Did Jaime realise what Bolton's motivation was?

Question

In A Storm of Swords 1, when Jaime Lannister and Roose Bolton meet in Harrenhal, the following conversation takes place (Jaime's PoV):

"I'm a captive here, not a guest. Your goat cut off my hand. If you think some prunes will make me overlook that, you're bloody well mistaken."

That took Roose Bolton aback. "Perhaps I am. Perhaps I ought to make a wedding gift of you to Edmure Tully... or strike your head off, as your sister did for Eddard Stark."

"I would not advise it. Casterly Rock has a long memory."

"A thousand leagues of mountain, sea, and bog lie between my walls and your rock. Lannister enmity means little to Bolton."

"Lannister friendship could mean much." Jaime thought he knew the game they were playing now. But does the wench know as well? He dare not look to see.

What does Jaime mean by 'knowing the game they are playing'? Does he mean the game of two enemies making some sort of deal that's advantageous to both sides (Bolton's motivations being exactly what he says they are later in the same conversation), or does he realise that

Bolton has sold out to the Lannisters (i.e. to Lord Tywin) and is planning to betray Robb Stark

? We've been led to believe, by Jaime's own PoV scenes and by Brienne, that Jaime wasn't a part of what I mentioned in the last spoiler-tag, but does this scene suggest that actually he did know about it before the Red Wedding?

Answer 1

At this point Jaime has no reason to believe that Bolton has sold out the Starks. He's been locked up in the Riverrun dungeons for most of the war, with very little information being fed to him. What Jaimes means by "the game" was Bolton trying to find the most advantageous position to hold. Basically, he's negotiating with Jaime

"Perhaps I ought to make a wedding gift of you to Edmure Tully . . . or strike your head off, as your sister did for Eddard Stark"

Here Bolton states what he should do as a Stark vassal. The fact that he hasn't done any of this, and presents it in the form of a suggestion, means that Bolton is hoping to hear any alternatives that Jaime has to offer.

"I would not advise it. Casterly Rock has a long memory."

Jaime states that doing so would make him a mortal enemy of the Lannisters. A threat basically.

"A thousand leagues of mountain, sea, and bog lie between my walls and your rock. Lannister enmity means little to Bolton."

Bolton dismisses the threat. Lannister enmity is not enough of a threat for him to change his mind. Does Jaime have anything else to offer?

"Lannister friendship could mean much."

Jaime changes tack, promising Lannister friendship (and all that entails) should Bolton release Jaime.

And so on and so forth. At this point Jaime believes that he's negotiating Bolton's into betraying the Stark and allying himself with the Lannisters. He has no idea that Lord Tywin had already done so.