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Yes.

The buyer would might have been willing to pay $15,000+, but wanted to anchor (and start low) so went $4,500. The real max was introduced when the seller gave the $15,000 number... buyers never want to or will reveal their number (i.e. the $7500 was a lie.)

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Thanks! So basically (typically, of course depending on circumstances) any number explicitly stated by the buyer is less than the true maximum and you can expect to converge on a higher price?

Normally, yes, and as was mentioned higher in the thread this initial figure is referred to as an "anchor," meaning that it has the psychological effect of implying that anything higher than that number is somehow a real concession on the buyer's part, when the reality is that the opening number could have just been higher. It's rather like when a store says "this is normally $500 but now it's on sale for only $250" instead of just pricing something at $250 in the first place. Getting to Yes, also mentioned above, is a useful book on negotiation.

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