Chain Store Paradox

What if you’re trying to keep competition out of multiple markets? Imagine that Acme operates in 10 markets, and, while it currently has no competition, rivals are considering moving into each of its areas. The rival enters a market by building a store or factory, so once a rival enters a market, it won’t leave.

Could Acme use limited-range suicide pricing as a warning shot to prove its willingness to fight? If a competitor entered one area, Acme could set extremely low prices for just that one market. True, it would lose money with that store, but might it not scare away the competition from other markets? If for some reason the competition didn’t take the hint and entered two markets, then Acme could use suicide prices for the stores in both of these markets. Would not such a strategy keep at least some of Acme’s stores safe from competition? Does repeated play add credibility to Acme’s suicide pricing threat?

Interestingly, even if Acme operates in multiple markets, it couldn’t effectively use suicide pricing to deter entry. Game theorists refer to this counterintuitive result as the chain store paradox. To understand the chain store paradox, consider why Acme might want to impose suicide pricing in market #1. By setting suicide prices in market #1, Acme says to rivals:

I set suicide prices in market #1 after you entered, so you should believe that I would set suicide prices in any other market you enter. Since you can never make money in any market where I charge extremely low prices, you should never enter any of my other markets.

While this statement seems logical, consider what would happen if the competition has already entered 9 markets and considers entering a tenth. Say that the competition would enter the tenth market if and only if Acme did not set suicide prices for this market. Would Acme ever charge suicide prices in its tenth market? No! The only reason Acme would ever set suicide prices would be to deter future entry, since setting suicide prices in a given market means you lose money in that market. If the competition had already invaded all of Acme’s markets, there would be absolutely no point in Acme trying to deter future entry. Consequently, all competitors know that Acme would never set suicide prices in the tenth market if its other 9 markets had already been invaded.

Now consider this: should Acme ever set suicide prices in the 9th market? Again, the only point of setting extremely low prices is to deter entry in future markets. The supposed purpose of suicide prices is to send a signal to the competition it had better not enter future markets because if it did, then you would set suicide prices in these markets, too. We have already established, however, that Acme would never set suicide prices in market 10. Thus, there would be no point in setting suicide prices in market 9 because doing so would not send a signal about what you would do if the competition entered all 10 of your markets. Everybody already knows that in market 10 you will set “reasonable” prices regardless of whether the competition enters.

Given that Acme will never use suicide prices in the ninth and tenth invaded markets, should it ever bother using them in market 8? Again, the only possible purpose of setting low prices is to signal what you would do if the competition entered even more markets. Setting suicide prices in market 8 constitutes a threat to the competition that if it entered markets 9 or 10, you would set suicide prices there, too. No one, however, should believe this threat, since it would never be in your self-interest to set extremely low prices in markets 9 and 10. Consequently, you shouldn’t ever bother setting them in market 8.

Obviously, this chain of logic continues, and you shouldn’t set suicide prices in market 7, 6, 5, and so on. This reasoning applies all the way back to market 1. Acme, consequently, can never use suicide prices to deter entry.