Kreps (1990) - Corporate Culture And Economic Theory

• 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.