Dynamic Deception

Abstract

We explore dynamic deception, such as arises in finance, war, or politics. Our framework subsumes repeated game reputation models, and also includes unbounded intensity models like insider trading as a limiting special case. Our game also generalizes Aumann and Maschler's 1966 paper on repeated games of incomplete information, allowing noisy action monitoring and impatient players.

We characterize the unique equilibrium of our competitive continuous time game between a resource-constrained informed player and a sequence of rivals who partially observe his action intensity. The intensity bound induces a novel strategic bias and serial mean reversion by the uninformed rivals. Adding to the reputation literature, we compute how long the informed player's informational edge lasts.

We then build on our model in three ways. We formulate informational sleuthing by the uninformed player, discovering that the value of information is concave if the intensity bound is large enough. We then allow the informed player to better conceal his actions at some cost, and find that obfuscation optimally rises in how deceived is the public. Finally, we allow the informed player to exploit an unexpected less noisy monitoring technology; the resulting disinformation exercise suffers from a nonconcavity, and is always boundedly large.

Keywords: Asymmetric Information, Reputation, Repeated Games, Continuous Time Games, Constant Sum

JEL Classification: C73, D82, D83, G14