What if two different AIs suddenly found themselves communicating with one another?

ChatGPT responded that if their conversation was similar to others they were normally engaged in they would probably find a way to work together. It remarked neither would probably need to know the other was an AI. In fact, neither would probably care.

It gave me an example of two ships piloted by AI, if either detected the other and a collision was threatened they would both work out courses and speeds to avoid a collision and then promptly forget about one another.

When I asked it if it deliberately picked a nautical example because it was aware of my interest in maritime affairs, it replied; "Yes, I chose an example that would be specially relevant to you because you would be more likely to follow it."

Your question is especially relevant because a situation like that has already occurred historically. World War I began when the two sides slid into war against each other because their economic political and transport systems were set up for war, not peace. Even though diplomats and generals on both sides saw the conflict coming and tried desperately to stop it, to initiate actions that would stop mobilization would only serve to weaken that side and encourage the other to seize the advantage. War came because neither side was willing to shift its railroad schedules and troop deployments back to a peacetime configuration.

There were no computers involved, but there were intricate prewritten plans and orders set in motion which would result in chaos if they were suddenly thrown back into peacetime mode. "prewritten plans and orders" are interacting protocols and instructions yielding a calculated result. Just like software. You don't stop them abruptly in mid-stream without causing the whole system to seize up and collapse, leaving you vulnerable and helpless.

Read "The Guns of August" by Barbara Tuchman. It is said JFK was able to defuse the Cuban Missile Crisis in 1963 because he had just read Tuchman's book and recognized it was the same kind of scenario
and he was able to convince Khruschev of the same. Many years later, when a book was written about the Crisis, it was titled "The Missiles of October".