Capitalist Extra income of cash, and faster resources. This means that you can gain plenty of resources for your army and tons of cash for structures. I recommend getting an armory with this government because of its sped-up income.
Communist Extra income of manpower, and you gain influence and cash from your kills. This is unique to communist, and since you gain influence you can use that for special units that you would require more time to deploy without a special operation tower. Downside is slower electricity outcome
Facist Extra income of electricity, you build structures and units faster as well. This means that you can do things generally faster. Rush technique is commonly used
Monarchy Extra income of influence. That's all that is confirmed.
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Armors
Light armor This armor is used on marines and snipers. Resistant to: Nothing, really. Weak to: Explosive damage, positron weapons.
Titanium Used by most air units and the most Romans. Resistant to: Machine guns. Weak to: I honestly have no idea.
Chronite Used by tanks, Groditz, and a few other units Resistant to: Any light weapons. Weak to: Positron weapons.
Special armors Mostly used by influence cost units. Resistant to: Varies. Weak to: Varies.