may have/ might have

The two words are generally interchangeable.

I might go home early if I’m tired.
He may have visited Italy before settling in Nuremberg.

There is a distinction between may have and might have in certain contexts. If the truth of a situation is still not known at the time of speaking or writing, either of the two is acceptable:

By the time you read this, he may have made his decision.

I think that comment might have offended some people.

If the event or situation referred to did not in fact occur, it's better to use might have:

The draw against Italy might have been a turning point, but it didn't turn out like that.