Kreps (1990) - Corporate Culture And Economic Theory

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• This page is referenced in BPP Field Exam Papers

Reference(s)

Kreps, D. (1990), "Corporate Culture and Economic Theory," in J. Alt and K. Shepsle, Eds. Perspectives on Positive Political Economy, Cambridge University Press (Book excerpts available through Google Books)

Abstract

No abstract available - this is a book chapter.

Summary

Until Kreps market beliefs were tied to a single entity or identity. Krep's contribution was to seperate identity from entity to create a long-lived reputation.

A Folk Theorem Model

Suppose there is a buyer and a seller involved in an infinitely repeated game. This game is like an infinitely repeated one-sided prisoner's dilemma or the infinitecentipede game. The game is sequential and the buyer moves first (though the same solution results from a simultaneous move game).

The buyer has actions:

[math]A_B \in \{Trust, Not Trust\}\,[/math]

The seller has actions:

[math]A_S \in \{Honor, Abuse\}\,[/math]

The pay-offs [math](\pi_B, \pi_A)\,[/math] are:

[math]Not Trust: (0,0)\,[/math]

[math]Trust, Abuse: (-1,2)\,[/math]

[math]Trust, Honor: (1,1)\,[/math]

The unique Nash equilibrium of the stage game is [math]Not Trust\,[/math], solved by backwards induction. However, when the game is infinitely repeated, [math]Trust, Honor\,[/math] can be sustained using a Grim Trigger, as per the Folk Theorem. The proof is simple - use the continuation values of the 'supported' equilibrium against those of the 'punishment' equilibrium for both players, and take the strictest requirement on the discount factor.

For the buyer:

[math]\underset{\text{Supported Cont. Value}}{\underbrace{ 1+\sum_{t=1}^{\infty} \Beta^t \cdot 1 }} \ge \underset{\text{Punishment Cont. Value}}{\underbrace{0}}\,[/math]

For the seller:

[math]\underset{\text{Supported Cont. Value}}{\underbrace{ 1+\sum_{t=1}^{\infty} \Beta^t \cdot 1 }} \ge \underset{\text{Punishment Cont. Value}}{\underbrace{2+0}}\,[/math]

Using the sum of an infintie geometric series:

As [math]n\,[/math] goes to infinity, the absolute value of [math]r\,[/math] must be less than one for the series to converge. The sum then becomes

[math]s \;=\; \sum_{k=0}^\infty ar^k = \frac{a}{1-r}\,[/math]

The strictest requirement on the discount factor is given by the seller's contraint which yields:

[math]\frac{1}{1-\beta} \ge 2 \; \therefore \beta \ge \frac{1}{2}\,[/math]

Short Lived Agents

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:

For [math]t=1\,[/math]:

• 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\gt 1\,[/math]:

• the buyer plays [math]Trust\,[/math] iff the seller has a name and the name is not associated with any past abuses, and [math]Don't Trust\,[/math] otherwise
• If [math]\forall t'\lt 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\gt 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:

1. The 'good' equilibrium above is "supported by its own structure", but the beliefs are not payoff relevant
2. There are other equilibria including "I'll never trust because I'll be abused" and the 'good' equilibrium is the most fragile.
3. There are no dynamics of reputation - the reputation doesn't get better when it is honored
4. The 'bond' (the reputation) isn't priced - furthermore the economy isn't really closed, the value of the reputation drops to zero dependent on actions, but no-one collects the value.