## Crushing the competition – at any price

It was Selten’s chain store paradox that first attracted me to economics, with a heady mixture of logic, psychology and military strategy

Forty years ago a German economist, Reinhard Selten, published a working paper with the title “The chain store paradox”. It was simple and profound and showed a discomfiting disconnect between the fashionable mathematical tools known as “game theory” and the recommendations of common sense.

This is the set-up. Imagine a chain store with 20 branches, one in each of 20 small towns. Lacking any competition, these branches charge high prices and are lucrative. In each town, an entrepreneur is considering opening a rival shop. These 20 local entrepreneurs will, one by one, decide whether to compete against the chain store or to sink their capital into something else.

Much depends on the chain store’s response to a competitor. The chain store could be aggressive, ruthlessly slashing prices. That would make life painful for both retailers. The entrepreneur, finding herself committed to a low-margin business, would wish she’d invested her money in something else. Or the chain store could be accommodating, letting prices stay high and sharing a profitable market. So what will happen?

Selten offered two lines of reasoning. One of them is intuitive: the chain store will launch a brutal price war against the first entrepreneur with the temerity to set up as a rival. It will lose money in that market but other entrepreneurs will take note of the bloodbath and will steer clear. The reward for giving up one or two cosy local duopolies is that in the other 18 or 19 towns the chain store will remain a monopolist. The chain store will use price wars as a deterrent, and the deterrent will work.

The alternative line of reasoning is a matter of inductive logic. Consider the 20th and final town. Deterrence is pointless there, since there are no further entrepreneurs to deter. The chain store may as well eschew a price war and accommodate the competitor. Yet if it is obvious that there will be no price war in the 20th town, what about the 19th? If everyone knows there will be no price war in the 20th, what would a price war in the 19th be designed to achieve? Again, deterrence is pointless. But if neither the 20th nor the 19th town will see fierce competition, what is the point of deterrence in the 18th town? The logic rolls back to the beginning of the game; it shows that deterrence is futile and will not be used at any stage.

Selten, an expert in game theory, knew that the second scenario was logically watertight. But as a practical matter he found the first scenario “much more convincing”. If he were the chain store, Selten wrote, he would launch price wars in the hope of deterring later competitors. “I would be very surprised if it failed to work.”

If deterrence works in practice, how to make it work in theory? Selten devoted himself to sharpening up game theory to deal with such apparent paradoxes, and in 1994 he was one of two men to share a Nobel memorial prize with John Nash, he of A Beautiful Mind.

One step forward is to add some vagueness or uncertainty. Can we be sure that the decision will be repeated only 20 times? Can we be sure that the competitors really understand each other? What if the chain store manager is a thug who loves to crush the competition and cares not at all for his shareholders’ dividends? Deterrence becomes a logical solution as well as an intuitive one.

It was Selten’s chain store paradox that first attracted me to economics, with a heady mixture of logic, psychology and something approaching military strategy. And it is a hypothetical game with some close parallels today.

Brad Stone’s excellent book, The Everything Store: Jeff Bezos and the Age of Amazon, paints Amazon’s founder to be a visionary entrepreneur, dedicated to serving his customers. But it also reports that Bezos was willing to take big losses in the hope of weakening competitors. Zappos, the much-loved online shoe retailer, faced competition from an Amazon subsidiary that first offered free shipping and then started paying customers \$5 for every pair of shoes they ordered. Quidsi, which ran Diapers.com, was met with a price war from “Amazon Mom”. Industry insiders told Stone that Amazon was losing \$1m a day just selling nappies. Both Zappos and Quidsi ended up being bought out by Amazon.

When the weapons of war are low prices, consumers benefit at first. But the long term looks worrying: a future in which nobody dares to compete with Amazon. Apple is a striking contrast: the company’s refusal to compete aggressively on price makes it hugely profitable but has also attracted a swarm of competitors.

Consider a grimmer parallel. Vladimir Putin’s Russia is the chain store. Georgia, Ukraine and many other former Soviet states or satellites must consider whether to seek ties with the west. In each case Putin must decide whether to accommodate or open costly hostilities. The conflict in Ukraine has been disastrous for Russian interests in the short run but it may have bolstered Putin’s personal position. And if his strategy convinces the world that Putin will never share prosperity, his belligerence may yet pay off.

I feel a little guilty comparing Bezos and Putin. My only regret about Bezos’s Amazon is that there aren’t three other companies just like it. I do not feel the same about Putin’s Russia.

Also published at ft.com.