Villages increase their Greed if the difference between Resource in Use and Resource available is higher than 20.
If the Greed reaches a medium level, the villagers will want to go to war with a weaker village.
If the Greed reaches a high level, the villagers will want to attack the nearest Giant. Note that they stop fighting against other villages.
Once locked, a Giant can kite the villagers around the world because villagers do not change target until they die.
It is possible to reset the Greed damaging a village or killing its army.
Failing to complete a project will result in Greed but completing one won't decrease current Greed.
If the villagers lose a battle at war, they lose 1 greed.
Greed is not the only factor to determine war declarations.
In late game, if a village is much more prosperous than its neighbour it will attack it even with 0 greed.
Also, the more warmarks, the more an army is effective and willing to go to war.
Danger is portrayed at the bottom of the Village Panel. Some Animals provide Danger, increasing the Danger to a certain level displayed in the Panel will completely stop the Greed from growing.