I´ll make you an offer you can´t refuse....

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If you offer peace (to the AI) 4 stars below what you have, they have to accept. How is it the other way around? When do you get something like: ¨If you don´t accept this will affect stability....¨
When they have four crosses on you?

 

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You get a message detailing the terms, and "this is better than we can accept, and if we dont accept it stability will suffer", then tells you what the loss in stability will be.