Athena and Poseidon for Athens
Athena and Poseidon each offered a gift to the city: she the olive tree, he the sea (or a horse). The city chose Athena's gift, and she became its patron [S5]S5 · Pseudo-Apollodorus, Library (Bibliotheca)c. 1st–2nd c. CE (transmits earlier)text[S6]S6 · Pausanias, Description of Greecec. 150–180 CEtext.
Ancient Greek religion is a historical religion. Its myths are attested in primary literary and material sources; disagreements between authors (Hesiod vs. Orphic vs. local cults) are preserved as variants, not resolved.
A civic aition (origin story), not a battle; the 'gifts' differ slightly across sources [S5]S5 · Pseudo-Apollodorus, Library (Bibliotheca)c. 1st–2nd c. CE (transmits earlier)text[S6]S6 · Pausanias, Description of Greecec. 150–180 CEtext.