Difference between revisions of "Kreps (1990) - Corporate Culture And Economic Theory"

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(New page: ==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 exce...)
 
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*This page is referenced in [[BPP Field Exam Papers]]
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==Reference(s)==
 
==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 [http://books.google.com/books?hl=en&lr=&id=JBrDXvye-1UC&oi=fnd&pg=PA221&dq=Kreps,+D.++%22Corporate+Culture+and+Economic+Theory&ots=d4JUQusjjf&sig=7RVgXjAlocVC8FDJd2Ke1MsbjxY Google Books])
 
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 [http://books.google.com/books?hl=en&lr=&id=JBrDXvye-1UC&oi=fnd&pg=PA221&dq=Kreps,+D.++%22Corporate+Culture+and+Economic+Theory&ots=d4JUQusjjf&sig=7RVgXjAlocVC8FDJd2Ke1MsbjxY Google Books])
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==Abstract==
 
==Abstract==
 
No abstract available - this is a book chapter.
 
No abstract available - this is a book chapter.
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==Summary==
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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.
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==A Folk Theorem Model==
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Suppose there is a buyer and a seller involved in an infinitely repeated game. This game is like an infinitely repeated one-sided [http://en.wikipedia.org/wiki/Prisoner%27s_dilemma prisoner's dilemma] or the infinite[http://en.wikipedia.org/wiki/Centipede_game centipede game]. The game is sequential and the buyer moves first (though the same solution results from a simultaneous move game).
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The buyer has actions:
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:<math>A_B \in [Trust, Not Trust]\,</math>
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The seller has actions:
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:<math>A_S \in [Honor, Abuse]\,</math>
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The pay-offs <math>(\pi_B, \pi_A)\,</math> are:
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:<math>Not Trust: (0,0)\,</math>
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:<math>Trust, Abuse: (-1,2)\,</math>
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:<math>Trust, Honor: (1,1)\,</math>
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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 [http://en.wikipedia.org/wiki/Grim_trigger Grim Trigger], as per the [http://en.wikipedia.org/wiki/Folk_theorem_(game_theory) 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.
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For the buyer:
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<math>\underset{\text{Supported Continuation Value}}{\underbrace{ 1+\sum_{t=1}^{\infty} \Beta^t \cdot 1 }} \ge \underset{\text{Supported Continuation Value}}{\underbrace{0}}\,</math>
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For the seller:
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<math>\underset{\text{Supported Continuation Value}}{\underbrace{ 1+\sum_{t=1}^{\infty} \Beta^t \cdot 1 }} \ge \underset{\text{Supported Continuation Value}}{\underbrace{2+0}}\,</math>
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Using the [http://en.wikipedia.org/wiki/Geometric_series#Formula sum of an infintie geometric series]:
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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
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:<math>s \;=\; \sum_{k=0}^\infty ar^k = \frac{a}{1-r}\,</math>
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The strictest requirement on the discount factor is given by the seller's contraint which yields:
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:<math>\frac{1}{1-\beta} \ge 2 \; \therefore \beta \ge \frac{1}{2}\,</math>
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==Short Lived Agents==
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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.

Revision as of 16:49, 28 April 2010


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


For the seller:

[math]\underset{\text{Supported Continuation Value}}{\underbrace{ 1+\sum_{t=1}^{\infty} \Beta^t \cdot 1 }} \ge \underset{\text{Supported Continuation 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.

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