Information-Theoretic Limits of Strategic Communication

34 Pages Posted: 25 Jul 2018

See all articles by Maël Le Treust

Maël Le Treust


Tristan Tomala

HEC Paris - Economics & Decision Sciences

Date Written: July 13, 2018


In this article, we investigate strategic information transmission over a noisy channel. This problem has been widely investigated in Economics, when the communication channel is perfect. Unlike in Information Theory, both encoder and decoder have distinct objectives and choose their encoding and decoding strategies accordingly. This approach radically differs from the conventional Communication paradigm, which assumes transmitters are of two types: either they have a common goal, or they act as opponent, e.g. jammer, eavesdropper. We formulate a point-to-point source-channel coding problem with state information, in which the encoder and the decoder choose their respective encoding and decoding strategies in order to maximize their long-run utility functions. This strategic coding problem is at the interplay between Wyner-Ziv’s scenario and the Bayesian persuasion game of Kamenica-Gentzkow. We characterize a single-letter solution and we relate it to the previous results by using the concavification method. This confirms the benefit of sending encoded data bits even if the decoding process is not supervised, e.g. when the decoder is an autonomous device. Our solution has two interesting features: it might be optimal not to use all channel resources; the informational content impacts the encoding process, since utility functions capture preferences on source symbols.

Suggested Citation

Le Treust, Maël and Tomala, Tristan, Information-Theoretic Limits of Strategic Communication (July 13, 2018). HEC Paris Research Paper No. ECO/SCD-2018-1288, Available at SSRN: or

Maël Le Treust

ENSEA/ETIS - UMR CNRS 8051 ( email )

6, avenue du Ponceau
Cergy-Pontoise, 95014

Tristan Tomala (Contact Author)

HEC Paris - Economics & Decision Sciences ( email )

1 rue de la Liberation
Paris, 78351

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