§7.3, quotation attributed to SCiDA. The document quotes SCiDA (Heinrich Heine University Düsseldorf and the University of Exeter) directly, and gives no citation for it. The quotation is said to come from their submission to the CMA’s February 2026 call for evidence, a document this project does not hold; the phrases do not appear in SCiDA’s later response to the steering consultation, which it does hold. The quotation is therefore reproduced as submitted and has not been re-verified against its source. It should not be relied on or quoted onward from here. If it is inaccurate, tell us and the correction will be published with its date.
Third-Party Submission to the CMA's Call for Evidence on Recent Developments in Relation to Apple's and Google's App Store Rules
Submitted by: Ivan Savich, Creator of the Black Hole Index
Date: April 2026
Contact: ivan.savich@blackholeindex.com
Website: https://blackholeindex.com
1. Introduction
1.1. I welcome the opportunity to respond to the Competition and Markets Authority's call for evidence on recent developments in relation to Apple's and Google's app store rules. This submission provides a quantitative perspective on structural lock-in in mobile platform ecosystems, using the Black Hole Index (BHI) --- a measurement instrument I developed specifically to quantify the structural cost of leaving a platform.
1.2. I am an independent researcher and the creator of the Black Hole Index, a structural lock-in measurement framework that produces a single dimensionless ratio (B = Capture / Escape) for any platform. The methodology draws on 70 years of economics: CES production functions (Solow, 1956), switching cost theory (Farrell and Klemperer, 2007), network effects (Katz and Shapiro, 1985), and status quo bias (Samuelson and Zeckhauser, 1988). 112 platforms across 12 sectors have been scored. The full methodology, interactive calculator, and all scores are publicly available at blackholeindex.com.
1.3. I have no commercial relationship with Apple, Google, or any party to this investigation. All views expressed are my own. All data used is publicly available.
2. Why Quantitative Lock-In Measurement Matters for This Investigation
2.1. The CMA's investigation into Apple's and Google's mobile platforms focuses on app review, app ranking, use of developer data, interoperability, and --- in this call for evidence --- steering restrictions. These are all mechanisms through which platform operators can increase or maintain structural lock-in.
2.2. However, the current regulatory framework lacks a standardised quantitative measure of how locked-in users and developers actually are. The Digital Markets, Competition and Consumers Act 2024 (DMCCA) designates firms based on Strategic Market Status, which considers factors such as market power, position of strategic significance, and substantial and entrenched market power. These are assessed qualitatively. BHI offers a complementary quantitative instrument.
2.3. The distinction matters because procedural commitments (such as those accepted from Apple and Google on 1 April 2026) address process transparency, not structural lock-in. A platform can comply with every transparency requirement while maintaining a structural escape cost that makes switching economically prohibitive. BHI measures this structural cost directly.
3. The Black Hole Index: Summary of Methodology
3.1. BHI scores 11 parameters on anchored 0--10 rubrics with 5-point descriptions for each parameter. These are grouped into Capture (forces that hold users in) and Escape (forces that allow users to leave):
Capture parameters:
- Data Depth (d): Volume and irreproducibility of accumulated data
- Memory (m): Platform's retention of user history, preferences, and context
- Action (a): Depth of actions and workflows embedded in the platform
- Process (p): Integration into organisational or personal processes
- Network (n): Network effects and social graph dependencies
- Closeness (c): Frequency and depth of user interaction
Escape parameters:
- Portability (x): Ease of exporting data and migrating to alternatives
- Substitutability (s): Availability and quality of competing alternatives
- Human Fallback (h): Ability to perform tasks without the platform
Extended parameters:
- Organisational Depth (o): Depth of enterprise/institutional integration
- Momentum (t): Growth trajectory and adoption velocity
3.2. The formula aggregates these parameters using CES (Constant Elasticity of Substitution) functions with synergy corrections:
B = Capture / (epsilon + Escape x feedback)
Where epsilon = 0.1 (regularisation constant preventing division by zero), and feedback = max(0.3, 1 - 0.35 x CoreBase) is a diminishing-returns term that weakens escape options when capture is high. B < 1 indicates users can leave freely, B > 2.5 indicates structural lock-in, and B > 5 indicates infrastructure-level dependency.
3.3. Preliminary validation against real-world retention data yields Spearman rho = 0.77 (p < 0.001) on a 14-platform subset with directly comparable retention metrics (from SEC filings, CIRP surveys, and industry reports). Observable metrics are available for 42 platforms in total. The full methodology is published at blackholeindex.com/methodology and in the research paper at blackholeindex.com/paper.
4. BHI Analysis: Apple's Mobile Platform
4.1. Apple's mobile ecosystem scores as follows:
| Parameter | Score (0--10) | Interpretation |
|---|---|---|
| Data Depth (d) | 8 | iCloud photos, contacts, health data, keychain --- deeply accumulated |
| Memory (m) | 8 | Purchase history, app library, personalisation across 15+ years |
| Action (a) | 7 | Apple Pay, Siri shortcuts, HomeKit automations |
| Process (p) | 8 | Embedded in daily routines: communication, navigation, health, payments |
| Network (n) | 9 | iMessage (blue bubble), AirDrop, FaceTime, Family Sharing, Find My |
| Closeness (c) | 9 | Primary device, used 4+ hours/day, always-on companion |
| Portability (x) | 3 | Limited data export, no iMessage portability, app purchases non-transferable |
| Substitutability (s) | 4 | Android exists but switching requires replacing entire hardware ecosystem |
| Human Fallback (h) | 4 | Difficult to function without smartphone in modern life |
| Org Depth (o) | 6 | Apple Business Manager, MDM integration, institutional deployments |
| Momentum (t) | 6 | Stable installed base, modest growth, strong retention |
Result: B = 5.22 (Infrastructure-level lock-in)
4.2. Apple's lock-in is not the result of any single feature being irreplaceable. It is the cumulative effect of a dozen interlocking mechanisms: iMessage creates social pressure (n = 9), iCloud stores irreplaceable data (d = 8), app purchases are non-transferable (x = 3), and hardware accessories (Watch, AirPods, HomePod) deepen ecosystem integration (p = 8). Each product individually has alternatives. Together, the switching cost is the sum of all simultaneous replacements.
4.3. The Capture side (1.910) is driven by high closeness (c = 9) multiplied by strong network effects (n = 9) and deep process integration (p = 8). The Escape side (0.366) is low because data portability is limited (x = 3), substitutability requires full ecosystem replacement (s = 4), and smartphone dependency means human fallback is weak (h = 4).
5. BHI Analysis: Google's Mobile Platform
5.1. For comparison, Google/Android scores:
| Parameter | Score (0--10) | Interpretation |
|---|---|---|
| Data Depth (d) | 9 | Gmail, Photos, Drive, Maps history, Chrome data |
| Memory (m) | 7 | Extensive but more portable than Apple's |
| Action (a) | 7 | Google Assistant, Google Pay, Workspace integrations |
| Process (p) | 8 | Search, Maps, Gmail embedded in daily workflows |
| Network (n) | 9 | Android ecosystem, Google Workspace collaboration |
| Closeness (c) | 9 | Primary device and services, always-on |
| Portability (x) | 5 | Google Takeout provides data export; higher than Apple |
| Substitutability (s) | 4 | Switching to iOS requires re-purchasing apps |
| Human Fallback (h) | 5 | Slightly higher than Apple due to web-accessible services |
| Org Depth (o) | 7 | Google Workspace, Chromebook deployments, Android Enterprise |
| Momentum (t) | 7 | Growing in enterprise, dominant in developing markets |
Result: B = 4.62 (Deep structural lock-in)
5.2. Google's lock-in (B = 4.62) is approximately 12% lower than Apple's (B = 5.22). The primary difference is on the Escape side: Google provides better data portability through Google Takeout (x = 5 vs Apple's x = 3), and its services are web-accessible, providing a slightly higher human fallback (h = 5 vs 4). However, Google's Capture side (2.029) is actually higher than Apple's (1.910), driven by deeper data accumulation (d = 9) and greater organisational depth (o = 7).
5.3. This quantitative comparison suggests that while Google's platform is more structurally open on the escape dimension, it captures more deeply through data accumulation and institutional integration.
6. Implications for Steering Restrictions
6.1. Steering restrictions --- rules that prevent developers from directing users to payment methods or offers outside the app store --- directly affect three BHI parameters:
- Portability (x): Steering restrictions reduce developer and user portability by preventing alternative payment flows and limiting the ability to establish direct customer relationships outside the platform.
- Substitutability (s): By forcing all transactions through the app store, steering restrictions reduce the practical substitutability of distribution channels, even where alternatives nominally exist.
- Closeness (c): Mandatory in-app purchase flows increase transaction frequency through the platform, deepening the closeness score.
6.2. Removing steering restrictions would increase x and s scores for both platforms, directly reducing B. A sensitivity analysis using the BHI Observatory (blackholeindex.com/observatory) demonstrates this effect:
| Scenario | Apple B | Google B | Change |
|---|---|---|---|
| Current state | 5.22 | 4.62 | --- |
| Portability x +2 (steering removed) | 4.60 | 4.19 | -12% / -9% |
| Portability x +2, Substitutability s +1 | 4.35 | 3.97 | -17% / -14% |
6.3. This analysis suggests that effective removal of steering restrictions could reduce structural lock-in by approximately 9--17%. However, this assumes that removal is substantive rather than procedural. If platforms implement alternative payment options with significant friction, adverse user experience design, or informational asymmetries (as has been observed in some EU DMA compliance efforts), the actual effect on portability and substitutability scores would be minimal.
7. Assessment of Apple's Commitments Through a BHI Lens
7.1. The commitments accepted by the CMA on 1 April 2026 cover four areas: app review, app ranking, use of developer data, and interoperability. Assessed through BHI parameters:
| Commitment Area | BHI Parameters Affected | Expected Impact on B |
|---|---|---|
| App review transparency | None directly | Negligible |
| App ranking non-discrimination | Closeness (c) marginally | Minimal |
| Data use restrictions | Data Depth (d) marginally | Minimal |
| Interoperability channel | Portability (x), Substitutability (s) | Potentially significant, but procedural not substantive |
7.2. The commitments primarily address procedural transparency. They do not reduce the structural forces that create lock-in: accumulated data (d = 8), network effects (n = 9), or limited portability (x = 3). A platform can comply fully with all transparency commitments while maintaining B = 5.22.
7.3. This is consistent with the observation made by SCiDA (Shaping Competition in the Digital Age, a joint research project of Heinrich Heine University Dusseldorf and the University of Exeter) in their submission to the CMA's February 2026 call for evidence, that Apple's interoperability commitment is "fundamentally procedural rather than substantive" and that "the broad discretion preserved by the assessment criteria significantly limits its practical impact."
7.4. Steering restrictions represent the most direct mechanism through which the CMA could reduce structural lock-in, because they directly affect the Escape parameters (x, s) rather than merely adding transparency to the Capture parameters.
8. Comparative Context
8.1. To contextualise Apple's and Google's lock-in levels, BHI scores across the full 112-platform database provide useful benchmarks:
| Platform | B Score | Category |
|---|---|---|
| 17.03 | Structural maximum (super-app in monopoly context) | |
| Synopsys/Cadence (EDA) | 13.0 | No alternative exists for advanced chip design |
| Apple | 5.22 | Infrastructure-level lock-in |
| MS Copilot | 4.73 | Highest AI lock-in despite worst user satisfaction |
| 4.62 | Deep structural lock-in | |
| ChatGPT | 1.96 | Popular but structurally replaceable |
| Netflix | 0.43 | Near-zero lock-in despite 325M subscribers |
8.2. Apple and Google occupy positions in the upper quartile of all scored platforms. Their B scores indicate structural lock-in significantly above the threshold (B > 2.5) at which users face material switching costs. This is consistent with the CMA's SMS designation of both platforms.
8.3. The comparison with Netflix (B = 0.43) is instructive: Netflix has 325 million subscribers and high brand recognition, yet near-zero structural lock-in. Users can cancel and switch to Disney+, HBO Max, or Amazon Prime Video within minutes, losing only algorithmic recommendations. Lock-in is not about size or popularity --- it is about structural escape cost. This distinction is central to the CMA's remit under DMCCA.
9. Recommendations
9.1. I respectfully suggest the CMA consider the following:
(a) Adopt quantitative lock-in measurement alongside qualitative assessment. BHI or similar instruments can complement the CMA's existing qualitative toolkit by providing standardised, comparable, and reproducible measurements of structural lock-in across platforms and over time.
(b) Prioritise substantive steering removal over procedural commitments. The BHI sensitivity analysis (Section 6.2) demonstrates that effective steering removal could reduce Apple's structural lock-in by 12--17%. Procedural commitments on app review and ranking, by contrast, have negligible effect on B scores.
(c) Monitor B scores over time. Quarterly re-scoring of Apple and Google on BHI parameters would provide the CMA with an objective measure of whether interventions are reducing structural lock-in or merely changing its surface presentation.
(d) Require substantive interoperability, not procedural channels. Apple's interoperability commitment preserves full discretion to decline requests. BHI analysis shows that portability (x) is Apple's lowest Escape parameter at 3/10. Increasing portability through mandated interoperability would have the largest single-parameter effect on reducing B.
10. Conclusion
10.1. The Black Hole Index provides quantitative evidence that Apple (B = 5.22) and Google (B = 4.62) maintain infrastructure-level structural lock-in in their mobile platform ecosystems. This lock-in is driven primarily by high Capture forces (data depth, network effects, process integration) combined with low Escape forces (limited portability, high switching costs, smartphone dependency).
10.2. The commitments accepted on 1 April 2026 address procedural transparency but do not materially affect the structural parameters that drive lock-in. Steering restrictions represent the most direct lever available to the CMA for reducing structural lock-in, as they directly affect the Escape parameters in the BHI framework.
10.3. I remain available to provide further analysis, including custom BHI assessments of specific platform features, sensitivity analyses for proposed interventions, or methodology briefings for the CMA team.
Ivan Savich Creator, Black Hole Index
ivan.savich@blackholeindex.com | blackholeindex.com | x.com/BlackHoleIndex
References
- Farrell, J. and Klemperer, P. (2007). 'Coordination and Lock-In: Competition with Switching Costs and Network Effects.' In Handbook of Industrial Organization, Vol. 3.
- Katz, M. L. and Shapiro, C. (1985). 'Network Externalities, Competition, and Compatibility.' American Economic Review, 75(3), pp. 424--440.
- Samuelson, W. and Zeckhauser, R. (1988). 'Status Quo Bias in Decision Making.' Journal of Risk and Uncertainty, 1(1), pp. 7--59.
- Solow, R. M. (1956). 'A Contribution to the Theory of Economic Growth.' Quarterly Journal of Economics, 70(1), pp. 65--94.
- Arthur, W. B. (1989). 'Competing Technologies, Increasing Returns, and Lock-In by Historical Events.' Economic Journal, 99(394), pp. 116--131.
- Digital Markets, Competition and Consumers Act 2024 (UK).
- Regulation (EU) 2022/1925 (Digital Markets Act).