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.
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.
I think it might be important here that the dealer has to do this many times. Yes, sometimes he will need to take a loss on an item to free up inventory space. But for any particular item, if it doesn't sell it is more likely that the right buyer just wasn't present. If a dealer consistently follows the policy of ignoring his purchase cost, the result is that he goes out of business.
No, I don't think this makes sense. The dealer's opportunity to care about how much they paid for the table passed when they bought it. After that, all that matters when it comes to price-setting is how much they think buyers will pay, and any costs related to keeping it stocked
It's really hard to know how much any random person will value a given antique, considering the uniqueness of antiques and people. It's really easy to know how much you paid for a given antique. As a heuristic to keep in mind while bargaining "Always sell for more than what you bought for" seems like it would be helpful, even if in the abstract it doesn't seem like it should be important information.
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.]
I remember it on LW: http://lesswrong.com/lw/c4h/rationality_quotes_may_2012/6j75
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 immediately had the same thought, but on second thoughts, I don't think it's quite as simple as that - remember this isn't the only table the dealer will ever buy, and I'm not the only person he will ever sell a table to. The dealer needs to make a profit in general, and while it might make sense to make a loss on this particular table, it probably doesn't make sense to have the attitude "it's ok if I make a loss on tables that I sell". On the other hand, it's quite possible that the dealer would be better off if he had that attitude, as then he'd buy and sell more tables, and each table might still have a positive expected value. Either way, I think there is something to the idea that the dealer might want to remember what he paid for a table when deciding how much to sell it for.
Indeed, the concept of sunk costs sounds like a specifically CDT one to me, so I wouldn't be surprised if there were scenarios whereas TDT considerations mean that the fact that you know you yourself decided to pay $50 for a table, using the same decision theory as you're using now, is relevant.
I've heard "gentlefolk" used in communities where outright "cultural re-write" for less sexism and racism is tolerated or encouraged (rather than inducing apoplectic sputtering by some of the reactionary participants). Lesswrong, with the semi-regular and un-commented use of spivak, is one of these places.
On the other hand, to my ear, the penumbra of connotation included by "gentlemen's agreement" includes elements of feudal virtue and the glamor of evil, where gentlemen on hard times might become highway brigands rather than shop keepers or farmers, because it would be ignoble to work for a living rather than finding some way to prey on the productive members of society "like a proper gentleman".
Legitimate prey, in that era, only vaguely includes women, because women were mostly just "points" rather than players, formally existing as willing or unwilling chattel, rather than official players of the game. The residuum of this era seems to be what relatively sane feminists are talking about when they speak of "the patriarchy" and "rape culture".
There were exceptional women, but "gentlefolk" doesn't make me think of barely restrained rampaging female nobility, the way "gentlemen" subsumes a historical panoply of somewhat foppish, honor obsessed, sociopathic dukes and princes, who had "always winning at ultimatum games and games of chicken" as the essential business model of their caste.
The caste, to persist over time, needed a way to not tear itself completely to shreds through internal squabbling and so develops cultural norms regulating internal strife... hence, a "gentleman's agreement" could occur between its genuine members. Figuring out a way to identify genuine members (by some method other than never backing down when a peasant tries to get an even deal) loops you back to signaling, completing the circle of game theoretic horror.
In the meantime, yay for progress, bringing humans slowly out of the bad old days, one semi-horrible half-cynical compromise at a time :-)
With the terminological question, I think its worth comparing a "feudal horror" understanding of "gentlemen" with someone like Jeanette Rankin, the first female ever to be elected to the US House of Representatives, who was a pacifist and the lone vote against declaring war on the Japanese after Pearl Harbor. The word might have no cognate because it is inherently gendered? I think it's distinctly possible that there are few female gentlemen for basically the same reason that there are few female serial killers.
I'd appreciate links to essays or summat that give a clear-eyed assessment of the extent to which women were or weren't willing or unwilling chattel at various points throughout history. You seem to be referring to background knowledge that I don't have—the only "knowledge" of the history of the lot of women (and the culture of gentlemen) I have comes from clearly ideological narratives. Excepting the classical era, it seems like it'd be difficult for me to find analyses that avoided implicit moralizing and stuck to factual description. I'm especially interested in the lot of women during the High Middle Ages, which I tend to think of as a high-point of civilization. I would be surprised to learn that the lot of women then was as bad as it seems like it was in classical antiquity, or as it seems like it is today in much of the world including many Western subcultures.
(Interestingly I notice a small "arguments are like soldiers" effect going on on my part: when you say "yay for progress" you're specifically talking about women's rights, but my brain automatically reached for cached counter-examples to "progress" that have nothing to do with women's rights, and wanted to ask why someone who's studied complex systems and group epistemology is going along with the progress narrative, even though you never actually said nor really implied that you were going along with the progress narrative in general. I hope this is because I care about historiography and not because I've been mind-killed by ideology.)
I'm confused that you linked to the Wikipedia section on the influences of the Battle of Jena-Auerstedt. From what it says Prussia's subsequent reforms were primarily military in nature, and the occupation by France only lasted a few years. There doesn't seem to have been substantial cultural reform—(should we expect Prussia to have adopted the leftist norms & ideology of France due to such an ephemeral military occupation?)—and politically the primary consequence seems to have been an increase in German nationalism, which doesn't seem to have been such a good thing given the next century and a half of German history. Is there a primary source that goes into more detail about the relevant cultural consequences of Prussia's defeat in the War of the Fourth Coalition?
ETA: Just realized how off-topic this is. Also close to mind-killing if not itself mind-killing. Perhaps better suited to PM or email.
ETA2: This Wikipedia section is pertinent, though lacking in citations.
My knowledge of women's history in the high middle ages wouldn't be very good. However, as an Irish archaeologist, I can tell you that the chattel slavery of women in early medieval Ireland was so abundant that a female slave or cumal was treated as a unit of currency, being equivalent to 6 to 8 séoit (one of which is equal to the value of a three-year-old heifer). If I were still a student I would be able to find you more academic sources, but I've lost access to most of the journals I used to use. From what I remember, this practice did fall into decline after the arrival of Normans, though this generally attributed to a decline in economic significance rather than a shift in social conscience. If you can access J-Stor, "Lest the Lowliest Be Forgotten: Locating the Impoverished in Early Medieval Ireland" by JW Boyle will provide you with good background on this. I know it's not exactly what you were looking for, but it as an area which I am, to some extent, qualified to talk about.
I've found the Owning Your Shit blog to provide interesting alternative views for some of the standard feminist narratives, though unfortunately it doesn't cite any sources and is somewhat ideological as well.
Relevant articles for this context might be Can we redefine the terms, please? and okay, getting my shit together. They don't go as far as to discuss the Middle Ages, though.
the first female ever to be elected to the US House of Representatives, who was a pacifist and the lone vote against declaring war on the Japanese after Pearl Harbor.
The USA elected a representative that wouldn't even declare war after a comprehensive military strike by an enemy? Wow. I would not have expected that.
That's at best redundant. They became the enemy due to that particular military strike.
Not especially redundant and the "at best" has highly dubious connotations 'at best'. The "comprehensive military strike" is ambiguous without something that indicates whether it is "by us" or "by the other guys".
Even apart from that I wouldn't accept as remotely tenable the claim that Japan couldn't be described as an enemy just because active firefights were not in progress, in much the same way that the participants in a cold war cannot be enemies just because the war is cold. Would you really claim that prior to pearl harbor Japan during that war hadn't done anything that threatened American interests such that they couldn't be considered an enemy? Was America really naive enough not to realize that the previous actions of Japan and the positioning of their forces didn't make an enemy, even if it is one that America was until then able to leave to others to fight? Japan certainly didn't think so, or they wouldn't have bothered making a first strike while they were already busy.
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 won't compete" ?
I never participated in a "real" auction (ebay doesn't count) so I'm really wondering. Are there studies on the compared success of the two strategies ?
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 $50 raise, and won because their large bid was their final bid. Similarly, someone else once followed my $100 raise with a $600 raise, but if they had continued with incremental $100 bids I would have stopped after another round, saving them $300.
There's also the issue of plants- sometimes, the seller of an object will have a friend in the audience who will try to raise the price. They don't want to win the auction, just increase the price- and so if you double-jump, that can be a signal of a final bid, and the plant may be more reluctant to continue, as that might be close to your final bid.
(That is, "let's clear out the unserious bidders" and "I'm all in" are different messages that someone would want to send, and people will try to make the second sound like the first. Regardless of what your opponent is doing, you should always bid so long as the price isn't over the opportunity cost for you, but modeling your opponent appropriately will help you decide how much to raise by. Lower amounts are often but not always better.)
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 extremely rare now. Businesses set prices which can remain fixed for months disregarding promotional sales, and customers BATNA without even trying to make a counter offer until they find a shop with a better price- or else just give up on buying the table. This seems like it is mostly only viable and necessary in a modern economy which has reached the scale you get in today's cities (though once the cities start doing it the major stores apply the same policy to any smaller towns where they have branches so it tends to propagate beyond where it makes the most sense). More customers means several businesses can afford to operate within reasonable travelling distance selling the same product for their own prices, and with each business being larger the person you buy a product at a store from is almost never the majority shareholder or entitled to negotiate in any way. Unless you want to let the proles you hire for minimum wage sell your products for whatever they feel is fair, the only other option is to try and guess exactly how much your customers will value a table in the future, and hope that you do this better than the competition so you can actually make a profit. Businesses almost all play chicken without a steering wheel with the customers, losing money when a customer would gladly pay more, and turning down customers who give them an offer which would still let them make a profit. The post is still good, but it applies to something which I have never even tried in a commercial setting, only when negotiating a deal with a friend or relative.
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.