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arxiv: 2606.25283 · v1 · pith:B55GVQWHnew · submitted 2026-06-24 · 💰 econ.GN · physics.soc-ph· q-fin.EC

Competitive satellite placement and the geography of orbital risk: evidence from the geostationary arc

Akhil Rao , Nikodem Szumilo This is my paper

Pith reviewed 2026-06-25 20:18 UTC · model grok-4.3

classification 💰 econ.GN physics.soc-phq-fin.EC
keywords geostationary orbitsatellite placementcompetitive entryorbital debrisITU registryfirst-come first-servedeconomic geography
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The pith

A competitive entry model predicts the distribution of satellites along the geostationary arc with R² of 0.64.

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

The paper uses the complete ITU registry of geostationary satellites and a model in which operators enter slots to maximize expected profits under first-come first-served rules. This structural model accounts for the observed clustering of active satellites and also matches the locations of inactive payloads. It outperforms a fitted conditional logit model when predicting which specific slot an operator will choose. The results indicate that the current placement pattern is driven by population size rather than national income and places satellites in economically efficient locations, but only once slots have matured.

Core claim

Using the complete ITU registry and a simple competitive entry model, the authors predict the observed distribution of active GEO satellites with R² = 0.64. In walk-forward tests the structural model also predicts individual slot choices out of sample better than a fitted conditional-logit discrete-choice model. The same model predicts the distribution of inactive payloads in GEO with R² = 0.44. The current satellite distribution is relatively fair, driven by population rather than income, and places satellites in economically efficient locations, but this holds only for mature slots.

What carries the argument

A competitive entry model in which satellite operators select GEO slots to maximize expected profits under first-come first-served allocation.

If this is right

  • The geography of debris risk from inactive satellites can be predicted directly from launch patterns.
  • Satellite placement in GEO is driven by population size and is relatively fair across countries.
  • Placement is economically efficient in mature slots but not necessarily in newer ones.
  • A structural competitive model outperforms reduced-form discrete choice models for out-of-sample slot prediction.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar entry models could be applied to other orbital regimes once data on operator profits become available.
  • Regulators could use the model to forecast where risk concentrations will emerge before launches occur.
  • If profit expectations shift with new technology, the model predicts corresponding changes in the distribution of both active and inactive satellites.

Load-bearing premise

Satellite operators' slot choices are driven mainly by expected profits under first-come first-served rules without dominant unmodeled factors such as regulatory capture or geopolitical constraints.

What would settle it

A walk-forward test in which the profit-maximizing slot predicted by the model is chosen by fewer operators than a null model that ignores profit differences would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.25283 by Akhil Rao, Nikodem Szumilo.

Figure 1
Figure 1. Figure 1: The sequential entry mechanism in GEO. Each satellite (top) serves the consumers [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: the model reproduces the dense clusters above South and Southeast Asia, Europe, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: Data, model, and empirical fit. A: Global population density (log scale). B: Global GDP density (log scale). C: Reachable population (blue) and income (red) by longitude— the two candidate demand drivers. D: Observed satellite density (blue) versus CE model prediction (red dashed); R2 = 0.64. E: Observed satellite density versus GDP-based pre￾diction; R2 = 0.11. F: Scatter plots of observed vs. predicted d… view at source ↗
Figure 3
Figure 3. Figure 3: Sequential entry snapshots at four stages of constellation growth. Each panel [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Long-run deployment prediction (2000–2021). Each point is a 20 [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Rotation placebo. Fit vs. rotation angle. Orange = true alignment. Fit drops [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Mixed demand goodness-of-fit vs. income elasticity [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Population-weighted coverage quality versus GDP per capita. Each bubble [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Maximum Pareto-improving welfare gain versus constellation size. For each [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
read the original abstract

Some orbital locations are crowded while others remain unoccupied. We explain why using the geostationary orbit as a near-ideal laboratory: a mature, one-dimensional orbit in which satellite operators compete for position under first-come first-served allocation rules. Using the complete ITU registry and a simple competitive entry model, we predict the observed distribution of active GEO satellites with $R^2 = 0.64$. In walk-forward tests, the structural model also predicts individual slot choices out of sample better than a fitted conditional-logit discrete-choice model. Our model also predicts the distribution of inactive payloads in GEO with $R^2 = 0.44$, showing that the geography of debris risk can be predicted when it is a function of satellite launches. Surprisingly, we find that the current satellite distribution in GEO is relatively fair: driven by population rather than income and placing satellites in economically efficient locations. However, our model shows that this is only the case for mature slots.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper claims that a simple competitive entry model, calibrated to expected profits under first-come-first-served rules and applied to the complete ITU registry, predicts the observed spatial distribution of active GEO satellites with R² = 0.64. Walk-forward out-of-sample tests show this structural model outperforms a fitted conditional-logit discrete-choice model in predicting individual slot choices. The same model predicts the distribution of inactive payloads with R² = 0.44. The authors conclude that the current GEO distribution is relatively fair (driven by population rather than income) and places satellites in economically efficient locations, at least for mature slots.

Significance. If the structural interpretation holds, the work supplies a rare empirical test of competitive entry in a one-dimensional, mature resource with observable entry order, and demonstrates that the geography of orbital debris risk can be recovered from launch decisions alone. The walk-forward validation and direct comparison to a reduced-form discrete-choice benchmark are genuine strengths that raise the evidentiary bar above in-sample fit alone.

major comments (1)
  1. [Abstract and model section] The central claim that the R² = 0.64 fit and out-of-sample superiority reflect a valid structural representation of profit-driven slot choice is load-bearing on the assumption that unmodeled factors (regulatory capture, geopolitical constraints, technological lock-in) are not first-order. The abstract and model description supply no direct test of this premise—no country fixed effects, no geopolitical covariates, and no comparison of predicted versus actual entry around known regulatory events—leaving open the possibility that the reported performance reflects omitted-variable bias rather than the competitive-entry mechanism.
minor comments (1)
  1. [Abstract] The abstract supplies no information on model specification, parameter estimation, robustness checks, or selection into the ITU registry, which reduces the ability of readers to evaluate the reported R² values and walk-forward results at a glance.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive report and positive assessment of the paper's empirical contributions. Below we respond directly to the major comment.

read point-by-point responses

  1. Referee: [Abstract and model section] The central claim that the R² = 0.64 fit and out-of-sample superiority reflect a valid structural representation of profit-driven slot choice is load-bearing on the assumption that unmodeled factors (regulatory capture, geopolitical constraints, technological lock-in) are not first-order. The abstract and model description supply no direct test of this premise—no country fixed effects, no geopolitical covariates, and no comparison of predicted versus actual entry around known regulatory events—leaving open the possibility that the reported performance reflects omitted-variable bias rather than the competitive-entry mechanism.

    Authors: We agree that the structural interpretation depends on unmodeled factors not being first-order and that the current draft provides no direct test of this premise. The walk-forward out-of-sample superiority over the conditional logit offers indirect evidence, because any dominant omitted factors would likely be absorbed by the reduced-form benchmark, yet the structural model still outperforms. Nevertheless, this does not substitute for explicit checks. In revision we will add country fixed effects to the entry model, introduce a limited set of geopolitical covariates where data permit, and expand the model section to discuss the identifying assumption and its limitations. Direct event-study comparisons around regulatory changes are feasible only for a small number of well-documented ITU rule shifts and will be reported as supplementary analysis rather than a full test. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents a structural competitive entry model derived from first-come-first-served profit maximization that is used to generate predictions of satellite slot distributions. These predictions are evaluated both in-sample (R²=0.64) and via explicit walk-forward out-of-sample tests that outperform a separately fitted conditional logit benchmark. No quoted equations or sections reduce the central result to a parameter fit by construction, a self-citation chain, or a renamed empirical pattern. The model contains independent theoretical content (expected-profit entry under FCFS) that is tested against external data rather than being tautological with its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review conducted on abstract only; full model equations, estimation details, and data processing steps unavailable, so free parameters, axioms, and invented entities cannot be enumerated beyond the high-level domain assumptions stated in the abstract.

axioms (1)
  • domain assumption Satellite operators compete for GEO positions under first-come first-served allocation rules
    Explicitly stated as the institutional setting that generates the observed distribution.

pith-pipeline@v0.9.1-grok · 5707 in / 1379 out tokens · 30480 ms · 2026-06-25T20:18:18.155379+00:00 · methodology

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Reference graph

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