Prior to the Iran-Iraq War, OPEC oil production peaked in July 1979 at 30.5 mbpd. (Bear in mind it is only 35.3 mbpd today.) Oil production started falling precipitously from January 1980, and by August of that year -- a month before the start of the Iran-Iraq War -- was already down 5 mbpd. Of this, the lion's share came from Iran and Kuwait. With the start of the war in late September 1980, oil production fell another 1.3 mbpd and another 1.5 mbpd the following month. By the end of October 1980, OPEC oil production had fallen almost 9 mbpd below in July 1979 peak.
To this point, the Saudis had not changed production materially, either up or down. The Saudis did, however, increase production by 600 kbpd from Oct. 1980 to August 1981.
In September '81, however, the Saudis cut production by 900 kbpd to prevent oil prices from falling below $30. These cuts accelerated, such that 18 months later the Saudis were producing an astounding 6.9 mbpd below their Nov. '80 level of 10.4 mbpd. At this time, OPEC production was almost 17 mbpd below its July 1979 peak. It is almost incredible to write this today.
The Saudis eased these cuts through 1984, but then resumed a restrictive policy, with production falling 7.5 mbpd below the 1979 peak in September 1985. This held oil prices around $24 / barrel, but was clearly unsustainable. Over the next several months, the Saudis would ease the cuts. A year later, oil prices had fallen by 60% and the Great Moderation was underway.
The Saudis did not participate in the oil price spike which occurred in the Aug. 1979 - Aug. 1981 period, the first of those two recessions during the period.
However, the Saudis were the principal drivers of high oil prices from Sept. 1981 through year-end 1985, after which the oil price cratered.