Bargaining with your Right Brain

by Venkat on March 16, 2008

At the straw market in Nassau, in the Bahamas, — famous for stuff like the straw handbags below — I recently encountered a distinctive culture of bargaining that made me stop and ponder the subject (on a beach, aided by rum). The pondering resulted in a neat little flash of insight that allowed me to synthesize everything I know about the subject in a way that surprised me. The short version: game-theoretic and information-theoretic approaches to the subject are something between irrelevant and secondary. What drives bargaining behaviors and outcomes is story-telling skill. Here’s how you can learn the skills that really matter in being a successful bargainer.

Bahama

The Simple, Elegant and Wrong Answer

Buyer A and seller B are haggling over product P. Neither knows what price the other is willing to settle for, but A wants P at the lowest price B might sell, and B wants to sell at the highest price A might be willing to pay. You model the situation as a sequential move game, with each move being, at its simplest, a price. You might represent the progress of the game thus, as pairs of B-A call-response moves:

($200, $100), ($180, $120), ($160, $140), ($150, SOLD!)

At each turn, each player uses the history of previous offers/counter-offers to estimate the true limit of the other party, and makes an offer that induces the other to move his price-point as much as possible while revealing as little as possible of his own limit. Throw in some bounded rationality and a value on time, and you have the sort of framing economists like.

You could mathematically model this (no doubt, somebody already has analyzed this to death and proved all sorts of convergence results). One example of such an analysis is in the classic game-theoretic decision analysis book, Thinking Strategically (an excellent read, by the way, for what it sets out to do).

But neat though this mathematical formulation is,  it is fundamentally wrong-headed. Bargaining isn’t primarily driven by parties attempting to (bounded) rationally guess each other’s limit points by doing (non-trivial) real-time analysis of number sequences. Yes, the alternating sequence of numbers does carry information, but in most real situations, information is primarily conveyed in other, non-quantitative ways, and the relevant information isn’t even about price. Let’s examine two examples before I present my alternate model of bargaining.

Real-World Examples

Example 1: The Bahamian Turtle

In Nassau, I bought this coconut-shell toy turtle for my nephew, for $5:

Turtle

The seller, a pretty young woman, came up to us and engaged us with, not one, but three moves all at once, and persuaded me to close, before I had a chance to make a counter-offer:

Seller: You like this turtle? Nice toy for child! Eight dollars!

Seller (conspiratorial whisper, eyes darting left and right): Tell you what, I make you a deal, only six dollars.

Me (doubtfully): Hmm…

My Wife (enthusiastically): oh, it’s so cute; we should get one for Arjun [my nephew]!

Seller: Alright, I give it to you for five dollars. What color bead you want lady? [the thing has a bead on the string that is not visible in this picture].

This one is, in a sense, a non-starter example, since I got played before we got to bargaining. Let’s take a longer example where I acquitted myself better.

Example 2: The Jaipur Good-Cop/Bad-Cop

In Jaipur, India, on a vacation recently, my wife wanted to buy herself a traditional Rajasthani kurta, or shirt. Translating from Hindi, the exchange went roughly as follows (I may be misremembering the prices, but the gist is accurate):

Me: How much?

Seller: 300 rupees

Me: That’s too much, how about 175?

Seller: Come on sir, at that price, I won’t even recover my costs!

Me: No, 175 is the reasonable price for this kind of item.

Seller: Arrey, come on sir! Just look at this fine needlework; you may have seen similar stuff for less in other shops, but if you look closely, the work isn’t as delicate!

Me: Of course I can see the quality of the work, that’s why we want to buy it, now come on, quote me the right price.

Seller: Okay sir, for you, I’ll let it go for 250 (starts folding up the kurta).

Me: No no, this lady may not be Indian, but I am; be reasonable [my wife is Korean, and since I hadn’t mentioned that she was my wife, the shopkeeper had almost certainly assumed I was her local guide — many other shopkeepers had in fact called out to me to bring her into their stores, offering me a commission!]

Seller: But I did quote the price for you sir, for foreigners, we normally ask for at least 4-500!

Me: Fine, tell you what, I’ll give you 190.

Seller: Come on sir, at that price, I don’t even make a profit of 10 rupees!

Me: Fine, let’s do this deal. 200; final offer.

Seller (looking upset): But…

At this point, the seller’s boss, probably the store owner, who’d been poring over a ledger in the background, looked up, interrupted and said shortly, “Can’t you see the lady wants it? Just give it to them for 200, let’s cut this short!”

I have several other examples I could offer (in the US, bargaining tends to be restricted to larger purchases like cars), but these two examples suffice to illustrate the points I want to pick out.

The Phenomenology

There are several features of interest here. Here is a round dozen:

    1. Fake moves: In the Bahamian example, consider the rapid series of three prices offered with a very quick change of subject to the color of the bead at the first sign that I wanted to buy. This bargaining is clearly fake, the numbers being part of the initial courtship ritual rather than the actual price negotiations, which were short-circuited.
    2. Bargaining as bait: The sellers in the Nassau marketplace promote their wares with a curious mix of American retail rhetoric (“C’mon honey! Everything 50% off today”) and more traditional bargain-hunter bait (“You want a handbag sir, for the pretty lady? C’mon I make you a deal!”). I suspect very little serious bargaining actually takes place, since the customers are largely American cruise ship tourists, who are not used to bargaining for the small amounts in play in these transactions.
    3. Qualitative Re-valuation: Consider the variety of non-quantitative moves in the Jaipur example. In the ‘fine needlework’ move, the seller attempted to change my valuation of the object, rather than move the price point. I accepted the point, but indicated I’d already factored that in.
    4. Narrative: A narrative also developed, inviting me to cast myself as the knowledgeable insider who was being offered the smart Indian deal, as opposed to the high-mark-up offered to clueless foreigners. This is a key point that I will return to.
    5. Deal-breaker feints: Twice, the seller attempted to convince me that I was offering him a price he could not accept. These are rhetorical feints. A similar move on the customer’s part is to pretend to walk away (that old saw about the key to negotiation being the willingness to walk away isn’t much use in practice, but pretending to walk away is very useful).
    6. Closure Bluffs: another interesting feature of the Indian example is the closure bluff; a non-serious price accompanied by closure moves (such as starting to package the item), on the off-chance that the other party may panic and fold early.
    7. Good Cop: Finally, note the second individual stepping in to make the deal towards the end (this dynamic is particularly common in traditional retail stores in India, where the owner, or seth and accountant, or munim, will often be watching the salesmen at work, stepping in at the right moment. The psychological key to this is an implicit sense of escalation and respect: “forget that unimportant lackey, clearly you’re a smart customer and I, the boss, will deal with you personally and cut you a special deal that my lackey isn’t authorized to offer.”)
    8. Ritual: In most cultures of bargaining, there are also moves of ritual significance. In India, the best-known one is the bohni, or first sale of the day. Sellers will often plead with customers to close the deal, since it would constitute the bohni and also assert that the price being offered is a really good deal because of the seller’s anxiety to finish his bohni. This is not entirely a pragmatic sort of move — the bohni does matter to traditional merchants, who will often actually take a bit of a hit on the first transaction for luck, to get the cash flow started. Curiously, I also encountered a much more open version of this in the Bahamas, where one shopkeeper said it plainly, “C’mon honey, first customer gets best deal!” I suspect anthropologists would find an equivalent in every culture besides modern fixed-price retail.
    9. Knowledge Bluffs: Though I didn’t use them, knowledge bluffs are common in bargaining (“I saw that same thing in Delhi for half the price!”) . These are bluffs because if the buyer really knows something about the cost structure of the seller, that information is usually quickly deployed and factored out, reducing the bargaining to a matter of “what is the convenience-value to me of buying here rather than in that other place?” Why do they still work? I’ll tell you in a moment.
    10. The Justice Bluff: Surprisingly, in the form of a bluff, a notion of fair price often enters even the purest free-market exchanges. This  is usually brought into play via displays of mock anger at being treated unfairly. Surprisingly, even sellers will do this, attempting to convey a clear sense of disgust by putting away the items under discussion. But there are boundaries: sellers will rarely plead to make a sale on the basis of personal need, since this subtly moves the situation from a peer-transaction to a (morally unacceptable) charity transaction. My mom once bought some vaseline from a tearful door-to-door saleswoman who apparently genuinely broke down and said, “buy some just out of sympathy please!” My mom caved.
    11. Boundary Blurring: If a full transaction has three parts (discovery/selection, negotiations, closing), elements of bargaining often creep out of their nominal home in the middle section. For example, in traditional Indian full-service retail, the sales staff will often pull out a vast selection — more than necessary or asked for — visibly doing a lot of work, creating a clear sense of pressure. On the other side, towards the end of a transaction, sometimes the customer will throw in surprise in-kind requests after the deal seems closed. “Alright, I am buying this car from you for more than I wanted, how about you throw in some floor mats?”
    12. Non-influence of actual knowledge: Though there is a lot of bluffing, there is not much actual information about price limits in play. In every example I’ve encountered, at least for small amounts, buyers and sellers do not attempt to guess limits directly (beyond having a ballpark “reasonable” figure in mind that may be utterly irrational). It is obvious that the buyer may not even have a “walk away” limit price in his/her head, but what is not so obvious is that even the seller may not have such a price in mind. Cost structures can be murky even to sellers, and other hard-to-value elements may be in play, like prospects for future sales, desire to clear slow-moving inventory, and the like. Actual price information usually enters the picture only when the amounts are significant, in which case the parties generally do their research beforehand, and attempt to factor that information out of the bargaining stage altogether. Bargaining is primarily about ownership of the unknown factors in pricing, and is a high-cost process, and it is in the interest of both parties not to bother bargaining about mutually-acknowledged certainties.

      The Right Model

      So that’s all very well. There are lots of psychological subtleties involved. But is this all really important? Is it possible to just cut the Gordian knot and become really good at some sort of game-theoretic model? Would all the bluffing and qualtiative nuances vanish under the right sort of time-series modeling?

      The answers are yes and no respectively. Yes, you do need to work with the full thing; game theory won’t cut the Gordian knot for you. And no, you will not be able to subsume all the bluffing and complexity no matter how much you crunch the numbers. So you do need to appreciate the qualitative sound-track of the bargaining, but no, don’t be discouraged — I am not suggesting that the only meaningful model is a localized sui generis ethnography. Universal models and approaches to bargaining are possible.

      What actually happens in a bargaining transaction is the co-construction of a storyline that both sides end up committing to. Every move has a qualitative and a quantitative part. The prototypical transaction pair can be modeled roughly as:

      ((p1, v1) , (p2, v2))

      Where the p’s are qualitative statements and the v’s are price statements. The key is that the qualitative parts constitute a language game (in the sense of people like Stalnaker). Each assertion is either accepted or challenged by subsequent assertions. The set of mutually accepted assertions serves to build up a narrative of increasing inertia, since every new statement must be consistent with previous ones to maintain credibility, even if it is only the credibility of a ritual rather than literal storyline.
      This is the real reason why there is apparent spinning-of-wheels where the price point may not move for several iterations. For example in the Indian kurta case, I rejected the seller’s assertion that 175 would represent a loss, but acknowledged (but successfully factored out) the “this is fine needlework” assertion. Though the price point wasn’t moving, the narrative was. At a more abstract level, a full narrative with characters and plot may develop. This is also the reason why knowledge bluffs work — even if the seller knows the buyer cannot have seen the same item for half the price in another store, he cannot call out the bluff in an obvious way since that would challenge the (always positive) role in which the buyer is cast.

      The key conclusion from all this? The transaction moves to closure when the emerging logic of the narrative becomes overwhelming, not when price transparency has been achieved. To bargain successfully, you must be able to control the pace and direction of the development of the narrative. At a point of narrative critical mass, something snaps and either a new narrative must displace the old one (rare), or there must be a movement towards closure.

      Becoming a Right-Brained Bargainer

      So here is my magic solution: become good at story-telling based conversations.

      • Walk in, not with a full-fledged plan/story, but a sense of what roles you can comfortably fill (straight-dealer? cynic? know-it-all? Innocent student without much to spend?)
      • As the conversation progresses, try to sense what roles the other party is trying on for size, and suggest ones favorable to you (“Look, I try to buy only from local merchants, and you guys do are doing a great job for the economy of our town, but…”). Say things that move towards a locked-in role on both sides that favors you. In the example above, I got “locked in” into the role of “knowledgeable local” on disadvantageous terms.
      • Look out for the narrative logic as it develops. For example, I successfully resisted an attempt to bring “fine needlework” assertion into play, which would have moved the story from “guy looking for cheap deal” to “connoisseur transaction” and a premium-value storyline.
      • There are critical/climactic points where you can move decisively for closure; watch and grab. In my case, I thought I had one when the seller offered the “Not even 10 rupees” move, but the owner cutting in for the kill and accepting was a clue that I could have pushed lower.
      • Be aware of the symbolic/narrative significance of your numerical moves. If the seller moves from 200 to 180, and you move from 100 to 120, the very symmetry of your move shows that you have no information at all to use for leverage, and the transaction is likely to proceed dully to a bisection unless you do something creative. If the seller offers 500 and you say 250, that reveals that you may be using a “start at half” heuristic, which might create an opening for the seller to launch a storyline of “really, 500 is a fair price, here’s why.” Offering “275” instead creates the right sort of ambiguity. If you do want to drive towards a symmetric-bisection storyline, make sure you pick an irrational starting point, but not one so irrational that it reveals you know nothing about the price (irrationally low opening offers can work, but you need a 201 level bargaining course to learn why).

      Now, this isn’t easy. You have to become a storyteller. But I never said I was going to offer an easy answer; merely a better one than a misguided attempt to do real-time game-theoretic computations.

      tubelite March 20, 2008 at 11:21 pm

      Good one. I like the idea of bargaining as an iterative collaborative story-creation, like improv. And like improv, it has its own “rule of agreement”, which is – “you have to be consistent with the fake positions you’ve both built, though you both know it to be fake”.

      Personally I am very uncomfortable with these situations, and my usual gambit is to immediately deploy the straight-shooter mode after the first offer P1: “P1 is too much. I don’t like bargaining, so give me your best price and I’ll take it or leave it. Saves your time and mine”. The seller usually gives me a price P2 somewhat higher than his absolute best, P3. I immediately decline and leave the shop, going to the next one. From the difference between P1 and P2, I have a much better guess of P3, which I then use to my advantage.

      I’m lying, of course. I let my wife do the bargaining.

      I recently read a Pinker, where he attempts to explain the game theoretic advantage of the irrationality of emotions. He makes a parallel with a bargaining situation, where one side convincingly demonstrates a handicap (“I am not authorized to sell below X”, or “I will be making a loss at that price”) to gain an advantage.

      Venkat March 21, 2008 at 3:49 am

      The first approach you outline is time consuming, but probably the only provably effective way to improve your knowledge of the market over time — using a random sample of first bids to improve your knowledge of the average seller’s limit. There is a nice example in probability textbooks of a similar model. Assume you are judging a beauty contest where contestants parade past you in sequence, and you can only designate someone the winner when that person is the one on stage, and you you have only one shot at it. Then you can show that you should let about 37% of the queue parade past, silently judging them, and then pick the first person after that for whom your subjective rating is equal or more than the highest you encountered in the first 37%. The result arises basically because you need to build up an accurate sample estimate before judging, to maximize your probability of picking the true top-ranker (there is some risk of course, that the topper will parade past you in the sample, or be in the tail somewhere after you commit).

      The second part of your comment — that gets into broader negotiation strategies that go beyond bargaining (which is a simple class of negotiation involving 2-headed price limits). The best treatment I have seen of THAT is Schelling’s classic “Arms and Influence.” There is a whole bunch of such tactics. They range from burning bridges/boats — Caesar and Cortez respectively — to brinkmanship, practiced extensively in the cold war as a way to modulate the power of nuclear bombs. These sometimes occur in bargaining over prices, but in general seem to occur more in more complex negotiations. They have in common a judicious mix of emotional manipulation, demonstrable commitment to action and actual risk.

      Joseph Abrahamson November 12, 2009 at 12:35 pm

      This is a really fascinating reduction on haggling, and I wholeheartedly agree. I spent a summer in China and as a conversant Mandarin speaker had a crash course in haggling with the vendors there. The game was always much less about price and much more about weaving a story which let you demand whatever you wanted of the other person. Even though I didn’t have the best grasp on the language, I eventually learned to spin little stories that would help me take advantage of the situation, especially with my obvious roles as the somewhat-rare white guy who speaks Chinese.

      My favorite haggling story was when my Chinese friend helped me purchase a digital translator. She wove a story (I was able to grasp small bits of it) that I was a student extremely interested in learning Mandarin and that this sort of thing was good for the economy. The seller didn’t want to buy it, but I caught on and managed to step into the role giving my friend quite a lot of power over the narrative (and an eventual wonderful price, less than a tenth the offered). The point being that this was both a good way for me to begin to learn the ropes but also that having two people able to play roles together against the salesperson tends to make for an excellent setup — after all, the salesperson is pretty liable to do it against the buyer as well.

      The second anecdote I found interesting was toward the end when I attempted to purchase a few fake rolexes for my brother. I used the tried and true techniques of buying two for maybe 50% over the offered-and-haggled price for one, faking the walk, threatening to mention ridiculous “just for you” prices to the crowd, but what really broke the deal was the story that these were gifts for my brother. By redirecting the haggling almost so that my non-attending brother was the haggler, I was able to act as a sort of proxy on the deal and pretend to be way more rational than the seller is likely to paint you normally.

      “2 for 25 is all I can do. These are just gifts for my brother’s birthday, I think he’ll like them but I already spent a lot on him.”

      “They’re worth much more than that, 2 for 50.”

      “I’ve already spent a bunch for him. He just wants a watch and I think that these are in my budget.”

      In any case, that kind of transference eventually got me two watches and a new band for just 25y when my friend had literally just bought one for 50y a few seconds before. I was able to draw out the narrative a lot longer by showing my concern for my brother’s wishes without being directly refutable.

      Chris Watkins November 15, 2009 at 9:44 pm

      I usually start below 50%, in a touristy context – except where they have marked prices, in which case they may or may not come down a little.

      Re: “the bohni does matter to traditional merchants, who will often actually take a bit of a hit on the first transaction for luck, to get the cash flow started… I suspect anthropologists would find an equivalent in every culture besides modern fixed-price retail.”

      I’ve seen this in Indonesia too – in Java, Bali, and maybe Sumatra. There’s ancient religious and cultural influence from India – it’s possible this is an example. When they receive their payment, they then lightly hit their goods with it, for good fortune.

      I’d be interested hear an anthropologist’s perspective. Couldn’t find bohni on Wikipedia…

      Then there’s the late sale factor – if it’s been a slow day, you can often get a better price when merchants think you might be their last (or only) chance of selling something that day.

      Chris Watkins November 15, 2009 at 9:49 pm

      Oh, and walking away is key. Amazing how quickly the price drops.

      SG November 20, 2009 at 3:40 pm

      My personal history as a negotiator is pretty atrocious, because I typically don’t go after something until I want it, and then I tend to display my desire for the product in question too clearly.

      But I have had two experiences where I was approached by a street seller to buy something, and because I truly did not want the goods the final price was absurdly in my favor. In one case I was trying to get the seller to go away and a 200 cord purchase went down to 10 cords, and I felt so bad for the guy that I bought it from him to give him face (this wasn’t China where prices are typically 10x inflated).

      In thinking about the “negotiation as a narration” model, it seems what you’re saying is that one could theoretically order a list of possible states of mind according to the price that corresponds to that state. Then the goal becomes to get each of the participants into a frame of mind which corresponds to the highest price coordinate (buyer and seller on x and y axis). In this way it’s not so much storytelling as it is persuasion – not persuasion towards a price, mind you, but coaxing into a role. Like the horse whisperer… the “Peddler whisperer”.

      Far from clashing with the old saw about “willingness to walk away” being the key to successful negotiation, it seems your theory actually subsumes that wisdom and in fact proves why this is the case: if one considers the continuum I described above, then the optimal pair of roles would be {“embarrassed seller trying to save face”, “disinterested buyer with face to give”}.

      Ben Lehman February 19, 2010 at 11:56 pm

      Wow, this reminds me exactly of my experiences with marketplace bargaining in China. Trying to explain to other Westerners how to do it* has never worked: from now on I’ll just point them at this article.

      yrs–
      –Ben

      * Me: You don’t just halve their first price. I know it says that in the guidebook but they all know that. Think about actual value.
      Them: But … I just want to buy it for the right price.
      Me: There is no right price! It’s … ARGH just let me do it.

      Venkat February 20, 2010 at 3:53 pm

      Heh! I’d like this post to be the definitive guide to bargaining, but I am afraid I am not good enough at it myself. I think this post works better as a description than as a prescription, but if somebody manages to “learn” how to bargain through this, I’ll be pleased.

      Jonathan July 8, 2011 at 9:56 pm

      In one interesting case in the Philippines, I called a driver to go to a little town. The autorickshaw ride INTO a town was very low, but the ride back out was much more expensive. I realized they were trying to screw me on the whole deal and had used the cheap ride in to extort money on the ride out. I went around to taxi drivers and other drivers trying to get a better price and the price kept going up. I VERY nearly just stiffed the driver when I got to my resort, which had armed guards (knowing I would never return to that town), but my friend convinced me that wouldn’t be nice.

      I think some analysis of the issue of “nice” would be worthwhile. It obviously isn’t “nice” to collude to rip of people with white skin, either. If the dealer “opponent” is willing to use any advantage they can, then when will most people abandon “nice” and use their own backhanded tactics? In my own final analysis, the reason I finally acquiesced was my friend’s fear of loss of face and the fact that such a small amount of money was at stake.

      DavidC August 3, 2011 at 1:16 am

      You’re probably more familiar with his work than I, but I thought Schelling’s book The Strategy of Conflict did a nice job connecting the ‘mathematical’ with the ‘softer’ elements. I read it a couple years ago, but I do remember that “focal points” (particular choices that stand out from a range of possibilities) were an important example in bargaining (but I think even more important in multi-agent games). I’m convinced the narratives you’re talking about have a much broader importance, but I think one way they could come into play is by providing focal points.

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