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Kreps (1990) - Corporate Culture And Economic Theory (view source)
Revision as of 16:49, 28 April 2010
, 16:49, 28 April 2010no edit summary
*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 [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])
==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 [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).
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 [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.
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 [http://en.wikipedia.org/wiki/Geometric_series#Formula 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.
