According to my professor at b-school, the first person to throw out a number loses.
Not in my experience. A lowball or highball anchor can steer the negotiation to where you want it. It can also help you to quickly establish whether both sides are in the same ballpark - so you don’t waste time on a process that won’t lead anywhere.
It doesn’t matter who goes first. The most important thing in a negotiation is to communicate. Good communication fosters productive iterations.