You, gamer at home, take control of a government and must find a way to handle the waves of immigration from the remote reaches of earth to not only preserve your nation but maintain its growth and harmony for generations.
Do you want to play as an island nation? How big?
Do you want to play as a continental power?
Do you want to play as a small landlocked nation?
Source of Invasion
Are your invaders coming from Arab, African or South American nations?
Are your invaders from right next door, a small sea, a channel or an ocean away?
Invaders will keep coming. The rate varies per your handling of the initial waves. This is not Space Invaders were they keep coming and only speed up; you can change the rate. Do you shoot them on sight? Do you blow up their boats? Do you take an Israeli approach? Walls? Do you hold and release like a lobster that is too small? Do you implement some changes to your foreign policy or policies you have not even enacted in the source nations (Free IUDs)? Walls, camps, deporting current co-ethnics of invaders, etc are all your tools.
It does not stop simply with the handling of the invaders. This is grand strategy so the strategy is not simply with the march of zombies towards your nation. How do you handle your neighboring nations, how do you handle socioeconomic peer nations, can you find another comparable nation dumb enough to take them in, how do you handle the media? How do you handle the media????
Cost of living stats
Internal migration in response to the invasion (see California's internal migration out starting in the '90s)
Budget gaps or surpluses
Social Welfare utilization
Gameplay would require one to employ many different means and think creatively. Maybe blowing up boats is PR nightmare, but maybe it is not if you first arrest NGOs and confiscate their boats, and then deem what happens to the invader boats as national security. What if extrajudicial means are applied and third parties are dealing with migrants in international waters? The press can report on charred remains of rafts and boats found on shore, but no one knows how they got there.
Forget single player mode, this could be a great multiplayer gaming experience. After all this is not a one man job, and players will understand one president or premier cannot fix this problem.