The oil market has often been modeled as an oligopoly where the strategic players are producers. With climate change, a new sort of game appeared, where environmental militants play a significant role by opposing some projects, to contain oil production. At the same time, consumers continue to use increasing amounts of oil, independently of oil price fluctuations. Should we oppose oil projects, reduce demand or both? We investigate in this paper the double prisoner’s dilemma in which individuals find themselves, with respect to oil consumption and their environmental stance towards the oil industry. We find that the collective outcome of such game is clearly better when a frugal behaviour is adopted, without being militant. The Nash equilibrium, resulting from the individual strategies, leads by contrast to the worst possible outcome: high prices, high consumption and high environmental (negative) impact. An effective environmental action should avoid opposing oil supply sources (a costly militant act) and help consumers becoming more frugal.