Dutch social psychologist Geert Hofstede has a lifetime of work on cultural power on his personal website. We don't have to go all the way to the Netherlands to use his wisdom. Hofstede's cultural dimensions theory is a lens through which we can view a nation's cultural inclinations. Comparing the six Hofstede scores of Iran, Saudi Arabia, and Turkey can tell us how they are likely to interact as regional powers. The Hofstede Centre has enough data on each of these countries to make meaningful comparisons.
I pulled the Hofstede Centre's country comparison drop-down menu for the three countries in question. I also viewed their data on the United States as a baseline for comparison. The US scores high on individualism, masculinity, and indulgence. Iran scores higher than the US on power distance and uncertainty avoidance. Saudi Arabia scores higher than the US on power distance, uncertainty avoidance, and long-term orientation. Turkey also scores higher than the US on power distance, uncertainty avoidance, and long-term orientation. The obvious first impression from this baseline comparison is that these three Middle Eastern powers have very different cultural priorities than the US. Their higher power distance scores predispose them to accept autocratic regimes. High preferences for uncertainty avoidance would favor maintenance of their existing social orders and formal rules, even if this comes at a high cost in economic losses or human suffering.
Comparing the three countries to each other reveals that Saudi Arabia has by far the highest power distance and masculinity. This implies that Saudi Arabia has the most to lose from disruptions to its social order by ISIL or other non-state actors, and that it would respond to such disruption in a more masculine way. Note that a masculine policy from Saudi Arabia is not necessarily the same as an effective military response. Saudi armed forces are notoriously ineffective, as their difficulties in combating Yemen's Houthi faction make clear. The strong Saudi commitment to fighting in Yemen leaves it strategically vulnerable to any ISIL penetration of its northern border. Any social stress from fighting an insurgency on two borders would be exceptionally acute for Saudi Arabia given its high Hofstede scored for masculinity and uncertainty avoidance.
Third Eye OSINT assess that Iran, Saudi Arabia, and Turkey will continue to prefer proxy fights against ISIL and each other in the near term. The countries' strong preferences for maintaining social order, as measured by their Hofstede scores, currently outweigh any inclination to express their rivalry in more masculine forms like direct combat. Cultural norms offer one predictive approach in conjunction with other considerations of geostrategy, such as demographic pressures, economic cycles, and competition for resources. The three primary Middle Eastern rivals will continue to test each other's influence. Their cultural preferences indicate how severely they will react to existential threats from non-state actors like ISIL.