This study aims to examine the role of business models (BM) in the context of digital transformation. The research methodology includes the following steps. First, the study develops a mathematical model to describe the role of BMs in bridging technology and market dynamics, including definitions, theorems, and axioms. Second, based on the mathematical model of BM as a ‘nudge’, three key findings are identified: (a) BM as a nudge significantly reduces market search costs after reaching a certain threshold, referred to as the ‘Chesbrough Point’; (b) BM as a nudge increases market size and diversity at any point following the ‘Chesbrough Point’; (c) Despite having BM as a nudge, technology experiences a long tail before reaching a sufficient market. Third, the study discusses the theoretical implications of BMs and their enhanced function as a nudge, particularly in the context of artificial intelligence and open innovation dynamics.