Expanding Multi-Market Monopoly and Nonconcavity in the Value of Information

TL;DR

This paper explores how the value of information for a monopolist in multiple markets can behave non-monotonically, influenced by demand growth and system parameters, challenging classical static assumptions.

Contribution

It introduces a dynamic Bayesian model showing non-monotonic value of information in multi-market monopolies, extending classical static analysis.

Findings

Value of information can be non-monotonic in signal variance.

Non-monotonicity depends on demand growth rate.

Classical static models always show monotonic relationships.

Abstract

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.