One of the most common ways people give away deception is through inconsistent behavior. A recent case I mediated is a perfect illustration. The two parties were very far apart. The plaintiffs were willing to settle for a bit less than their full suit but not much. They thought they had a winning case; on top of that they were emotionally invested, having (in their view) been treated quite unfairly. The defendant's position was that they were wasting their time. He'd declared bankruptcy subsequent to the debt being incurred and in addition he had a counter-claim against them for substantial damages.
By all appearances, it looked like a deal with no ZOPA, since each party thought their BATNA (going to court) was far better than what the other party might agree to. During a private meeting my co-mediator in the case expressed extreme skepticism that any deal would be reached, and the court liason (a highly-experienced mediator) said afterwards that she didn't expect an agreement either. I was almost certain that they would settle. Why? Poker experience.
It had come up during private session that the defendant had offered to pay nearly half of what the plaintiffs were suing for. Normally this might be a "final offer" at his reservation value as a last chance to avoid going to court but what struck me about it was that it was wholly inconsistent with his stated beliefs. If he indeed thought that bankruptcy protected him from the debt or that his counter-claim was likely to have the court award him money then why offer to pay half? He wouldn't. Either he was extremely risk-averse or he was bluffing.
Poker players are familiar with this form of bluff. The last card comes up in a game of Hold-'em and someone bets big. An experienced player calls because the bettor's play in prior rounds is inconsistent with a hand that would have benefitted from that card. Perhaps their early betting suggested a high pair or AK and they bet big on a 4 that created no straight or flush possibilities. The trick is looking at a party's behavior as a set rather than in isolated pieces. If some of that behavior is inconsistent with other words or actions it's likely that he or she is misrepresenting something (or, more charitably, is confused about their own interests). That contradiction is often a point well worth analyzing closely. After all, if someone is trying to conceal information from you it is likely to be information that you want to be aware of!
Almost every negotiation book discusses the importance of stepping back mentally during moments of stress. William Ury coined the phrase "going to the balcony" to describe the mental exercise of imagining that the negotiation is taking place on a stage and then removing yourself to the balcony to look down on it calmly and objectively. While it's certainly true that you should do this whenever your emotions are taking over it's just as important to do so whenever something your counterpart says strikes you as off. A contradiction between what a person says and their previous statements (or known facts) often signals a chance for you to gain important information. Make sure you take the time to reflect on those signals and to make the best inference as to what they mean.
(As it happened, the defendant did offer to settle for what the plaintiffs were asking.)