You should let them start especially when you don’t know the market.
That’s because neither side has perfect information going to the table.
By letting them anchor you also might get lucky: I’ve experienced many negotiations when the other party’s first offer was higher than the closing figure I had in mind.
That said, you’ve got to be careful when you let the other guy anchor. You have to prepare yourself psychically to withstand the first offer.
If the other guy’s a pro, a shark, he’s going to go for an extreme anchor in order to bend your reality. Themn, when they comeback with a merely absurd offer it will seem reasonable.
*If you’re dealing with a rookie counterpart, you might be tempted to be the shark and throw out an extreme anchor. Or if you really know the market, you might offer a number just to make the negotiation go faster.
–Never split the difference, p.130