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Let F be the fraction of worldwide oil output that the country produces. Let D be the price elasticity of demand for oil. And let the country reduce its output by the fraction X.
Then worldwide output reduces by FX. And this output reduction will cause worldwide oil price to rise by FX/D. For this to be profitable, the rise in price must be greater than the drop in output: FX/D > X. Therefore F/D > 1 and F > D is the condition that must be met. That is, the country's fraction of worldwide oil output must be greater than the price elasticity of demand.
D is hard to estimate, it varies depending on the time scale and absolute price of oil. In the short term elasticity is small but over the longer term people can adjust and find substitutes. Likewise, at low prices nobody cares, they don't cut demand if prices rise, but at some threshold it really hurts and we see a noticeable demand effect. In some periods D has been very small, maybe 0.01 or even less. Other estimates have it as high as 0.1 or 0.2.
Many countries produce more than 1% of worldwide output, but if D is as high as 0.1 then there are only three such countries: Saudi Arabia, Russia, and the U.S. At D=0.2 there are no countries in the world producing 20% of oil.
Therefore, unilaterally cutting oil production could be a profitable strategy for a country if we are in a regime where demand response is inelastic. Even a small cut by a small country could produce a significant price rise which would bring in as much money as before. However if we get into a situation where demand is more elastic and production cuts don't lead to price rises, the strategy will not be profitable for most countries.