Settlers of Cataan meets all qualities but three, and the third criteria can be met if you feel like picking up some expansions.
Some components of the game are random (resource collection is a function of shared dice rolls), but most of the game takes place with inter-player diplomacy; trading and deal-making.
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This isn't 1950. Girls develop way later than they used to because human lifespans have increased - Lavos_Fanboy