What is their relationship to you? If they are hostile, they will demand trades like that. Get them more friendly and it will get more reasonable. It could be related to something like that. 

I took some screencaps to demonstrate the issue more clearly: 

In the first picture, I want to trade some metal to this custom faction leader for Gildar.  You can see that the AI values my metal as being worth a reasonable sum.  

For the next stage in the trade, I request 150 Gildar for my compensation.  

And here's the first stage of the bug.  I wouldn't be surprised if the AI valued its Gildar over the face value, but this is absurd.  

This is the second stage of the bug.  Even after I remove the AI Gildar from the trade table, the ludicrous payment demand remains, sans 300 Gildar (possibly the amount the AI actually wants?)  The 7,200 Gildar figure persists until I select "I'd like to talk about something else", making any further deals impossible.  

I had considered that the AI might simply be over-valuing its Gildar to an incredible extent, but it's not- I can complete the trade by asking for two-figure sums, accomplishing it through installments.  The trigger seems to be requesting Gildar in excess of 100.  

Has no one else encountered this problem? 

Also, for what it's worth, that is not the right screens.

When you click the "Govern" button, you should have on your right a "Foreign Relations" screen, and in that screen you will have an option to select each faction you have contacted.  It's that screen that has the details about the AI's personality.  (You also have a "Speak To" option from that screen which will take you to the screens you showed.)

This is absolutely, certainly a bug, and a major one at that.  Here are more screencaps to further demonstrate the issue.  

Here you can see that requesting all of an AI's Gildar when they are at war does not cause them to massively overvalue it.  

The issue also isn't only caused by asking for all of an AI's Gildar- here I have requested under half, but still am met with an insane demand.  The problem also isn't that the AI has some plan requiring large amounts of Gildar, and therefore refuses to trade away its stockpile- I can complete this trade in four 50-Gildar installments.  The next two pictures should make the bug as clear as I ever can: 

 The AI considers this trade eminently acceptable.  

Delete the 100 Gildar figure, type in 110 instead, and the AI freaks out.  This is a bug.  

In addition to the above, like I noted earlier there is a second, related issue- 

Once you have encountered the bug, the massive AI Gildar request remains on the table, preventing further deals until you exit the trade dialogue. 

Please test it for yourselves if you still doubt that this is a problem.  I am disappointed that FE has such a major flaw in a very basic aspect of diplomacy.  

Thumps up to all the screen shots from MR Dej...

Hope this gets looked upon, I see at least 1 confirmed bug with these things, and one mishap in the behaviour of the AI calculations. (probably the same bug though).

Sincerely
~ Kongdej

I am sure that this isn't an AI personality quirk- as I noted three times previously, the AI is perfectly willing to trade me 200 Gildar for 40 metal or whatever, provided I ask for the Gildar in four 50 Gildar trades.  It's only when I ask for >100 Gildar that the AI bugs out and recalculates its Gildar as being worth thousands.  

I can think of several ways that that could be happening, including some ways that fit with the personality quirk.

It all boils down to the AI -- how it assigns values to things, what it thinks it needs, and what it thinks it does not need, and how those needs are expressed in code.

But, also, if the programming team thinks a 10x factor makes sense in a personality trait -- to represent not wanting to deal with people, is it really so difficult to imagine that they might use something similar in other contexts? 

I'm not sure you understand.  Even if the AI is assigning a 10x value to its Gildar (which I do not believe is the case- the math doesn't add up in the screencaps, and it makes no sense for the game to have several AI unwilling to trade the most basic of resources), resource-for-Gildar trades are still bugged.  If it is intended that the player should not be able to take large amounts of an AI's money, then I shouldn't be able to take 200 Gildar by making four trades for 50 Gildar each, which as I have said again and again players are free to do.  The issue only appears when you type a sum of Gildar >100 in the trade window.  If how the game handles trades right now is intentional, then this is an episode of monstrously poor game design.  I prefer to believe it is simply bad coding  

Hey Stardock, any word on this?  It's sort of an issue that you can't do three-figure Gildar trades.  That this bug has apparently gone unreported for so long has some sorry implications for how often players use the trade table.