Pragmatic languages with universal grammars

This paper constructs the equilibrium for a specific code that can be seen as a “universal grammar” in a class of common interest Sender–Receiver games where players communicate through a noisy channel. We propose a Senderʼs signaling strategy which does not depend on either the game payoffs or the initial probability distribution. The Receiverʼs strategy partitions the set of possible sequences into subsets, with a single action assignment to each of them. The Senderʼs signaling strategy is a Nash equilibrium, i.e. when the Receiver responds best to the Senderʼs strategy, the Sender has no incentive to deviate. An example shows that a tie-breaking decoding is crucial for the block-coding strategy to be an equilibrium. Efficiency is analyzed by comparing how close ex-ante expected payoffs are to those of noiseless communication. Moreover, we study how long communication should be to achieve a given payoff-approximation.