At least that was Antony's

At least that was Antony's plan, but it was not Cleopatra's. She had
determined that Antony should go with her to Alexandria. As might have
been expected, when the time came for the decision, the woman gained the
day. Her flatteries, her arts, her caresses, her tears, prevailed. After
a brief struggle between the sentiment of love on the one hand and those
of ambition and of duty combined on the other, Antony gave up the
contest. Abandoning every thing else, he surrendered himself wholly to
Cleopatra's control, and went with her to Alexandria. He spent the
winter there, giving himself up with her to every species of sensual
indulgence that the most remorseless license could tolerate, and the
most unbounded wealth procure.

There seemed, in fact, to be no bounds to the extravagance and
infatuation which Antony displayed during the winter in Alexandria.
Cleopatra devoted herself to him incessantly, day and night, filling up
every moment of time with some new form of pleasure, in order that he
might have no time to think of his absent wife, or to listen to the
reproaches of his conscience. Antony, on his part, surrendered himself a
willing victim to these wiles, and entered with all his heart into the
thousand plans of gayety and merry-making which Cleopatra devised. They
had each a separate establishment in the city, which was maintained at
an enormous cost, and they made a arrangement by which each was the
guest of the other on alternate days. These visits were spent in games,
sports, spectacles, feasting, drinking, and in every species of riot,
irregularity, and excess.