How did this rivalry between poleis manifest itself in the Peloponnesian War

How did this rivalry between poleis manifest itself in the Peloponnesian War

Ancient Greece had competing city-states, with divergent priorities. For example, Sparta and Athens held different qualities in esteem. What was a polis? Do you believe it was an effective means of governing? What did Sparta (as well as Athens) place at the top of its social hierarchy? How did this rivalry between poleis manifest itself in the Peloponnesian War?