Answer:
to strengthen their position against the Persians
Explanation:
The Peloponnesian League was a military league of Greek city-states that was led and organized by Sparta, that at that time was the most powerful city-state in the Peloponnese.
The main purpose of the League was to protect the city-states from the Persian invasions during the Persian Wars at the same time that struggled to hold back the Athenian influence.