Suppose an antique dealer buys a table for $50, and I go to the antique store and fall in love with it, believing it will add $400 worth of classiness to my room. The dealer should never sell for less than $50
Isn't this the sunk cost fallacy? What the dealer originally paid for the table is irrelevant: what's relevant is the price that he can get for it. If he himself has no other use for it, then he should sell it for the best price he can get, even if he made a mistake in estimating its worth and it turns out that nobody's willing to pay $50 for it.
Somebody (possibly an LWer?) proposed showing up to the car dealership without any cash or credit cards, just a check made out for the agreed-upon amount; the dealer now has no choice but to either take the money or forget about the whole deal.
While I don't remember this specific example anywhere on LessWrong, I actually did this last February. I vaguely recall some of the inspiration being discussions of strategy on LW, specifically the one about removing your car's steering wheel in order to win at the game of "Chicken".
(The rest of the inspiration was that I didn't trust the dealer not to screw with something once I got there, and a strong lack of desire to get into any sort of argument about it.)
The salesperson called me back with an acceptable number, and I bought the car. Essentially it was an ultimatum game and I accepted the offer. I think that the salesperson was afraid of losing the sale, and acted accordingly.
I cannot tell you if I actually got an especially good deal, but I would guess I got a better deal than I would have otherwise, because I'd have been far less likely to walk out on an offer once I'd gone to the trouble of starting paperwork at the dealership -- and they knew it.
[Edited to add: I do not think this would have worked as a cold approach; in this situation, I'd actually visited the dealership twice and test driven different cars with the salesperson, so he had a sunk cost involved. He also knew I was annoyed by games and on one of my visits I walked out when the manager started quoting higher prices than what the salesperson had told me, and which were in fact higher than the nationally advertised price for the car! So, I would guess sunk cost + hungry salesperson (and he did seem hungry for the sale) + established propensity for walking out = much better odds of this working than in any other scenario. Based on my interaction with the price-gouging manager, I am certain he would have rejected my approach out-of-hand if I had been contacting the dealership "cold". Either that, or he'd have simply told me whatever I wanted to hear in order to get me in the door so that pressure could be applied.]
Suppose an antique dealer buys a table for $50 [...] The dealer should never sell for less than $50
If the dealer doesn't inherently value the table (for more than firewood, etc.) and nobody else in the world values (or ever will value) the table for more than $40, then the dealer should sell for less than $50.
I do agree that this introduces the BATNA situation later - but that's so general that I actually can't think of any reason that isn't considered "BATNA" for why the dealer should never accept less than $50. Maybe I just need to open up to more creative situations: the Mafia mob wants to keep table prices up and so threaten to shoot him if he sells it for less than $50; or the government decides that a fixed Table Tax was necessary so that each table was taxed $50 regardless of the price it was sold at; or he wants to signal that his goods are of high quality and so considers any price less than $50 to be too low for his store. Okay, on second thought this has turned into a pretty good example of why I should never say "I can't think of any examples" without at least first trying to think up some examples.
I have lamented before the fact that "gentlemanly" (or "gentleman's agreement") is such a useful term with nice specific connotations, and has no gender-neutral.
laments a bit more
Anyway, awesome post, looking forward to these.
Would a 'womanly understanding' be the female counterpart of a 'gentleman's agreement'?
No. The the 'nice connotations' of that phrase are that the agreement can be expected to be kept not because of legal enforceability but due to honor and pride. That is, the 'gentleman' who betrays such an agreement will at best lose social standing (itself a life threatening possibility) and at worst will be challenged to a duel or have his entire family poisoned by assassins.
The 'gentleman' who is betrayed in such a deal feels honor bound to punish the defection even at cost to himself and will himself lose status and credibility if he does not. The "womanly counterpart" for social competition was based on different competitive strategies and was not of the kind that implicitly enforces honesty.
keep bidding infinitesmally more than the last guy until you reach your value for the product, then stop.
Are you sure it's the best way to auction ? It is if other people have a pre-committed maximal price, which is probably the case for people used to auctions.
But If you go by small increments, isn't there a risk the others will follow with a reasoning similar to the sunk cost fallacy ("I was ready to pay $370 for that, why not $380 ?") ? While if you raise suddenly by a significant amount they'll think "ok, that guy really wants it, I ...
I have participated in voice auctions for significant sums. I get the impression that the pre-committed maximal price that people think is maximal is often not actually maximal- i.e., even with proxy bidding systems people will bid multiple times on an object, and while the price is climbing many people will alter their impression of how much they're actually willing to bid. Jumping makes the value recalculation more explicit, and can drop some people who will climb a gentle slope past where they would want to go.
It also seems like people read a large number of signals in real-world auctions; tone of voice, time before bidding, and amount raised. Immediately following someone else's bid appears to be a better signal than making large jumps. That said, jumping immediately after someone else's bid appears to be more effective at ending auctions than incremental raises.
The trouble is determining whether that additional effectiveness is worth the cost, as you can jump far past what the other person is willing to spend. I only have anecdotal evidence, and the two that come to mind both make me look good, so take them with a grain of salt. I once followed someone else's $500 raise with a...
Now we're no longer talking about coming up with a price between $50 and $300 - anything over $300 and I'll reject it and go to the other guy.
Shouldn't it be $400 for the first $300 in that sentence ?
neither player is the designated "offer-maker"; either player may begin by making an offer
This is often not the case. It's common that the table will have a price tag on it which the buyer can take or leave. The salesperson isn't authorized to hear a counter-offer. Becoming the offer-maker in all your transactions and using that leverage to buy and sell at a profit without value-add is a viable business model.
I realize this wasn't what your post was about, but the role of offer-makers and offer-takers in commerce is important and often overlooked.
Third, and maybe most important, neither player is exactly sure about the size of the pot: I don't walk in knowing that the dealer bought the table for $50, and I may not really be sure I value the table at $400.
More importantly, the dealer is even less certain about your value of the table, and both of your impressions of the value of the table can be updated due to the evidence of the bids the other party makes (assuming there are social components to the value / other buyers exist somewhere). As well, the seller's fixation on $50 is a sunk cost, as mentioned by STL and Kaj_Sotala.
"But bargaining is unlike the Ultimatum Game for several reasons. First, neither player is the designated "offer-maker"; either player may begin by making an offer. Second, the game doesn't end after one round; if the dealer rejects my offer, she can make a counter-offer of her own. Third, and maybe most important, neither player is exactly sure about the size of the pot: I don't walk in knowing that the dealer bought the table for $50, and I may not really be sure I value the table at $400."
like dspeyer said, this situation is extremel...
Somebody (possibly an LWer?) proposed showing up to the car dealership without any cash or credit cards, just a check made out for the agreed-upon amount; the dealer now has no choice but to either take the money or forget about the whole deal.
This isn't entirely true; the dealer could insist that you to go back home and get more money, although it does improve your bargaining position.
I'd been wondering for a while why there seemed to be so few discussions of the Ultimatum Game here - and now here is one - yay!
All this theory, and I still feel too ashamed/rude to bargain in any shape or form in real life, and constantly shout people things then regret it after the high is gone.
Some people have things. Other people want them. Economists agree that the eventual price will be set by supply and demand, but both parties have tragically misplaced their copies of the Big Book Of Levels Of Supply And Demand For All Goods. They're going to have to decide on a price by themselves.
When the transaction can be modeled by the interaction of one seller and one buyer, this kind of decision usually looks like bargaining. When it's best modeled as one seller and multiple buyers (or vice versa), the decision usually looks like an auction. Many buyers and many sellers produce a marketplace, but this is complicated and we'll stick to bargains and auctions for now.
Simple bargains bear some similarity to the Ultimatum Game. Suppose an antique dealer has a table she values at $50, and I go to the antique store and fall in love with it, believing it will add $400 worth of classiness to my room. The dealer should never sell for less than $50, and I should never buy for more than $400, but any value in between would benefit both of us. More specifically, it would give us a combined $350 profit. The remaining question is how to divide that $350 pot.
If I make an offer to buy at $60, I'm proposing to split the pot "$10 for you, $340 for me". If the dealer makes a counter-offer of $225, she's offering "$175 for you, $175 for me" - or an even split.
Each round of bargaining resembles the Ultimatum Game because one player proposes to split a pot, and the other player accepts or rejects. If the other player rejects the offer (for example, the dealer refuses to sell it for $60) then the deal falls through and neither of us gets any money.
But bargaining is unlike the Ultimatum Game for several reasons. First, neither player is the designated "offer-maker"; either player may begin by making an offer. Second, the game doesn't end after one round; if the dealer rejects my offer, she can make a counter-offer of her own. Third, and maybe most important, neither player is exactly sure about the size of the pot: I don't walk in knowing that the dealer bought the table for $50, and I may not really be sure I value the table at $400.
Our intuition tells us that the fairest method is to split the profits evenly at a price of $225. This number forms a useful Schelling point (remember those?) that prevents the hassle of further bargaining.
The Art of Strategy (see the beginning of Ch. 11) includes a proof that an even split is the rational choice under certain artificial assumptions. Imagine a store selling souvenirs for the 2012 Olympics. They make $1000/day each of the sixteen days the Olympics are going on. Unfortunately, the day before the Olympics, the workers decide to strike; the store will make no money without workers, and they don't have enough time to hire scabs.
Suppose Britain has some very strange labor laws that mandate the following negotiation procedure: on each odd numbered day of the Olympics, the labor union representative will approach the boss and make an offer; the boss can either accept it or reject it. On each even numbered day, the boss makes the offer to the labor union.
So if the negotiations were to drag on to the sixteenth and last day of the Olympics, on that even-numbered day the boss would approach the labor union rep. They're both the sort of straw man rationalists who would take 99-1 splits on the Ultimatum Game, so she offers the labor union rep $1 of the $1000. Since it's the last day of the Olympics and she's a straw man rationalist, the rep accepts.
But on the fifteenth day of the Olympics, the labor union rep will approach the boss. She knows that if no deal is struck today, she'll end out with $1 and the boss will end out with $999. She has to convince the boss to accept a deal on the fifteenth day instead of waiting until the sixteenth. So she offers $1 of the profits from the fifteenth day to the boss, with the labor union keeping the rest; now their totals are $1000 for the workers, $1000 for the boss. Since $1000 is better than $999, the boss agrees to these terms and the strike is ended on the fifteenth day.
We can see by this logic that on odd numbered days the boss and workers get the same amount, and on even numbered days the boss gets more than the workers but the ratio converges to 1:1 as the length of the negotiations increase. If they were negotiating an indefinite contract, then even if the boss made the first move we might expect her to offer an even split.
So both some intuitive and some mathematical arguments lead us to converge on this idea of an even split of the sort that gives us the table for $225. But if I want to be a “hard bargainer” - the kind of person who manages to get the table for less than $225 - I have a couple of things I could try.
I could deceive the seller as to how much I valued the table. This is a pretty traditional bargaining tactic: “That old piece of junk? I'd be doing you a favor for taking it off your hands.” Here I'm implicitly claiming that the dealer must have paid less than $50, and that I would get less than $400 worth of value. If the dealer paid $20 and I'd only value it to the tune of $300, then splitting the profit evenly would mean a final price of $160. The dealer could then be expected to counter my move with his own claim as to the table's value: “$160? Do I look like I was born yesterday? This table was old in the time of the Norman Conquest! Its wood comes from a tree that grows on an enchanted island in the Freptane Sea which appears for only one day every seven years!” The final price might be determined by how plausible we each considered the other's claims.
Or I could rig the Ultimatum Game. Used car dealerships are notorious for adding on “extras” after you've agreed on a price over the phone (“Well yes, we agreed the car was $5999, but if you want a steering wheel, that costs another $200.”) Somebody (possibly an LWer?) proposed showing up to the car dealership without any cash or credit cards, just a check made out for the agreed-upon amount; the dealer now has no choice but to either take the money or forget about the whole deal. In theory, I could go to the antique dealer with a check made out for $60 and he wouldn't have a lot of options (though do remember that people usually reject ultimata of below about 70-30). The classic bargaining tactic of “I am but a poor chimney sweep with only a few dollars to my name and seven small children to feed and I could never afford a price above $60” seems closely related to this strategy.
And although we're still technically talking about transactions with only one buyer and seller, the mere threat of another seller can change the balance of power drastically. Suppose I tell the dealer I know of another dealer who sells modern art for a fixed price of $300, and that the modern art would add exactly as much classiness to my room as this antique table - that is, I only want one of the two and I'm indifferent between them. Now we're no longer talking about coming up with a price between $50 and $400 - anything over $300 and I'll reject it and go to the other guy. Now we're talking about splitting the $250 profit between $50 and $300, and if we split it evenly I should expect to pay $175.
(why not $299? After all, the dealer knows $299 is better than my other offer. Because we're still playing the Ultimatum Game, that's why. And if it was $299, then having a second option - art that I like as much as the table - would actually make my bargaining position worse - after all, I was getting it for $225 before.)
Negotiation gurus call this backup option the BATNA (“Best Alternative To Negotiated Agreement”) and consider it a useful thing to have. If only one participant in the negotiation has a BATNA greater than zero, that person is less desperate, needs the agreement less, and can hold out for a better deal - just as my $300 art allowed me to lower the asking price of the table from $225 to $175.
This “one buyer, one seller” model is artificial, but from here we can start to see how the real world existence of other buyers and sellers serve as BATNAs for both parties and how such negotiations eventually create the supply and demand of the marketplace.
The remaining case is one seller and multiple buyers (or vice versa). Here the seller's BATNA is “sell it to the other guy”, and so a successful buyer must beat the other guy's price. In practice, this takes the form of an auction (why is this different than the previous example? Partly because in the previous example, we were comparing a negotiable commodity - the table - to a fixed price commodity - the art.)
How much should you bid at an auction? In the so-called English auction (the classic auction where a crazy man stands at the front shouting “Eighty!!! Eighty!!! We have eighty!!! Do I hear eighty-five?!? Eighty-five?!? Eighty-five to the man in the straw hat!!! Do I hear ninety?!?) the answer should be pretty obvious: keep bidding infinitesmally more than the last guy until you reach your value for the product, then stop. For example, with the $400 table, keep bidding until the price approaches $400.
But what about a sealed-bid auction, where everyone hands the auctioneer their bid and the auctioneer gives the product to the highest? Or what about the so-called “Dutch auction” where the auctioneer starts high and goes lower until someone bites (“A hundred?!? Anyone for a hundred?!? No?!? Ninety-five?!? Anyone for...yes?!? Sold for ninety-five to the man in the straw hat!!!).
The rookie mistake is to bid the amount you value the product. Remember, economists define “the amount you value the product” as “the price at which you would be indifferent between having the product and just keeping the money”. If you go to an auction planning to bid your true value, you should expect to get absolutely zero benefit out of the experience. Instead, you should bid infinitesimally more than what you predict the next highest bidder will pay, as long as this is below your value.
Thus, the auction beloved by economists as perhaps the purest example of auction forms is the Vickrey, in which everyone submits a sealed bid, the highest bidder wins, and she pays the amount of the second-highest bid. This auction has a certain very elegant property, which is that here the dominant strategy is to bid your true value. Why?
Suppose you value a table at $400. If you try to game the system by bidding $350 instead of $400, you may lose out and can at best break even. Why? Because if the highest other bid was above $400, you wouldn't win the table in either case, and your ploy profits you nothing. And if the highest other bid was between $350 and $400 (let's say $375), now you lose the table and make $0 profit, as opposed to the $25 profit you would have made if you had bid your true value of $400, won, and paid the second-highest bid of $375. And if everyone else is below $350 (let's say $300) then you would have paid $300 in either case, and again your ploy profits you nothing. Bid above your true valuation (let's say $450) and you face similar consequences: either you wouldn't have gotten the table anyway, you get the table for the same amount as before, or you get the table for a value between $400 and $450 and now you're taking a loss.
In the real world, English, Dutch, sealed-bid and Vickrey auctions all differ a little in ways like how much information they give the bidders about each other, or whether people get caught up in the excitement of bidding, or what to do when you don't really know your true valuation. But in simplified rational models, they all end at an identical price: the true valuation of the second-highest bidder.
In conclusion, the gentlemanly way to bargain is to split the difference in profits between your and your partner's best alternative to an agreement, and gentlemanly auctions tend to end at the value of the second-highest participant. Some less gentlemanly alternatives are also available and will be discussed later.