Some Dynamic Market Models

Abstract: In this text, we study the temporal behavior of markets using models expressible as ordinary differential equations. The markets studied are those where each customer buys only one copy of the good, for example, subscription of smartphone service, journals and newspapers, and goods such as books, music and games. The underlying model is the diffusion model of Frank Bass. Evolution of markets with no competitors and markets with several competitors are analyzed where, in particulat, the effects of churning upon the market evolution is investigated. Analytic solutions are given for the temporal evolution of several types of interactive games.