With the dictator dead, Antony is now the lone consul. Even in OTL he was very powerful after the assassination, now that Caesar is dead and Antony can play the grieving son, literally adopted by the great man, he should be unstoppable for at least a while. Destroys or drives away his enemies, hunts remaining enemies down in the east while leaving loyal men in the west. As alcibiades says, he will probably become decadent in the east as in OTL. Maybe less so now that he has to keep an eye on the west, maybe more so now that he doesn't have to worry about a powerful genius like Augustus at his back. Who knows, without the need to maintain his high position he might do as James Purefoy suggested and retire to private estates to plow his fields and fuck his slaves, just like old Cincinnatus.
Or maybe life and gathering of power in the east before setting out, disastrously or with glory, to conquer Parthia? Could he end as Crassus did, or maybe even a latter-day Alexander, an exalted madman? One thing is sure I think, that he didn't have the vision or drive to institute a settlement like Augustus's. He would continue to use bought tribunes and the threat of violence to maintain the legitimacy of his power.