Thing is, the oil companies have just as much incentive if not more. They're corporations; their motivation is profit. Now, the easiest way to get profit from oil is not to produce more oil but to charge more for it. Meanwhile, finding and extracting more oil is becoming more and more expensive and, frankly, more of a hassle. And risky! And impolitic.
The oil companies own the refineries, not just the means of production. So to a large extent, they can make their profits regardless of where the oil comes from, and -- to another very large extent -- oil is oil. It doesn't matter much to the refinery or the gas station or the plastics factory if the oil comes from the Gulf of Mexico or the Arabian Peninsula. De Beers can make gem-quality diamonds in factories, but flooding the market wouldn't improve their profits. Oil gets used up a lot faster than diamonds, but the principle is the same.
Plus -- rather importantly -- since oil's becoming harder to produce, if the rate of production is slowed now, the relatively easy-to-get oil will last longer. So, again, it's better to do whatever to drive the price of oil up, if you're an oil company.
The people trading petroleum futures have even better incentives to drive up the price per barrel, in theory, but since most of the serious traders are speculators who buy and sell ahead of the curve, the last thing they want is too little volatility in the market. They're not really making their money from the value of oil but by fleecing slower investors who are trying to make money from the value of oil. But even the futures sharps have better incentive than ecoterrorists to blow up a drilling rig.