In the regular dealer-network car buying world, I think the "pay cash" incentive for discount works because it tells a dealer you're serious, you want to buy today, and you'll stop shopping if they take your money immediately. They value volume as much as profit.
Past couple of times I went to purchase a car through a dealer I started as if I was going to finance, then switched to cash on the last volley with the "I'll pay $x today, in cash, and do the deal right now." I also show up in grubby-ish clothes, bring the wife and kids, etc.
It has worked for "normal" cars (Hondas for me). Actually, in that case the dealer first said "no" to the cash offer, so I walked away. About 2 hours later I got a phone call: "was thinking about the deal, your kids clearly liked the car, I have one left on the lot, I'll take the cash."
I find it a little odd, since dealer financing is such a robust money maker for dealerships you'd think they would be disappointed with cash, but in the end they'd rather sell more cars, and "some money" beats "no money." The discount wasn't all that much for cash, sometimes an option I didn't want is free, but enough to be worth the effort.
I didn't miss haggling (or the drama) one bit for the purchase of my Model S. Ordered online, wired them the money, showed up to pick up my car, and drove off-- so smooth. I feel I got what I paid for, and the sting of the purchase disappeared somewhere between the factory and home
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/Mitch.