Suppose you're involved in a price negotiation as the seller and you've decided to make the first offer. How high should it be?
Students of negotiation psychology will point to the power of anchoring and a fair amount of research that shows that aggressive opening offers tend to lead to better final agreements. Clearly, however, there are limits -- if your offer is too aggressive you risk angering the other party or being seen as unserious.
I saw this first-hand when I was asked by a healthcare provider to negotiate reimbursement rates with their insurance partners. They'd previously retained a different consultant whose negotiating strategy seemed to be, "Ask for the moon and then try to settle for the sky." In an environment where many providers were being forced to accept lower reimbursement rates, she was asking for massive increases (over 50% in some cases). When I took over I found that many of the insurance representatives were angry and confused, and were doubtful that we were negotiating in good faith or that we understood their reality.
On the other hand, too low an opening offer risks leaving money on the table. If the ZOPA is from $100 to $200 and you (the seller) open with $180, you've given up 20% of the ZOPA before we even get started.
In their book Negotiation Genius, my HBS professors Max Bazerman and Deepak Malhotra propose a useful rule of thumb for targeting your opening offer. Assuming you've done your homework and have a good idea of what their reservation value is, your opening offer should be slightly more aggressive than that. In other words, if you think the highest price the buyer might pay is $200 you might open as the seller with $210. An opening like this is likely to seem reasonable, albeit demanding, and your counterpart is then in the position of negotiating you down in order to get you into the ZOPA.
Bazerman and Malhotra offer another rule for your opening offer. It should never be so high that you can't finish the sentence, "I think $X is fair, because..." Providing a reason for your offer greatly reduces the risk that the other party will see it in a negative light and has the added benefit of combining your anchor with favorable framing.
Going back to our healthcare provider, I approached their insurance partners with rate increase proposals that were high but that came with a profitability analysis. We showed that the provider (a non-profit) was losing money while the insurance companies were saving a great deal since for many of the procedures the alternative provider was a hospital -- which was much more expensive.
By showing that they were capturing the lion's share of the value created by the relationship we made our demands much more reasonable and our threat to walk away (i.e. to terminate the contract) much more credible. We also focused the discussion on the benefit the insurance companies were receiving (rather than the general state of the healthcare market or the fact that other providers were seeing rate decreases). As long as that was the topic it was impossible for the insurance companies to argue that a rate increase wasn't appropriate.
The end result was significant increases from all the major private insurers and a net result that far exceeded the organization's target.
This analysis assumes a reasonably high level of uncertainty about information. The more the two parties know, the more cautious you should be about a really aggressive offer. To take an extreme example, suppose the ZOPA is $100 to $200, both parties know it and know that the other knows it. In that case, an offer of $210 by the seller isn't going to be well-received. There's no "because" that justifies an offer you know full well the other party can't accept.
Another thing to consider is the relationship effect. If you're buying a car from a stranger you may not care much whether they think you worked them over afterwards, but if you're negotiating with one of your firm's strategic partners or one of your top clients that's very different. That doesn't mean you can't try to capture a large piece of the pie, but make sure you're considering value in the fullest sense, rather than just the cash on the table in this particular deal.
Finally, you need to think about the nature of the deal itself. If it's a clean sale, then today's price may be all that matters. If what you're negotiating is the division of rewards from a collaboration, that's a very different matter. Smart negotiators sometimes meet a generous offer with a counter-offer that is more favorable to the other party because they realize that the first offer won't be sustainable over time. (A simple example is an American university that asked a famous European scientists how much he'd require as salary if he became a professor. His offer was significantly lower than the going rate for prominent professors so they countered with more than double what he'd asked for. If they'd accepted his low rate he would soon have learned that he was underpaid and might have left even if they'd belatedly made up the difference. By treating him well, they helped ensure a good relationship.) Before you make your offer, ask yourself how you'd feel on the receiving end knowing what you know. If it would offend you, it might offend the person you're making it to.