Buying Sunglasses in Brazil (or how to restore commitment in bargaining)

The last time our family went to Brazil, our little ones arrived poorly prepared. We did not bring any sunglasses. Why would we? London’s winter sky rarely requires them. Brazil? That’s a different story. Upon our first five-minute walk between the luxurious apartment blocks, we were struck by the brightest of sunlight. Instead of buying coconut water and a delicious mamão formosa for breakfast, the children and I stumbled into pharmacies. Several of them, because in Brazil’s more affluent neighbourhoods, these stores exist at most street corners. We were looking for a rotating display stand of cheap, mass-produced plastic sunglasses in every colour. Once the children had made their selection—pink and blue, presumably—I expected us to walk over to the counter, greet the vendor and pay. Alas, to no avail. I did not know Brazil well enough. The more affluent Brazilians buy their sunglasses from credentialed optician boutique stores following an extensive consultation and bargaining process. The initial price tag and product segment of sunglasses sold certainly reflect this. Those unhappy with their choice set can turn to informal street vendors or buy online (where the authenticity of sun protection factors will be guesswork).

I will not tell you why Brazilians cannot buy cheap and safe sunglasses. Seller market power certainly plays a role here. (Incidentally, I have written on the rationale behind sparse menus.) I do, however, wish to mention that the Brazilian state is not entirely innocent in fostering the described market structure. The state (per health regulator ANVISA regulation RDC n44/2009) prohibits pharmacies from selling corrective lenses. To further enshrine market power, a proposed 2011 law would have required an ANVISA license for all shops that sold eyewear products (including sunglasses). Thankfully, it never came to that. But it reflects poorly on the welfare-harming impulses of some politicians.

What I will tell you about are practical remedies for bargaining problems. Our teacher: the Brazilian sunglasses vendor. To get there, we better resume the story.

Our second attempt at buying sunglasses began with better preparation. Having encountered no optician store before—however two supermarkets and three pharmacies—our dear friend informed me of a street crossing nearby with four optician stores, almost side-by-side. We split, and our then two-year-old son and I ventured out. One store looked rather exclusive. People more attuned to fashion would recognize the picture-perfect models wearing designer glasses displayed in the window. For better or worse, this boutique did not sell any sunglasses for children and, in any case, appeared above and beyond my desired budget.

Ill judgment sent me to the store farthest away across the crossing. Not every consumer can gauge the price level of a store from its outside appearance. I certainly do not. The store was eight metres wide, the inside twice as deep. Soon, I noticed that this store, furnished in décor no less fashionable, sold the same expensive brands amid the same pleasantly chilly temperatures—too late, however, to make an early exit. As my son and I entered, a first vendor held the door for us. Immediately after, a second vendor greeted us and walked us over to a table. We shook hands with a third, more senior vendor and then sat down with him. A fourth vendor brought me a glass of water and complementary lemonade for my son, while a fifth vendor offered to prepare me a cup of coffee. By now, I had lost track of the total number of vendors present, but in my recollection, a sixth vendor was seated at the counter. I was on a first-name basis with three of them.

The reader could be forgiven for recalling a passage from Sir Arthur Lewis’ article Economic Development with Unlimited Supplies of Labour. There, Lewis writes: ‘Most businesses in under-developed countries employ a large number of `messengers,’ whose contribution is almost negligible.’ I do not wish to imbue this impression onto optician stores in contemporary Brazil. These vendors are professionals who are employed for their ability to create value. How do I know this? I once sat in a car with the highly successful owner of several optician stores in Brazil. She thought deeply about staffing. Similar to London restaurants, these optician stores operate as part of a franchise, with staff rotating across the owner’s various locations.

But I am digressing too much. Our objective is to learn bargaining tricks from the lesser ranks, not about matching theory from the boss. In my story, the choice set was poor. The store was selling three infant-sized sunglasses at the time, all made of heavy metal. To add insult to injury, the initial price tag was north of £100 (700 Reais). At this point, I could have stormed out, my two-year-old in tow. But that would have reflected poorly on my manners—and my son’s mood: he hadn’t yet finished his lemonade. So, we stayed. To my credit, I did manage to decline the coffee.

The slightly disturbing aspect about bargaining is its possibly infinite nature, especially when leaving is not an option. Could game theory help me out? Infinite horizon-bargaining games were first analysed by Rubinstein. Bargaining ends when both parties accept the last-proposed price or when the buyer makes an exit. Until such an event occurs, many prices can be proposed. Of course, this does not happen in a theoretical equilibrium. Here, the buyer and the seller reach an agreement without costly delay. Possible continuations of the bargaining game merely define the threats that pin down prices. Explaining why this is so is one of the distinctive pleasures that only game theory lecturers get to enjoy in life. But I did not expect Rubinstein bargaining to unfold, not least because coffee and lemonade have no part in it. More fundamentally, the Rubinstein solution to the infinite-horizon bargaining game is far from ideal from the vendor’s perspective. The vendor’s ability to downward-revise prices indefinitely constrains the buyers’ price expectations. Put simply, if I can expect further discounts, my willingness to accept high prices is inhibited. As such, the Rubinstein solution represents too great a compromise from the seller’s point of view.

Here is what happened in real life. My vendor, let’s call him Fulano since I am bad with names, started dropping the price. In Brazil, this was to be expected. Unlike in Rubinstein’s game, Fulano had to pick up psychological cues from my polite utterings to gauge my willingness to pay. The price was bound to drop, but it couldn’t continue indefinitely lest Fulano lose his job. My inner theorist kept wondering: How could Fulano bring this to a close? How could he convince me that his final offer was indeed his last one? How to end this with a definitive ‘that’s it, the price will not fall any further—take-it-or-leave-it’ without leaving me incredulous?

Here is the principle that I cannot teach through formal proof or theorem. Instead, practitioners will readily share it with you: To restore commitment power, a negotiator must defer decision rights (accepting or rejecting a given price) to an outside party. I have seen many versions of it play out in real live, and the Brazilian opticians’ approach illustrates it perfectly. After negotiating the price down over several rounds (eventually reaching 60% of the initial price tag), my vendor offered a final, significant discount. He presented this discount as an uncertain favour to me. It was presented as a favour because the total discount was substantial—less than half the initial price. It was uncertain because the vendor needed to call the store owner for approval. Calling the owner is a clever tactic. First, it ties their hands; they will not call their boss twice on my behalf. It is also psychologically astute in that it turns Fulano and me into allies. Previously, all the pampering with coffee and lemonade had glossed over the fact that we were engaged in a tug-of-war over the price. From a financial perspective, Fulano’s gain was my loss. Once Fulano made the final call, we were adversaries no more; both of us wanted the deal. (Of course, the very fact Fulano had picked up the phone prematurely hurt me, but human psychology can be artful in ignoring such inconvenience.)

Epilogue: Did Fulano’s boss accept the price Fulano suggested? That’s beside the point. Despite negotiating, I had never agreed to Fulano’s price. And when Fulano’s boss said ‘yes,’ I did the unexpected: I politely said, ‘I’ll think about it,’ and regretfully bid farewell to the three vendors I knew by name, as well as the other three. If I’m going to spend a significant amount of money, I want to be sure the sunglasses won’t pose a health hazard if my son wears them while playing football. So much love wasted. But despair not; it was all part of lifelong learning. I eventually visited another store in a different part of town, where I met the wonderful Leticia. During our haggling, I discovered that the sales strategy I had encountered was quite common, albeit with a twist. When it was Leticia’s turn to call the boss for an even steeper discount on a branded bundle, the price actually went up. And despite not being served coffee (it was too late in the day), I decided to accept the offer this time.