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Haven:
Humans. A power-based race.
Elves. A magic and power-based race.
Dwarves. A power and technology-based race.
Dungeon:
Necromancers. A magic-based race.
Dark Dwarves (brothers of the Light Dwarves, who, as a result of a demon attack, joined the Dungeon). A power-based race.
Dungeon (not dark elves, but normal gargoyles, predators, shadows). A magic-based race.
Chaos:
Chaos Demons, power and chaos.
Orcs, power and chaos.
Eastern Humans. Chaos magic.
And the motivation for the races can be different. For example:
Necromancers study any magic and are willing to do anything for knowledge; they are ready to accept anyone into their ranks, even a dwarf, as long as he shares their point of view.
Mages sell their knowledge to other races, which is how they survive, and necromancers, who undermine their economy by providing knowledge to those who want it, are a thorn in their side. As a result, the Mage Empire may collapse, and to survive, they want to destroy the necromancers.