The result for the well-meaning company is harsh. Its advertising might hurt the rival in the sense that consumers pay fewer fees there, but it is increasing the number of sophisticated consumers and teaching them to choose the other guys. It is unlikely to draw in the sophisticates. “That business won’t make much money once you understand how the world works,” Mr. Laibson said. “What’s the benefit to the company?”

It is a far better business strategy to have the naïve subsidize the sophisticated. The way the market solves this problem, in other words, is not by educating consumers, but by having the sophisticated consumer exploit the opportunities. Sophisticated consumers are not really taking advantage of companies, nor are companies taking advantage of consumers, as much as companies are helping those sophisticated consumers take advantage of the less sophisticated consumer.

For example, you see an offer for a room at Nontransparent Hotel for $75 (which costs the hotel $100 to provide). The guy checking in behind you also rents a room, but will rack up $70 in fees from the minibar, the phone and garage parking (all of which cost the hotel $20 to provide). You, on the other hand, were not tempted by the minibar, used your cellphone for calls and took public transportation to the hotel. The other guy subsidized your room.

Smart consumers now have a strategy. They should go to the company offering the discounted product even if the company has loads of hidden fees. The sophisticated consumer then exploits the company by taking the below-cost product and shunning the fees. “It’s a perpetual battle between the firm that fools consumers into paying fees and the smart consumer who can avoid them,” Mr. Laibson said.

Getting cheaper goods and services subsidized by the naïve consumers works as long as you know what you could be charged. But it does not pay if too many people know the same thing.

Shrouding of information rarely goes away because there are new generations of myopic consumers and even the sophisticated consumers are forgetful or distracted and end up paying for add-ons. The professors say that new shrouding techniques constantly evolve as companies find fresh ways to generate additional revenue. “Now that the world is more complicated with more products, there are more opportunities for people to make mistakes,” Mr. Gabaix admits.

That said, outsmarting companies is hard work. Hewlett-Packard does not tell consumers the price-per-page cost of its printers on its Web site, for example. You have to hunt for the information and do the math yourself. Hotels in South Florida rarely tell you while you are making reservations or checking-in that you will face a $25 “resort fee,” which is ostensibly imposed to cover your use of the pool and deck chairs. A recent study of purchases on eBay showed that consumers responded to direct costs more than to shipping costs.