In a Cournot Oligopoly, firms believe their rivals will hold their output constant if it changes its output, wouldn't this normally lead to a

In a Cournot Oligopoly, firms believe their rivals will hold their output constant if it changes its output, wouldn't this normally lead to a prisoners dilemma situation where essentially all firms believe they can add excess quantity to the market? Is there a common solution aside from hoping you'll get away with it? This reminds me of OPEC and their quotas. Are there more notable industries like this? I would think diamonds but DeBeers owns such a large amount of supply it doesn't seem applicable.