Some Dynamic Market Models

TL;DR

This paper analyzes the temporal dynamics of single-product markets using differential equation models, focusing on diffusion processes, competition, and churn effects, providing analytic solutions for market evolution in various scenarios.

Contribution

It introduces a differential equation-based framework for modeling market dynamics with multiple competitors and churn, offering new analytic solutions for market evolution over time.

Findings

Market evolution can be described analytically using differential equations.

Churn significantly impacts market stability and growth.

Multiple competitors influence market dynamics in complex ways.

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.