A variation on the prisoner's dilemma

17 September 2004

Let us suppose there there exists a small town, which has two bakers. Currently, the bakers sell their bread for $1:50 per loaf. Both bakers have been in the business a long time, and their cost structure for bread is pretty much the same. It costs them $1:00 to produce a loaf.

So, their profit per loaf is 50 cents. Each baker sells the same number of loaves (800) each day. So, in total, each baker is making $400 in profit per day.

After doing some (very good) market research, one of the bakers discovers that dropping the price by 10 cents, will increase sales by 30%. The competitor’s sales will decrease by a similar amount. In other words, if one baker drops the price, they will sell 1040 loaves and by making a profit of 40 cents each loaf, the baker will get $416 in profit. Of course, the other baker is now only selling 560 loaves, and making $280 dollars.

Should both bakers drop their price to $1:40 then there will be no change in the number of loaves sold by each baker (800), and their total profit will be $320.

So, should either baker drop the price of bread?

In the original prisoner’s dilemma if there was only one change to sell bread then the ‘best’ thing either baker can do is drop their prices. However, if there are likely to be repeated rounds, then the baker should wait and see if the other baker drops their price.

Of course the problem becomes more complex when there are more bakers in the town–with many bakers, breaking ranks can lead to the classical economics situation of the “tragedy of the commons”. But, I feel, that at the heart of these type of situations is the issue of trust. Can we trust our competitor to do the right thing? And yet… and yet classical market theory seems to be based on people acting in their own (self) interest.

As an aside, has anyone tried the 100 prisoner’s problem? I’m surprised this hasn’t shown up in BCG interviews yet (or has it?).