Aldarad said:
Sometimes I get the possibility to ask an AI to change to the same civic as me. If I ask nice does it cost me "goodwill" and is there any gain by having the same civics?
It doesn't actually cost you anything, per se. As with any other request of the AI, you may need to bribe the AI into accepting the deal. There's also no actual benefit to doing this, aside from the possible ramifications associated with switching and running a particular civic.
For example, you may want to gift Theology to an AI. On the following turn, you should be able to ask the AI to convert to Theocracy. You would want to do this in order to prevent the spread of religion to the AI. Perhaps you want the AI to remain your religion (boosting your relations with it). Perhaps you want the AI to remain its own religion, while spreading your religion to other AIs (who would view your target civ as a heathen, and be more inclined to go to war with it).
Religious civics provide perhaps the most direct and readily apparent returns in this sense. Economic civics are perhaps the next best means of manipulating an AI. Shutting down foreign trade routes or eliminating a free specialist in every city can have some powerful consequences. You could also force the AI to adopt any Labor civic besides Caste System (which it seems to be rather fond of) in order to reduce its Great People production.
The only other real uses of this would be to force one AI leader to adopt the favorite civic of another AI leader (boosting relations between the two), or to force it into a period of Anarchy (depending on game speed, number of civic switches, and if the AI is or is not Spiritual). Given that the AI will not care if it adopts your leader's favorite civic, you cannot use this to directly improve relations between the AI and yourself. I suppose you could also use this to prevent a Spiritual AI from adopting a particular civic or religion for the five-turn civic change restriction imposed after changing a religion or civic, but that's more a question of why would you even bother.
I don't recall ever asking (in the case of good relations or at the end of a war in which I did not eliminate the given civ) or bribing (in all other cases) an AI to switch a civic, so I cannot comment as to how expensive it is to convince one to do so. I'm sure it's dependent on your relations with the AI. Good relations with or after devastating in a war a particular civ will reduce the cost. Neutral or otherwise fence-sitting leaders will probably ask for more in return in order to change civics.
Religion is easily enough controlled by controlling its spread; the AI will adopt the most well spread religion in its cities, unless it controls the Holy City of a given religion; it will spread to that religion once it spreads the religion to enough cities to provide a moderate amount of income if it were to build a shrine to that religion (regardless of whether the shrine is up or not, as far as I can tell).
I almost have to wonder why you would even bother. With very few exceptions (such as the Theocracy switch), the benefit gained by forcing an AI to switch civics is balanced by the cost of forcing that change, yet, as free as you are to switch your own civics, so to is the AI. That is to say, for whatever you pay the AI to switch, it can just turn around and switch back starting five turns later (even for a Spiritual civ), so, in essence, you paid it something for almost nothing in return.