Persian Wars
nothing
If I understand the question correctly, it was The Peloponnesian War from 431 to 404 BC that Athens and Sparta fought each other. Sparta was the victor.
The city-states of Athens and Sparta fought each other in the Peloponnesian War .
peloponnesian war
in the pelopponesian war
The city states of Athens and Sparta and their allies fought each other in the Peloponnesian War .
Peloponnesian War
The Peloponnesian Wars.
they had fought together and against each other
Each other. Athens and Sparta, with their respective Greek allies, fought each other. The Persian Empire later sided with Sparta against Athens, but mostly it was Greek against Greek.
Peloponnesian War.
Athens and Sparta did not fight each other in isolation. They fought as allies and as adversaries in various conflicts over a couple of hundred years. So Athens did not defeat Sparta or Sparta defeat Athens. They were involved in wider conflicts in the battles.
They all were - a matter of survival as they constantly fought each other. Sparta and Athens led opposing leagues.