Multiplicative Normal Noise and Nonconcavity in the Value of Information

摘要

This paper investigates a Bayesian inverse problem of a price setting monopolist facing a random demand. In contrast to previous investigations an unknown true market potential of demand is distorted by two independent Gaussian errors, a zero-mean additive and a unity-mean multiplicative one. The multi-period game allows for learning from realized market demands (signals). Interestingly increasing the level of noise of a multiplicative error in this dynamic setting can actually improve the Value of Information of signals to the firm, a result that cannot hold for a single additive error or in a static context .