negotiate
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Contrary to the commonly held wisdom, people who make theopening offer in a negotiation have the upper hand.
The advantage is owed to something psychologists call the anchoring principle. It's a cognitive bias where people rely too much on the first piece of information they have.
In a salary negotiation, for example, whoever makes the first offer establishes the range of possible variation from that anchor. If you start high, the hiring manager may adjust the figure down slightly. But that's typically a stronger position than starting low and trying to negotiate up.
"Most people come with the very strong belief they should never make an opening offer," says Northwestern University management professor Leigh Thompson. "Our research and lots of corroborating research shows that's completely backwards. The guy or gal who makes a first offer is better off." 
Marketers use the anchoring principle to trick you into thinking something is cheaper than it actually is. A "discount" tag that still shows the original price on a pair of pants is a prime example, since you tend to focus on the deal you're getting rather than the price you're paying.
In a negotiation, you can use that bias to your advantage. "Whoever makes the first offer essentially drops an anchor on the table," Thompson says. "I might say that your opening offer is ridiculous, but nevertheless, unconsciously, I've been anchored." 
What's more, the opening offer helps orient the other person's perception of the value ofwhat's being negotiated for. An aggressive opening offer makes people consider the positive qualities of an object, since it forces them to decide whether it's worth the cost, says Columbia Business School professor Adam Galinsky. On the other hand, a low opening offer makes people stingily consider what might go wrong, since lower prices are associated with negative qualities. 
"My own research suggests that first offers should be quite aggressive but not absurdly so,"Galinsky says. "Many negotiators fear that an aggressive first offer will scare or annoy the other side and perhaps even cause him to walk away in disgust. However, research shows that this fear is typically exaggerated. In fact, most negotiators make first offers that are not aggressive enough." 
To start with a high but not overly aggressive offer, you could just introduce a number — rather than explicitly ask for it. 
Harvard Law School's Program on Negotiation details why:  
"The most effective anchors further reduce risk because, rather than placing firm offers on the table, they merely introduce relevant numbers. A job applicant may state his belief that people with his qualifications tend to be paid between $85,000 and $95,000 annually, or he might mention that a former colleague just received an offer of $92,000. This assertion is not an offer; it’s an anchor that affects the other side’s perceptions of the zone of possible agreement."
The next time you enter a negotiation, don't play coy. Put your offer on the table first.