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.

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:

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.

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.