Open Sourcing GPTs: Economics of Open Sourcing Advanced AI Models

Mahyar Habibi

REVIEW 3 major objections 5 minor 49 references

Open Sourcing GPTs: Economics of Open Sourcing Advanced AI Models

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Owners are most likely to open source an LLM at moderate size, the paper argues.

desk verdict A careful empirical package with a genuinely new latent-space method and a solid LLaMA event study, but the headline inverted-U rests on a single numerical calibration with no sensitivity analysis. read the letter →

arxiv 2501.11581 v1 pith:EM5QC5ZB submitted 2025-01-20 econ.GN q-fin.EC

Mahyar Habibi This is my paper · ORCID

classification econ.GNq-fin.EC

keywords opensourcelargelanguagemodelsgeneral-purposetechnologyinverted-UrelationshipcompatibilityresearchspilloversfirmsizeLLMecosystem

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that a profit-maximizing firm's decision to open source an advanced large language model is a trade-off between accelerating the technology's growth through community contributions and securing immediate revenue by keeping the model closed. The empirical parts show that LLMs are compatible with the research-and-development portfolios of many technologically diverse firms, that a larger quality lead over the best open source alternative makes open sourcing less likely, and that opening a frontier model can stimulate outside research activity. The paper's central prediction is an inverted-U relationship: open sourcing is most likely for owners with an intermediate share of LLM-compatible applications, while very small and very large owners keep their models closed. If correct, this means moderate market concentration could be good for the open source ecosystem of multi-purpose software.

What carries the argument

The carrying object is a two-state dynamic programming problem with Bellman equations for the value of an open model, $V^O(q)$, and a closed model, $V^C(q, q_B)$, where $q$ is the model's quality and $q_B$ is the quality of the open-source alternative. Open-sourcing is irreversible and lets external compute contribute to next-period quality; a closed model is priced through an API, and the price influences how fast the rival model improves. Proposition 1 establishes a unique quality threshold $q^*$: the firm open sources when $q < q^*$ and stays closed when $q > q^*$. Proposition 2 shows the firm sets its API price below the static revenue-maximizing level to slow the rival's growth. Varying $m$, the mass of applications the firm owns, produces the inverted-U relationship between firm size and the width of the open-source window.

What would settle it

One check would be to sweep the model's parameters, especially the open-source ecosystem efficiency $\phi$ and discount factor $\beta$, and ask whether the open-source window is hump-shaped in the firm-size parameter $m$ on a broad grid; the current paper reports the shape only at its baseline parameter values. A complementary empirical check would estimate the open-sourcing decision against a continuous measure of the owner's share of compatible applications across a larger sample of model releases, rather than the categorical Big-Tech indicator used in the regression.

Watch

Extended reading notes

Core claim

The author models a tech firm that owns all software producers in a segment of a downstream application sector and can irreversibly open source its higher-quality LLM or license it through an API. Open sourcing sacrifices current API revenue but lets internal and external compute improve the model's quality over time; a closed strategy earns immediate license fees while allowing the rival open model to catch up. Solving the dynamic discrete-choice model shows that the firm opens the model when its quality lead over the open alternative is modest and keeps it closed when the lead is large. The same mechanism delivers the paper's central prediction: as the owner's share of compatible applications grows, openness first rises and then falls, because small firms need API revenue, dominant firms already internalize most applications, and intermediate firms gain the most from community-accelerated growth.

Load-bearing premise

The inverted-U shape is demonstrated by numerical simulation at one illustrative parameter vector, so the claim rests on the assumption that the qualitative shape survives across plausible values of the discount factor, ecosystem efficiency, and firm size rather than being an artifact of that particular calibration.

Editorial extensions

If this is right

A model with a large quality lead over the best open source alternative is unlikely to be open sourced, which matches the persistence of closed frontier models.
Large tech firms should open source more often than other for-profit firms, since their broad application portfolios internalize more of the community's quality improvements.
Open sourcing a frontier model can be an R&D catalyst, with the paper's estimates implying a 40 to 140 percent increase in contributions by LLM researchers after the release studied.
Moderate concentration in the application market, not low or high concentration, is what should sustain a vibrant open source ecosystem for general-purpose models.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The framework implies a testable prediction beyond the paper's sample: as the best open-source alternative improves, the absolute quality lead at which a firm switches from open to closed should also rise, so the open-source window shifts but does not disappear.
The same logic should apply to other general-purpose software whose owners also sell compatible applications, suggesting that ownership share of complements, not firm revenue, is the right predictor of open-sourcing.
The paper stops short of welfare analysis; if open-sourcing accelerates research activity, a social planner might favor openness even for models with large quality leads, because the spillover compounds over time.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

This paper is worth reading. It does three empirical things and one theoretical thing, and the empirical parts are mostly careful. The patent-classification latent space method (CPC n-grams plus SVD) is a real methodological contribution, and the sanity check with known firm pairs is good. The LLaMA event study is the strongest piece: a plausible control group, several robustness checks (synthetic DiD, a narrow window around GPT-4's release, alternative treatment definitions), and the 40–140% range is honestly reported. The quality-lead regression is suggestive but fragile; N=86 with MMLU available only for a selected subset, and the paper itself flags the selection concern.

The theory is the soft spot. The mechanism is intuitive: small firms want API revenue, large firms don't need the community, and intermediate firms benefit most from open-sourcing. But the inverted-U headline is demonstrated only in one numerical example (Table 6, Figure 10), and the paper explicitly says those parameters should not be taken literally. There is no analytical characterization and no sensitivity analysis. The appendix even shows the open-source window is zero for sufficiently small phi, so the inverted-U could degenerate under plausible parameters. That is the load-bearing claim of Section 6, and it needs more than one hand-picked calibration.

There is also a mild circularity: the model is 'motivated by' the empirical findings, then generates predictions 'aligned' with the same findings. That is not fatal—the model does produce a genuinely new prediction about firm size—but the paper should be more careful about claiming confirmation.

The paper is honest about its limitations, which I credit. But the central new prediction is currently conditional, not established. A serious referee should push for (a) sensitivity analysis across the parameter space, (b) at least a partial analytical argument for single-peakedness, and (c) the code, which is referenced but not actually included.

Bottom line: this deserves peer review and would be a useful contribution to the economics of open-source AI even after revision. I would bring it to a reading group, and I would cite the patent-space method and the LLaMA results. Just do not let the inverted-U pass without more support.

Recommendation: send it out for review, expecting a major revision.

Referee Report

3 major / 5 minor

Summary. This paper studies why for-profit firms open-source advanced LLMs. It constructs a latent technology space from USPTO patent CPC codes and a fine-tuned LLM classifier to show that LLMs are compatible with many technologically diverse firms. A regression on CRFM ecosystem data finds that a larger quality lead over the best open-source model reduces the probability of open-sourcing, that for-profit developers are less likely to open-source, and that Big Tech firms are more likely to do so. An event-study and difference-in-differences analysis around the release of LLaMA finds increased GitHub contributions among LLM researchers. The paper then develops a dynamic discrete-choice model in which a firm owning a share m of LLM-compatible applications trades off closed API revenue against the accelerated quality growth made possible by open-source contributions. The model produces threshold open-source windows, and a numerical value-function iteration predicts an inverted-U relationship between firm size m and open-sourcing propensity. The paper concludes that moderate market concentration may benefit open-source ecosystems of multi-purpose software technologies.

Significance. If the results hold, the paper offers several contributions: a new latent-space method based on hierarchical patent classifications, plausibly causal evidence that open-sourcing LLaMA stimulated research-related activity, and a theoretical framework connecting GPT-like applicability to open-sourcing decisions. The empirical DiD analysis is carefully checked with synthetic DiD, narrow event windows, and alternative treatment definitions. However, the central theoretical prediction is currently supported only by a single numerical experiment at parameters the paper says should not be taken literally, with no sensitivity analysis or reproducible code. Moreover, the model's 'predictions aligned with empirical findings' are not independent confirmations because the model was explicitly motivated by those same findings. The significance of the paper is therefore conditional on strengthening the theoretical robustness and on clarifying the status of the empirical-theoretical alignment.

major comments (3)

[Section 6.3, Figure 10 and Table 6] The inverted-U relationship between firm size and open-sourcing propensity is computed by value-function iteration at the single parameter vector in Table 6, and Section 6.2 states that these values 'should not be taken literally.' The paper provides no analytical characterization of the shape in m, no sensitivity analysis over β, γ, α, ψ, ϕ, λ, and cD, and no code (Appendix C.2 only refers to 'accompanying code'). Because Figure C.2 already shows that the open-source window is zero for sufficiently small ϕ, the inverted-U could be an artifact of the baseline calibration. This is the paper's headline prediction, so it needs either a proof of single-peakedness under stated conditions or a systematic sensitivity analysis with reproducible code and data.
[Section 5.1, Table 2] The quality-lead regression is estimated on 86 models with available MMLU scores, and score availability is likely correlated with model prominence and open/closed status. The Big-Tech dummy is defined by only three firms, and the specifications include no time fixed effects or developer-level clustering. Since the theoretical framework in Section 6 is explicitly motivated by these empirical regularities, sample selection in this table weakens the empirical grounding. Please report robustness to selection/score imputation, time fixed effects, and alternative clustering, or temper the interpretation accordingly.
[Section 6.3 with Section 1] The model is introduced as 'motivated by these findings' and its output is then described as providing 'predictions aligned with empirical findings.' This is not an independent validation: the model is not calibrated to reduced-form moments, and the inverted-U is not tested against data. The theoretical results should be presented as consistency checks, or the paper should provide an out-of-sample empirical test of the inverted-U using the constructed LLM-compatibility measure.

minor comments (5)

[Figure 10 and Section 6.3] The phrase 'Open Soruce' appears in the Figure 10 title and in the surrounding text; this should read 'Open Source.'
[Appendix C.2, Tables C.4 and C.5] Both tables are captioned 'VFI Parameters- Opens Model,' but Table C.5 describes the closed-model solution; the caption of Table C.5 should be corrected.
[Equation (3)] The profit function is written with inconsistent subscripts as π_{i,τ,t} in the text and π_{i,t,τ} in the equation, and the licensing price appears as both P_{τ,t} and P_t. Please standardize the notation.
[Table 1] The table notes refer to a 'Transformer Sim.' column, but the actual column is labeled 'LLM Compatibility'; the note and column header should be aligned.
[References and general text] The reference for Meta (2023b) contains the placeholder '[insert date you accessed the site]', and the text contains typos such as 'daset' in Appendix A.1 and 'Huggingace' in Section 5.1; these should be cleaned up.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the theory is motivated by empirical findings, but its predictions, including the inverted-U, are derived from an independently specified dynamic model and are not fitted from the data.

full rationale

The paper's empirical findings motivate the model, and Section 6 reports that the theoretical analysis generates predictions aligned with those findings, but this alignment is not a reduction. The model parameters in Table 6 are not estimated from the regressions; the quality-lead result (Proposition 1) and the inverted-U size result (Section 6.3, Figure 10) come from solving the Bellman equations (5)-(7) by value function iteration, not from reading the empirical estimates back into the model. The closest candidate for circularity is the inverted-U claim, which is demonstrated only at one parameter vector that the paper itself says should not be taken literally (Section 6.2); that is a calibration robustness concern, not a definitional or fitted-input circularity. There are no load-bearing self-citations, no imported uniqueness theorems, and no ansatz smuggled in through prior work of the author. The empirical claims are tested against external data (MMLU quality gaps in Table 2; LLaMA DiD on GitHub contributions in Tables 3-5), while the theoretical model is solved independently of those estimates. No circular step satisfying the quoted-reduction standard was found.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The theoretical predictions, especially the inverted-U, are not derived from first principles alone; they are produced by numerical simulation under hand-picked parameters (Table 6). The empirical compatibility and event-study results rest on domain-specific identification assumptions rather than machine-checked proofs or shipped artifacts.

free parameters (9)

β (time discount factor) = 0.9
Hand-picked baseline parameter in Table 6 for the numerical value function iteration; affects the open-source window size and the inverted-U.
γ (AI compatibility parameter) = 1.0
Hand-picked baseline parameter in Table 6; determines how quickly profits decay with incompatibility in Equation 3.
α (shape of production function) = 0.45
Hand-picked baseline parameter in Table 6; controls returns to compute in the profit function and the demand relation.
m (size of Firm A in the application sector) = 0.2
Baseline mass of owned compatible applications in Table 6; Figure 10 varies m to generate the inverted-U, but no theory proves the shape is general.
ψ (efficiency of internal development) = 0.5
Hand-picked baseline parameter in Table 6; governs how internal compute improves model quality in the closed state.
ϕ (efficiency of open source ecosystem) = 0.5
Hand-picked baseline parameter in Table 6; governs external contributions to open model quality and is central to the trade-off.
λ (LLM development improvement factor) = 5.0
Hand-picked baseline parameter in Table 6; used in the development decision after observing qB.
cD (LLM development cost factor) = 0.4
Hand-picked baseline parameter in Table 6; scales the cost of developing a new model as cDqB.
Cosine similarity threshold for LLM compatibility = 0.7
Hand-chosen threshold in Section 4.2 to classify firms as LLM-compatible; the empirical claim that LLMs are broadly compatible depends on this choice.

assumptions (5)

domain assumption Software producers are uniformly distributed on [0,1] and profit from LLM use is e^{-γx}(q k)^α - k - P (Equation 3).
This functional form and distribution drive the demand relation (Equation 4) and the shape of the numerical results.
domain assumption Firm A owns all producers in [0,m] and can irreversibly open source its model; open source quality grows with external compute through ϕK_{-A}.
The trade-off between internal production profit and API revenue depends on this ownership and growth structure.
domain assumption GitHub contributions by identified LLM researchers proxy for research activity, and non-AI repository contributors form a valid control group.
The LLaMA DiD causal interpretation rests on this proxy and on control-group validity; the paper acknowledges pre-trends and potential spillovers.
domain assumption Patents citing Vaswani et al. (2017) and classified under CPC code G06F40 represent LLM-related technology, and the 0.7 cosine threshold defines compatibility.
The empirical compatibility measurement in Section 4.2 depends on these identification choices.
standard math The dynamic programming value functions are differentiable and first-order approximations around q* are valid for the proofs of Propositions 1 and 2.
The proofs in Appendix C use linear approximations rather than exact global arguments, so the threshold result is approximate.

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Pith. "Pith review of Open Sourcing GPTs: Economics of Open Sourcing Advanced AI Models." pith.science (2026). https://pith.science/paper/EM5QC5ZB

@misc{pith2026250111581,
  author       = {Pith},
  title        = {Pith review of: Open Sourcing GPTs: Economics of Open Sourcing Advanced AI Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EM5QC5ZB}},
  note         = {Machine review of arXiv:2501.11581}
}

read the original abstract

This paper explores the economic underpinnings of open sourcing advanced large language models (LLMs) by for-profit companies. Empirical analysis reveals that: (1) LLMs are compatible with R&D portfolios of numerous technologically differentiated firms; (2) open-sourcing likelihood decreases with an LLM's performance edge over rivals, but increases for models from large tech companies; and (3) open-sourcing an advanced LLM led to an increase in research-related activities. Motivated by these findings, a theoretical framework is developed to examine factors influencing a profit-maximizing firm's open-sourcing decision. The analysis frames this decision as a trade-off between accelerating technology growth and securing immediate financial returns. A key prediction from the theoretical analysis is an inverted-U-shaped relationship between the owner's size, measured by its share of LLM-compatible applications, and its propensity to open source the LLM. This finding suggests that moderate market concentration may be beneficial to the open source ecosystems of multi-purpose software technologies.

Figures

Figures reproduced from arXiv: 2501.11581 by the authors.

**Figure 1.** illustrates the number of open and closed models for ten leading organizations according to the ecosystem dataset from the Center for Research on Foundation Models (CRFM) at Stanford University1 . Google, OpenAI, Microsoft, and Meta lead in the number of models released. While most organizations have released both open and closed models, their strategies for open-sourcing vary significantly. Prominent AI startups su… view at source ↗

**Figure 5.** Quality Evolution of Frontier Open and Closed LLMs Notes: The figure depicts the evolution of the performance of open and closed frontier LLMs in the CRFM data as measured by the Massive Multitask Language Understanding (MMLU) benchmark. A frontier open (closed) model is defined as a model that outperforms its preceding open (closed) models on this specific benchmark. The name of the developers are provided in paren… view at source ↗

**Figure 6.** Impact of LLaMA on Contributions of LLM Researchers Notes: The figure plots the coefficients from the event-study regression, as described in equation 2. The dependent variable is the relative deviation of contributions from their mean pre-event level, defined as yit = (ci,t − ci, pre ¯ )/ci, pre ¯ . The vertical line marks the introduction date of LLaMA. The shaded areas denote 95 percent confidence intervals, calc… view at source ↗

Figures from the paper (1 more)

**Figure 11.** Figure 11: LLM Development Decision Notes: The figure depicts the expected value of developing new AI model relative to the quality of existing open source model, across various firm sizes. Additional modeling specifics are provided in [PITH_FULL_IMAGE:figures/full_fig_p037_11.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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