1. Introduction
The concept of lock-in — the state in which a user, organization, or economy becomes structurally dependent on a platform and faces prohibitive switching costs — has been central to information economics since Arthur (1989) formalized increasing returns and path dependence. Farrell and Klemperer (2007) provided the definitive survey of switching costs and network effects, establishing that lock-in emerges from the interaction of sunk investment, learning costs, contractual commitments, and network externalities. Shapiro and Varian (1999) translated these ideas into managerial strategy, while Rochet and Tirole (2003) formalized two-sided market dynamics that amplify lock-in through cross-side network effects.
Despite this rich theoretical foundation, no standardized measurement instrument exists for quantifying structural lock-in across platforms and sectors. Existing approaches fall into three categories, each with significant limitations:
BHI addresses this gap by proposing a formalized, parametric instrument that: (a) decomposes lock-in into 11 observable dimensions with anchored scoring rubrics; (b) aggregates these dimensions using theoretically motivated functional forms from production economics; (c) produces a single dimensionless score comparable across platforms, sectors, and time periods; and (d) includes a dynamic extension modeling the co-evolution of lock-in and human capability decay.
The instrument draws an explicit analogy to the Reynolds number in fluid dynamics — a dimensionless ratio of inertial forces to viscous forces that predicts transitions between laminar and turbulent flow. B is a dimensionless ratio of capture forces to escape forces. Unlike the Reynolds number, whose critical thresholds were established through extensive empirical observation, BHI's thresholds are currently definitional and await empirical validation.
We emphasize that BHI is at a pre-empirical stage. The contribution of this paper is formalization and operationalization: specifying a complete, computable model with anchored rubrics, applying it to a substantive cross-section, and transparently documenting what has been validated and what remains pending. We do not claim that BHI produces validated measurements — we claim that it produces structured, reproducible assessments that can be subjected to validation.
The remainder of this paper is organized as follows. Section 2 reviews related work on switching costs, network effects, and platform competition. Section 3 specifies the complete BHI model. Section 4 presents cross-section results for 100 platforms. Section 5 reports sensitivity analysis. Section 6 extends the model to dynamic lock-in evolution. Section 7 discusses limitations and the validation agenda. Section 8 concludes.