Nash Equilibrium and information transmission coding and decoding rules

The design of equilibrium protocols in sender-receiver games where communication is noisy occupies an important place in the Economic literature. This paper shows that the common way of constructing a noisy channel communication protocol in Information Theory does not necessarily lead to a Nash equilibrium. Given the decoding scheme, it may happen that, given some state, it is better for the sender to transmit a message that is different from that prescribed by the codebook. Similarly, when the sender uses the codebook as prescribed, the receiver may sometimes prefer to deviate from the decoding scheme when receiving a message.Noisy channel, Shannon's Theorem, sender-receiver games, Nash equilibrium

Pragmatic Languages with Universal Grammars

This paper shows the existence of an equilibrium pragmatic Language with a universal grammar as a coordination device under communication misunderstandings. Such a language plays a key role in achieving efficient outcomes in those Sender-Receiver games where there may exist noisy information transmission. The Language is pragmatic in the sense that the Receiver’ best response depends on the context, i.e, on the payoffs and on the initial probability distribution of the states of nature of the underlying game. The Language has a universal grammar because the coding rule does not depend on such specific parameters and can then be applied to any Sender-Receiver game with noisy communication.grammar, pragmatic language, prototypes, separating equilibria