Expanding Multi-Market Monopoly and Nonconcavity in the Value of Information
This addresses a theoretical gap in information economics for monopolists in dynamic environments, but it appears incremental as it extends known concepts to a more complex setting.
The paper tackles the problem of how a monopolist's value of information behaves in a dynamic multi-market setting with random demand growth, finding that it can be non-monotonic with respect to signal variance, unlike in static models where it is always monotonic. This result depends critically on the exogenous growth rate of the system.
In this paper I investigate a Bayesian inverse problem in the specific setting of a price setting monopolist facing a randomly growing demand in multiple possibly interconnected markets. Investigating the Value of Information of a signal to the monopolist in a fully dynamic discrete model employing the Kalman-Bucy-Stratonovich filter, we find that it may be non-monotonic in the variance of the signal. In the classical static settings of the Value of Information literature this relationship may be convex or concave, but is always monotonic. The existence of the non-monotonicity depends critically on the exogenous growth rate of the system.