Vladimir Putin, Recep Tayyip Erdogan and Mohammed bin Salman have a lot in common. The Russian, Turkish and Saudi leaders are all nationalists with regional ambitions. They are autocrats who have centralised power and have been ruthless with domestic political opposition. And they are all risk-takers, who are happy to use military force.

These three strongmen are also believers in the diplomacy of personal relations. Like mafia dons, they can be best friends one day and bitter enemies the next. That matters because their often conflicting interests are fomenting conflict across a swath of territory from the Middle East to north Africa and the Caucasus. If their rivalries get out of hand, civilians will suffer.

The relationship between Mr Putin and Mr Erdogan is particularly peculiar. The presidents of Russia and Turkey have backed conflicting sides in three regional conflicts — Syria, Libya and now Nagorno-Karabakh. At times, they have clashed directly — the Turks shot down a Russian plane over Syria in 2015. Turkish troops were killed in bombing raids in Syria, earlier this year, by Moscow-backed Syrian forces.

Yet the Russian and Turkish leaders retain a wary friendship. To the outrage of its Nato allies, Turkey chose to buy S-400 anti-aircraft missiles from Russia. When Mr Erdogan was almost overthrown in a 2016 coup attempt, Mr Putin quickly offered support, while the US remained silent.

The reason that the two presidents instinctively understand each other is linked to why they clash with each other. Both are anti-US autocrats, seeking to expand their influence into the power vacuum created by a reduced US role in the Middle East. They are willing to act, while the EU hovers on the sidelines. Mr Putin and Mr Erdogan are not the only ambitious, strongman leaders jostling for influence in their shared neighbourhood. A third key player is Prince Mohammed bin Salman — the crown prince and de facto leader of Saudi Arabia — who is much more closely aligned with Washington.

The willingness to use violence — at home and abroad — links all three. Mr Putin annexed Crimea in 2014, intervened in Syria in 2015 and has authorised a range of intelligence black-ops, including allegedly the attempted murder of Alexei Navalny, his most dangerous domestic political opponent. Prince Mohammed has launched a war in Yemen, blockaded Qatar and has taken responsibility as Saudi leader for the 2018 murder of the journalist, Jamal Khashoggi, although he denies personal involvement.

Mr Erdogan has sent Turkish troops into Syria and Libya and is risking another military conflict in the eastern Mediterranean with Greece — while supplying military support to Azerbaijan, in its struggle with Armenia. At home, the Turkish president increasingly locks up political opponents, journalists and civil-rights activists.

To some extent, these three leaders are engaged in a zero-sum struggle. The Turkish-backed government of Libya is battling Saudi and Russian-backed rebels. Turkey’s support for Qatar and the Muslim Brotherhood, and its closeness to Iran, enrages Saudi Arabia.

The Saudi-Russian relationship is more complex. Mr Putin helped to rehabilitate Prince Mohammed, after the Khashoggi murder, with an infamous high-five at a G20 summit in 2018. But the Russian and Saudi leaders fell out badly over oil prices this year.

By and large, however, the three leaders have been able to manage their conflicts. Russia and Turkey may be on opposite sides of the Syrian civil war — but their most urgent priorities are compatible. For Mr Erdogan, it is stopping the establishment of a secure Kurdish enclave within Syria. For Russia, it is preventing the fall of Syrian president Bashar al-Assad.

But these carefully balanced accommodations can easily come unstuck. After two weeks of fighting, the Russians brokered a ceasefire in the conflict between Azerbaijan and Armenia over Nagorno-Karabakh. But the peace is fragile, there are already reports of fresh fighting and, while Turkey is wholeheartedly behind Azerbaijan, Russia has a defence treaty with Armenia. Moscow is unlikely to tolerate the long-term expansion of Turkish influence on former Soviet Union territory.

All three leaders also have delicate balances to strike between foreign intervention and domestic stability. At the time of Mr Putin’s Crimea annexation, Russians joked that they were faced with a choice between the television and the refrigerator. The fridge was empty, but the TV was full of news of exciting military victories. Mr Putin’s popularity soared after his Crimean success. But, as the economy has struggled and nationalist fervour has subsided, he has faced new, fridge-driven discontent.

Mr Erdogan faces a similar trade-off. Turkey’s military adventures are bolstering his popularity at a time of economic weakness. But small wars overseas can eventually be seen as a waste of resources, particularly if they start to go wrong. Prince Mohammed has a version of the same dilemma. His decision to launch a war in Yemen excited many young Saudis. But a quick victory has not materialised and the Saudi economy is suffering from low oil prices.

As their economies struggle, all three leaders need more than ever to demonstrate strength overseas. The danger of clashes between them is rising.