I'm not sure if this can be considered a game or not, but it certainly is as fun as one.
NationStates
Basically, you create a country, choose a name, flag, currency, national animal etc. and answer some questions about your politics. Then it will determine what the country looks like.
After that, every week-day (this can be changed in Settings) an issue appears, and you can choose how to solve it. If you don't like any of the options, you can simply dismiss the issue.
It isn't very time-consuming, so you should try it out.
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“Folks say that if you listen real close at the height of the full moon, when the wind is blowin' off Nantucket Sound from the nor' east and the dogs are howlin' for no earthly reason, you can hear the awful screams of the crew of the 'Ellie May,' a sturdy whaler Captained by John McTavish; for it was on just such a night when the rum was flowin' and, Davey Jones be damned, big John brought his men on deck for the first of several screaming contests.”