, then the optimal production of oil would be at the point q* where MSC meets MSB.
The diagram above shows the effect that the government hope for, from advertising the harmful effects of oil mining and oil production. There would be a fall in the equilibrium quantity from Q to Q1 which means that we get closer to q*, where the externalities are reduced and there is no longer a misallocation of resources.
However, there is a risk of government failure, which is the possibility that government resources get wasted and there is still a misallocation of resources. For example, there is a large opportunity cost associated with setting up a national information campaign. The government should be certain that the size of the externalities are worth spending a large budget to solve, and that it would be solved successfully. Secondly, there is a chance that information will not be a big enouugh disincentive to reduce oil production, as firms are assumed to be driven by profits. Information on the other hand, could be easily ignored, which means that supply would not shift to the left by much and therefore the equilibrium quantity of oil would remain high and the market failure would still exist.