So the companies attempting to control
prices would either have to bring commodity
prices up almost immediately or risk having to find a place to store all of their production. (If a company produces oil but can't sell it, I've been taught to discount it to the very end of a well's production, which could be 15-20 years. So it kills the price of that barrel on paper. But I digress).
So to increase oil prices, we would need all of the supermajors (TOT, CVX, RDS, etc.