Noisy Talk

We examine the possibilities for communication between agents with divergent preferences in a noisy environment. Taking Crawford and Sobel's [4] (noiseless) communication game as a reference point, we study a model in which there is a probability epsilon in (0, 1) that the received message is a random draw from the entire message space, independent of the actual message sent by the sender. Just as in the CS model, we find that all equilibria are interval partitional; but unlike in CS, coding (the proportion of the message space used by any given set of types) is of critical importance. Via the appropriate coding scheme, one can construct equilibria that induce finitely many, a countable infinity or even an uncountable infinity of actions. Furthermore, for a given number of actions, there is typically a continuum of equilibria that induce that many actions. Surprisingly, the possibility of error can improve the prospects for communication. We show that for small noise levels there is a simple class of equilibria that are almost always welfare superior to the best CS equilibrium. There exists an optimal noise level for which these equilibria achieve the efficiency bound for general communication devices. Furthermore, for a range of biases introducing any amount of noise can be beneficial.