Computer blows itself up when they lose a city

[Longsight]

For some reason computer opponents are destroying all their cities and units as soon as I capture the first city. They then start again with a single city in a new location. What is going on here, and how do I fix it?

 

[Ares de Borg]

Deselect "Elimination" when starting a game.

 

[Elephantium]

You probably have Elimination mode enabled. Look for the option in the New Game screen (the one where you select which civ you'll play).

 

[DJ Bonebraker]

...Also deselect "Respawn AI Players" to keep them from popping up again when eliminated.