In the case of luxury brands, it is “This is a product for people who are willing (and able) to pay for quality)”. In the case of the discounters, it is “You will get the best possible deal every time you shop here.”
There’s a lot of truth to this, but there are some problems with it. First, sales are pretty far from “unheard of” at discounters. Consider dollar stores. Think this is a weird little niche? Between them, just Dollar General and Family Dollar operate about as many stores in the U.S. as does Starbucks. They are a huge part of what discounters are in the America. Here are current pages of sales at Dollar General and Family Dollar. Think about other competitors in each of Wal-Mart’s key segments. Here is a sale at Ross (“Dress for Less”) that provides at extra 10% to seniors on Tuesdays. Coupons are central to the grocery business. Here’s the Rite-Aid pharmacy (original name, “Thrif D Discount Center”) set of sales for this week. Here’s the current clearance sales circular for K-Mart. And so on.
It’s true that Wal-Mart has built a brand around the concept of Everyday Low Price (EDLP), but, while they weren’t the first retailer to do something like this, it was an innovation on their part. It is very far from inherent to discount retailing. The most important single driver of its introduction was that elimination of unpredictable spikes in demand allowed the creation of a much more cost-efficient supply chain. As with most of what Wal-Mart does, it was about cost reduction and logistical efficiency. Other discount retailers have attempted to copy this approach, sometimes successfully, but often not. Failures have mostly been due to inability to reap the potential cost reductions.
Different lower-end retailers have different strategies for EDLP vs. more promotional approaches (often called Hi-Lo), that tend to be driven by capabilities, installed infrastructure, historical brand / customer base and so forth. But in general, low-end retail tends to be a highly promotional / sales-oriented business, not the reverse.
These strategies tend to interact, and different retailers will often seek complementary niches. Not everybody who shops at discounters has the same psychology. Often, once Wal-Mart has entered a local market, for example, it can perversely increase the incentives for a Hi-Lo pricing approach for competitors, since Wal-Mart has already taken a disproportionate share of consumers for whom EDLP is most appealing.
Another factor that tends to influence whether a given retailer employs a no-discount strategy is the set of multi-dimensional trade-offs between the revenue decay from a product once it is put on a shelf, the velocity of inventory turnover for that product and the costs of holding the product in stock (both the opportunity cost of the capital tied up in inventory and actual cash costs). This is why Wal-Mart is not absolutely pure about EDLP. As Megan notes, you can sometimes get sales on electronics there, because they rapidly lose consumer value as new models are introduced. The same with clothing, where you will find seasonal clearance sales racks. This is one reason why you will often see explicit sales father up into income categories for women’s clothes (even more than men’s clothes, where fashion changes much more slowly, and therefore goods maintain value longer) and electronics than you do for other products.
It is true that there is normally less (explicit) discounting for high-end goods, all else equal. There is a lot, however. As per the prior comment, all else equal, you will tend to see this more for rapidly depreciating goods with significant holding costs and lower sales velocity. Another place you see it is very expensive items. Consider cars. Here’s an $87,000 Mercedes with “incentives” from the retailer. It’s harder to find sales (at least expressed publicly) for, say, Bentleys, which cost yet more. But what about your private jet? Here’s a Valentine’s Day promotional sale for private jet rental (“special value-added benefits from Avis, Sea Island, and Ermenegildo Zegna”!). Donald Trump has marked down his house from $125 million to $100 million. You can find discounts in almost any category and price level if the spend becomes a significant component of the buyer’s income or wealth. So it’s not so much “luxury brands” for which discounting is unheard of, but something more like “luxury brands for which the purchase price is small versus the typical buyer’s income, and either the retail experience is psychologically important or the item is a status symbol”. And, as with all such guidelines, there will doubtless be exceptions.