Mind Your Decisions

Rapid Inventory Turnover: How Clothing Sales Are Going Away. The Problem of Using Money Tips

Every Tuesday is a Game Theory article at Mind Your Decisions.

I discovered a money tip before I moved to college. I was living in Illinois and it was a chilly September. But I actually needed more summer clothes because I was moving to warmer California weather at Stanford. Since I was shopping out of season, most what I wanted was on sale and heavily discounted. It suggested a larger strategy to me.

This tip is one of my eccentric frugality measures: I buy most of my clothes out of season when they are on sale and store them until needed. I put up with limited selection and less popular clothes in exchange for deep discounts. I think about my strategy as a sort of “seasonal arbitrage.”

I’m going to take a moment now to explain the “wait for a sale” strategy in the language of game theory. I’m going to describe a simplified scenario where I buy a shirt from one store. The example will have some flaws, but read on and I assure you that it will illustrate some important game theory points.

A New Hope for Buying Shirts

I’m going to assume the following details to the game:

Value of shirt to me: $50
Value of buying a shirt to me: $50 – x, where x is the price I pay

Cost of shirt to store: $10
Value of shirt to store: P - $10, where P is price store sells

Assume the store initially retails the shirt for $40. If I buy the shirt, I get a $10 payoff and the store gets a $30 payoff. If I do not buy the shirt, the store can either decide to discount the shirt or not.

If I wait, let’s assume I buy only if the store discounts the shirt to $20. If the store discounts, then I get a $30 payoff and the store gets a $10 payoff. If the store does not discount, then I get a $0 payoff (I end the same as I started) and the store gets a -$10 payoff to represent the loss on an unsold shirt.

I can summarize the interaction in the following game tree (my actions and payoffs are in black, and the store’s are in blue):

Using the game tree, I can show why waiting for a sale works.

I start by analyzing my choice of “wait.” If I choose “wait,” it is clear that the store will pick “discount” to achieve a $10 payoff instead of the alternative -$10 payoff. Thus, if I choose “wait,” I will get a nice $30 payoff. On the other hand, if I choose “buy now” I only get a $10 payoff. So ultimately, the game will resolve with me waiting for the sale and the store discounting.

This is by no means a full description of business, but it is one way to think about it. And for my purposes, the strategy seems to work in practice. I also know many frugal people who also wait for sales. They are the kinds of people with strong discipline (though questionable fashion sense) and are the ones who check the clearance racks first. I am glad to have found a money tip to buy clothes for cheap. But I doubt it can last for too long.

The Clothing Empire Strikes Back

There is a problem with money tips: once you find a good one as a customer, it often becomes popular enough that it hurts profits, and thus businesses will respond back. This is true because the interaction is some thing of a “zero-sum” game: one person’s gain (low prices for customers) comes at another person’s loss (businesses having lower profits).

Stores are not too happy that customers are waiting for sales. It is inefficient for them to hold inventory and they are not selling as much volume at retail as they wish.

In response, they are changing their retail practices. Check out what one store is doing:

At Zara, the Spanish-owned clothing store, the turquoise and beige tunic on sale one day will be replaced by a yellow ruffled sundress the next. If you want the tunic, you have to buy it now, instead of waiting for a sale. According to the company, stores’ entire contents are turned over every three to four weeks, and new clothes arrive twice a week.

What’s the explanation for the new business practice?

“They’re training their customers to buy an item if they see something they like, because next week it might not be there,” says Robert Swinney, a doctoral student at the University of Pennsylvania’s Wharton School. “That way you get people to buy at full price.”

(The full story describes other tactics stores use–you can check it out here)

The bottom line is interesting too. Swinney’s research demonstrates that companies can raise profit by an average of 67% with the new strategy.

What are stores doing on a game theoretic level? They are using a tactic I earlier discussed about how to limit options to improve results. The stores are credibly showing they will not discount and this will punish customers who wait. The stores pursue this at the cost of a few unsold shirts.

In our game tree, this means they are removing the “discount” branch, and so the game is now:

When I analyze this game, it makes rational sense for me to buy right away and get a $10 payoff. If I wait too long, the shirt will no longer be available to buy, so I would end up with a $0 payoff.

The Return of the Customer

Of course, as stores begin to implement these new retail strategies, I can be sure people will respond with money tips to get cheap clothes. Let’s say that people are fed up with high prices. If enough people hold off on buying, the stores will have much unsold inventory. This could make it costly enough for businesses that the quick-rotating inventory strategy would be less profitable than traditional inventory methods.

This clothing story is a caveat about money tips in general because many tips become useless when lots of people start doing them. Companies respond and try to maintain profits. It can be time-consuming to keep up with which tips are useful and which ones are things of the past.

I think a better strategy is to educate yourself on why tips work so you make better decisions under any scenario. For instance, the clothing problem involves the important ideas of arbitrage, zero-sum games, and “limiting your options.” These are concepts that come up in all sorts of personal finance decisions. Besides being a smarter person, you can start using the ideas to out-game less knowledgeable opponents and become a better consumer.