# Game Theory, Chain Store Paradox and Wal-Mart

“If I had to play the game in the role of the incumbent, I would follow the deterrence theory. I would be very surprised if it failed to work. From my discussions with friends and colleagues, I get the impression that most people share this inclination.”

-Reinhard Selten

Reinhard Selten is a German economist, who won the 1994 Nobel Memorial Prize in Economics, which he  shared with John Harsanyi and John Nash. In game theory he came up with interesting concept of Chain Store Paradox. This concept is widely used in market competition and reputation.

Classical example given by Selten is that of a retail chain that has 20 stores in 20 different cities. After a period of time some local entrepreneur in one of the cities becomes their rival by opening a store which competes with store of retail chain. It can happen in 3-4 other cities.

Now the chain stores must decide whether to fight emerging entrepreneurs with price wars or to simply coexist. By using game theory, Selten theorized that there were two possible options…

1. Launching a price war with an emerging company to prevent others from joining the market
2. Let the competitors exist.

The payoff matrix of game is shown below.

In case of retail chain payoff is sum of payoffs of all 20 stores, for competitor it is that of his store only ex. if players decide to cooperate, payoff for retail chain is 20×2=40, for competitor it is 2. So payoff of retail chain will depend on which strategy is follows in each of the cities, ex. it may decide to fight with competitors in 8 cities, cooperate in  3 cities and deter competitor from competing in 9 cities, then payoff for retail chain = ( 8×0)+(3×2)+(9×5)= 51.

In first option the retail chain will get into price war, while it may make losses in the beginning, the competitor cannot sustain losses for long time and will eventually drop out. If it uses this strategy with first few competitors, this will act as deterrence for others who are planning to set up shop. They may invest money elsewhere.

Organisations like Wal-Mart use this strategy. It is difficult for competitors to match prices offered by Wal-Mart. Another example is Amazon. Amazon entered price wars to drive out competitors, and this strategy has worked well for them, causing them to beat out Zappos and many other competitors. By using this strategy they build reputation of being aggressive.

While price wars ensure that consumers always get the lowest prices possible, they also cost the company a huge portion of their profits, and if a company does not have a large-enough share of the market, they may end up bankrupt.

“Pretty much, Apple and Dell are the only ones in this industry making money. They make it by being Wal-Mart. We make it by innovation.”

– Steve Jobs

Some on the other hand go for second option i.e. they do not get into price war and let competitors exist. They play a different game; they use innovation to beat competition ex. Apple employs the second option of the chain store paradox, in which they refuse to enter a price war and continue to allow competitors to exist. They offer high-quality goods at premium price to customers, which their competitors cannot. This strategy is used by Apple to build reputation of being innovative.