This negotiation as written was just moving down by the same amount offered by the buyer, is that what the book would recommend as a technique? It gave a gain of $750 over splitting the difference from the start.
I haven't read the book, but, in general, it's not a good move to split the difference from the start, because there is usually at least one more round of back-and-forth. So once you've split the difference, you're already going to end up closer to the other person's initial bid.
e.g. "I want 10,000" -> "I'll offer 5000" -> "Let's spilt the difference and say 7500" -> "How about 6000?" -> ... now you're already between 6000 and 7500.
Great book, would recommend. Not surr how often it has been useful for me still it is a very pleasant read. The main idea is to not give in so easily and to find mutual wins, e.g. he gives the example that he could help the other party get an article in a magazine - barely related to the deal, cost nothing for him, but was worth a lot to the other party.
If you continued to play it out with computers you’d run into Zeno’s paradox. At some point the buyer stopped going to lower increase amount,s but it could happen in which case I guess you’d end up in the middle and quibbling over pennies.
The book does not recommend it as a technique for starting a negotiation but does include a chapter on the final barter/haggle over price and how best to handle it