What if Antony and Cleopatra had defeated Octavian?

Sally-Ann Ashton admires one of the statues of Cleopatra at the launch of a new exhibition at The British Museum in London 10 April 2001.

In 30 B.C., Mark Antony and Cleopatra VII died by suicide after they were defeated by Octavian's forces in a civil war.

But what if Antony and Cleopatra had defeated Octavian, the man who became Rome's first emperor? Would they have become rulers of Rome? How would history have been different?