Entropy and Some Recent Applications in Economic Theory
George J. Mailath May 1, 2012
• Lecture 1: Basics of Entropy and Relative Entropy, with an application to Reputations In this lecture, I will introduce entropy and relative entropy, describe the relevant properties, and then illustrate their usefulness in obtaining a remarkably short and unified derivation of the perfect monitoring and imperfect monitoring reputation bounds (for a non-entropy derivation, see Mailath and Samuelson (2006,§15.3–15.4)).
– Cover and Thomas (2006) is an excellent introduction to Information Theory.
– The derivation of the reputation bounds is from Gossner (2011), with an extension to impermantent types in Ekmekci, Gossner, and Wilson (2012).
• Lecture 2: An application to common learning.
This lecture applies relative entropy to obtain some positive results on common learning (Cripps, Ely, Mailath, and Samuelson, 2008) when the underlying stochastic process has intertemporal dependence (Cripps, Ely, Mailath, and Samuelson, 2012??).
References
COVER, T. M.,AND J. A. THOMAS(2006): Elements of Information Theory. John Wiley & Sons, Inc., New York, second edn.
CRIPPS, M. W., J. C. ELY, G. J. MAILATH, ANDL. SAMUELSON(2008): “Common Learning,”
Econometrica, 76(4), 909–933.
(2012??): “Common Learning with Intertemporal Dependence,” International Journal of Game Theory, forthcoming.
EKMEKCI, M., O. GOSSNER, AND A. WILSON (2012): “Impermanent Types and Permanent Reputations,” Journal of Economic Theory, 147(1), 162–178.
GOSSNER, O. (2011): “Simple Bounds on the Value of a Reputation,” Econometrica, 79(5), 1627–
1641.
MAILATH, G. J., AND L. SAMUELSON (2006): Repeated Games and Reputations: Long-Run Relationships. Oxford University Press, New York, NY.
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