A Simple Mathematical Model of the Innovator's Dilemma

Abstract

Incumbent companies lag behind new entrants in entering the product markets of disruptive technologies. This study presents a simple mathematical model of the innovator ’s dilemma (the “failure framework”), incorporating factors that determine the length of the market entry time lag. The model is based on a two-firm game involving an incumbent company and a new entrant in which cannibalization within the incumbent between its conventional technology-based business and a new disruptive technology-based business influence the incumbent ’s decision of whether and when to enter the disruptive technology product market. The originality of the model lies in the simple formulation of temporal changes in the demand for conventional technology products and disruptive technology products through the use of a line market with vertical line at a certain time based on the diagram presented by Christensen. The model shows that a new entrant enters the market for a disruptive technology product when its initial cost of investing in the business is below a certain level; in this case the incumbent also enters the market, but lags behind the new entrant. This study also identifies economic factors that affect the range of the time lag, something that Christensen (1997) did not do.

Keywords: Business strategy, Innovator's dilemma, Disruptive technology, Innovation, Christensen