Changes

The folk theorem implicitly requires that agents are long lived - the need a memory of whether anyone ever defected in the past to choose their strategy. Kreps's innovation was to create a long lived entity that is seperate from the identity of the individual players. Essentially the seller can buy a name for a price <math>p\,</math>, and if he does not abuse the name he can then, at the end of the period sell the name for the same price. If he does abuse the name it becomes worthless.

Suppose the strategies for the buyer and seller are as follows:

*The buyer plays <math>Trust\,</math> for sellers with a name and <math>Don't Trust\,</math> for sellers without a name

*The seller creates a name and <math>Honors\,</math> trust

For <math>t>1\,</math>:

*If <math>\forall t'<t\,</math> there has been no abuse by a name, <math>Buy\,</math> the name for price <math>p\,</math> and <math>Honor\,</math>

*Otherwise <math>Don't Buy\,</math> the name and <math>Abuse\,</math>

Therefore the stage utility maximization for the seller who has bought a name is:

<math>\underset{\text{Buy name and Honor}}{\underbrace{-p +1 +p}} \ge \underset{\text{Buy Name and abuse}}{\underbrace{-p + 2}}\,</math>

Which providing <math>p>1\,</math> gives a unique state game Nash equilbrium of <math>Buy\,</math> name and <math>Honor\,</math>.

Thus Kreps has created a perpetual entity (the bearer of the reputation) to overcome the short-livedness of the players. However, there are a number of critiques: