How were the olmec and the mayan civilizations organized?

By a hereditary ruler known as an ajaw. Spanish sources describe even the largest Maya settlements as dispersed collections of dwellings grouped around the temples and palaces of the ruling dynasty and lesser nobles. None of the Classic Maya cities shows evidence of economic specialization and commerce of the scale of Aztec Tenochtitlan. Instead, Maya cities could be seen as enormous royal households, the locales of the administrative and ritual activities of the royal court.

What war are you specifically talking about?