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This article investigates the role of noise in a multidimensional signalling game. A monopolist that offers a high- or low-quality product can signal its quality to consumers through its selection of price and advertising. It is shown that when the advertising channel is noisy there is no separating equilibrium where the monopolist will simultaneously employ both signalling mechanisms. Advertising will take place only when price is uncorrelated to quality. Furthermore, the noise complicates the process of consumer inference. This enables a low-quality firm to take advantage of consumer ignorance by partially mimicking the strategy of the high-quality firm.
Mark N. Hertzendorf (1993) studied this question.