Not enough info. What is the goal condition? If it's just survival, and there's one AI, this is a zero sum game. Is there any strategic reason the computer would not declare war immediately - some disadvantage that comes from declaring first?
1. The game is played on two 8x8 grids, one is the human player, the other is the AI.
2. Each tile on the grid holds 1 million people
3. There are eight citiies on the grid, placed randomly. A city adds 10 million to the population of the tile.
4. If a missile/bomb hits a tile, its entire population is killed
5. Victory is awarded to the side with the most surviving people. The side that started the war gets a negative modifier (called "world opinion") to their score (the specific value to be determined).
So, there is a disincentive to start the war right away, because you may not have a large enough margin of survivors to overcome the world opinion penalty for starting the war in the first place.
Does this help?