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Who Pays for Thinking? Billing Hidden Reasoning Tokens in Model Cloud Contracts

Chao Feng, Burkhard Stiller

arXiv:2610.35338v1cs.GT

TL;DR

Token-priced AI services may charge for intermediate reasoning and candidate answers users never see, prompting questions about how billing affects provider choices and welfare. The paper models users, a model firm, and an execution cloud, then calibrates pricing comparisons using measured service profiles. At equal average charges, billing structure can change participation and computation budgets; welfare depends on whether additional inference’s value outweighs its costs.

  • Problem

    Token-priced services can charge for unseen reasoning and candidate answers, while the model–cloud allocation of incentives and execution costs is left largely implicit in prior studies.

    Source: §1 · p. 1

  • Method

    A three-party model separates user billing, upstream cloud payments, and budget control, while measured service profiles and archived tariffs support calibrated pricing comparisons.

    Source: §1 · p. 1, §4.1 · p. 5

  • Results

    At equal average charges on the reference workload, metered and fixed pricing can support different budgets, with welfare favoring metered pricing when added inference’s value exceeds its error, waiting, and resource costs.

    Source: §1 · p. 1, §6 · p. 8

  • Takeaways & Limitations

    The welfare ranking turns on whether additional correct answers are worth their added error losses, waiting costs, and resource costs.

    Source: §6 · p. 8

    Pooling’s welfare effect depends on cost levels, and when fixed pricing makes both budgets acceptable, multiple budget choices can remain possible.

    Source: §3.3 · p. 4

Abstract

from arXiv · show

In token-priced language model services, users can see the prompts they submit and the answers they receive, but may also pay for internal reasoning and candidate answers that are not shown in the final response. This paper develops a three-party service model to study how charging for this intermediate computation shapes providers' decisions and social welfare. Users purchase answers from a model firm that pays an execution cloud, with either supplier controlling the computation budget. The model separates user billing from upstream payments and identifies when metered pricing encourages excessive generation, when fixed service prices restrict valuable computation, and how responsibility for execution costs changes these choices. A LiveCodeBench study measures answer quality, latency, token use, and resource consumption across five model deployments, with numerical billing comparisons for the three covered by archived tariffs. At equal average charges on the reference workload, the calibrated comparisons show that billing structure changes both service participation and the computation budgets suppliers select. For accepted services with different budgets, the measured outcomes define the user-value thresholds at which their welfare ranking reverses. Metered pricing yields higher welfare when the additional inference it induces creates net social value, whereas fixed service pricing is preferable when the costs of that computation outweigh its benefits.

1 Introduction

Token-priced services can bill users for unseen reasoning and candidate answers, raising questions about how those charges shape computation and whether its added value justifies its cost. The paper compares metered and fixed pricing in a three-party model and calibrated LiveCodeBench comparisons.

1 Introduction

  • The paper addresses a gap in studies of user–provider incentives by making the model–cloud allocation of incentives and execution-cost responsibility explicit.A larger user bill can reward the model firm while additional execution costs fall on the cloud.Source: §1 · p. 1
  • The three-party model separates user billing from cloud payments and budget control to analyze participation, computation choices, and welfare under metered versus fixed pricing.It also examines how pooling can change preferred budgets or make a previously rejected budget profitable, sometimes lowering welfare despite cheaper fixed services.Source: §1 · p. 1
  • A 106-task LiveCodeBench study measures answer delivery, latency, token generation, and resource use across five deployments, with archived-tariff pricing comparisons for three.The measured profiles and tariffs inform calibrated comparisons at equal average charges on the reference workload.Source: §1 · p. 1
  • Under a fixed capacity fee, separate participation can block a jointly profitable service that an integrated supplier would provide.Measured service profiles determine available budgets and user-value conditions for welfare comparisons.Source: §1 · pp. 1–2

2 Problem Formulation

The formulation models a cloud-hosted service in which a model firm buys computation and a supplier chooses the attempt budget. It distinguishes pricing rules, user surplus, and social welfare to compare equilibrium outcomes with socially efficient choices.

2 Problem Formulation

  • The comparison holds the trained model, execution configuration, and answer-selection rule fixed while considering a cohort served with cloud-purchased resources.Source: §2 · p. 2

2.1 Service profiles

  • Each attempt budget generates candidates, after which a selection rule returns an answer or abstention; service profiles capture the resulting outcomes.They include correct and incorrect delivery probabilities, latency, billable intermediate tokens, billed GPU hours, and real resource cost per request.Source: §2.1 · p. 2

2.2 User-pricing rules

  • Metered pricing charges for intermediate generation, while fixed service pricing includes it in a predetermined price independent of the selected budget.Both charge for an executed request, including abstention, and their price levels are aligned using a reference-workload rule.Source: §2.2 · p. 2
  • User surplus depends on correct-answer value, error loss, waiting cost, outside-option value, and the price under the selected rule.Source: §2.2 · p. 2

2.3 Welfare comparison

  • Social welfare deducts real service costs and the outside-option value from the service’s value, with not undertaking the service assigned zero incremental welfare.Source: §2.3 · p. 2
  • The analysis compares outcomes of pure subgame-perfect equilibria under each pricing rule, retaining rejection and tied choices.Outcomes follow from supplier incentives and participation conditions.Source: §2.3 · p. 2
  • Metered pricing is strictly better across retained outcomes when min G > 0, while fixed pricing is strictly better when max G < 0.Other cases retain dependence on equilibrium selection.Source: §2.3 · p. 2

3 Method

The analysis models how retail pricing, upstream payments, supplier participation, and control rights shape computation choices and welfare. It compares metered and fixed pricing, including how pooling and cost responsibility change those choices.

3 Method

  • The model compares metered billing for intermediate generation with fixed service pricing, deriving service participation and supplier budget choices under fixed contracts and control rights.It retains rejection and tied choices in the equilibrium outcomes.Source: §3 · p. 2

3.1 Contract setting

  • User pricing shapes model-firm revenue, while upstream GPU-hour payments, capacity fees, or revenue sharing determine how execution costs and returns to added computation are allocated.The model separates the firm’s or cloud’s control of the attempt budget from the payment arrangement.Source: §3.1 · p. 2

3.2 How pricing changes computation and welfare

  • Metered billing yields higher welfare when the larger budget’s additional value exceeds its additional cost; fixed pricing yields higher welfare when the reverse holds.Above that threshold, fixed pricing induces insufficient computation; below it, metered billing induces excessive computation.Source: §3.2 · p. 4

3.3 How pooling changes the pricing comparison

  • Pooling can shift metered pricing from the low to the high budget under either control assignment, and the welfare effect depends on the value and cost of the added computation.Under model control, pooling can also turn the cloud’s rejection of a proposed high budget into acceptance.Source: §3.3 · p. 4

3.4 Cost responsibility and larger budget menus

  • With positive model-firm costs below the stated threshold and both budgets participating, metering selects the high budget while fixed pricing selects the low; on larger menus, pooling weakly raises extreme cloud optima and selected model budgets.The larger-menu results require their stated participation and savings conditions.Source: §3.4 · pp. 4–5

4 Experiments

Across five deployments, measured service profiles and a three-party contract model show how billing, supplier participation, and budget control shape service provision. At equal average charges, metered pricing and fixed pricing can select different budgets, with welfare rankings depending on user value and the costs and benefits of additional computation.

4.1 Experimental setup and calibration

  • The evaluation measures 106 LiveCodeBench tasks across five deployments, with three repetitions and execution configurations; archived tariffs support numerical billing comparisons for three deployments.The service delivers the first candidate passing fixed screening tests and abstains if none passes; outcomes include correct and incorrect delivery, latency, token generation, and resource use.Source: §4 · p. 5, §4.1 · p. 5

4.2 Service participation and budget choice

  • For serial execution, reconstructed bills rise 7.7–8.7 times from one to eight candidates, while costs rise 1.3–2.0 times; metered billing selects eight candidates in both Qwen3.8 deployments under sharing.Fixed pricing selects one except for a model-controlled tie in Qwen3.8 thinking repetition r2; Qwen3.5 supplies neither service.Source: §4.2 · p. 6
  • Under a fixed capacity fee, metered pricing provides no service although the Qwen3.8 non-thinking, batch16, r0 high-budget service would yield 61.4 USD joint profit per 1,000 requests.The low-budget bill is below the firm’s fee, while high-budget cost exceeds the cloud’s payment; fixed pricing restores trade at one candidate.Source: §4.2 · p. 6, Table 2 · p. 6

4.3 Welfare comparison

  • For Qwen3.8 non-thinking, batch16, r0, eight candidates add 19 correct and 8 incorrect deliveries across 106 tasks, and metered billing has higher welfare above the threshold when both services are purchased.In the capacity-fee case, fixed pricing yields positive welfare whenever its low-budget service is purchased, while metered pricing yields zero because neither budget trades.Source: §4.3 · p. 6

4.4 Sensitivity analysis

  • Across all three batch16 repetitions, service and startup-inclusive cost accounting, and evaluated energy endpoints, metered billing selects eight candidates while fixed pricing selects one within the strict switching intervals.Reconstructing complete token bills preserves all 21 main-tariff budget profiles; pooling removes 12.4–76.1% of the serial increase in additional GPU time across 18 comparisons.Source: §4.4 · p. 7
  • With matching GPU models across two Qwen3.8 thinking-mode comparisons, thinking improves correct delivery and reduces errors at a given budget, while increasing cost and waiting time.Higher error losses favor the quality improvement, whereas higher waiting costs raise the value required to justify it; welfare thresholds change even when pricing rules induce the same budget pattern.Source: §4.4 · p. 7

5 Related Work

Related work examines strategic inference and token pricing, supplier payment and cost allocation, and answer quality and serving costs. This paper connects these strands by comparing billing rules while separating supplier participation decisions.

5.1 Metered pricing and strategic inference

  • Strategic-inference, menu-pricing, and truthful-billing studies connect user payments to provider behavior; this paper separates model-firm and cloud participation while holding tariffs and token counts fixed.Table 4 locates the comparison among related pricing and contracting models.Source: §5.1 · pp. 7–8, Table 4 · p. 8

5.2 Payments and cost responsibility

  • Industrial-organization, supply-chain, collaborative-service, and cloud-contract research informs the paper’s analysis of how payment and cost responsibility affect inference provision.A fixed user price removes marginal retail revenue, while a fixed capacity fee removes the model firm’s additional upstream payment.Source: §5.2 · p. 8

5.3 Quality, selection, and service cost

  • Test-time scaling, answer verification, automated evaluation, serving systems, and inference-cost models address quality or execution; this study combines measured service profiles with supplier participation to compare billing rules and welfare thresholds.The measured profiles include delivered correctness, errors, latency, and resources through online answer selection.Source: §5.3 · p. 8

6 Conclusion

The calibrated comparison links billing rules to supplier incentives, participation, and computation budgets. When metered pricing induces more computation, its welfare advantage depends on whether the added inference’s social value exceeds its costs.

6 Conclusion

  • Metered billing adds revenue for intermediate computation, while fixed pricing removes that increment; control and cost responsibility shape the resulting budget incentives.Under a fixed capacity fee, separate participation can block a jointly profitable service that an integrated supplier would provide.Source: §6 · p. 8
  • Metered billing yields higher welfare when additional correct-answer value exceeds added error losses, waiting costs, and resource costs; fixed pricing wins when that balance reverses.This comparison applies under revenue sharing and user purchase when the resulting services have different budgets.Source: §6 · p. 8
  • Equal average charges on the reference workload can support different computation budgets under revenue sharing and user purchase.Welfare depends on how revenue, cost, and control align private computation choices with net social value.Source: §6 · p. 8

AI Use Declaration

The authors disclose AI assistance in code development, data analysis, and internal manuscript review, while retaining responsibility for the research and final content.

AI Use Declaration

  • AI tools assisted with code development, data analysis, and internal manuscript review; the authors determined the research questions and design, conducted experiments, and take responsibility for the final content.Source: AI Use Declaration · p. 8

A.1 Cost responsibility and finite menus

The appendix establishes robustness and selection properties for finite-budget supplier decisions, including participation ties and configuration-dependent bills. It also states the scope of the flexible-term benchmarks.

A.1 Cost responsibility and finite menus

  • Reallocating fixed total cost preserves strict comparisons, traded budgets, and welfare differences for sufficiently small positive cost shares, while both suppliers bear positive costs where total cost is positive.Under model control, lower cloud costs expand acceptance when E is fixed; arbitrary choices among tied optima need not be ordered.Source: §A.1 · p. 9

A.2 Participation ties and exit

  • The solver retains pure subgame-perfect outcomes by backward induction, including acceptance or rejection at zero payoff, budget ties, and exit.All supported pure outcomes enter O_j, and G contains their cross-pricing welfare differences.Source: §A.2 · p. 9

A.3 Configuration-dependent profiles

  • With configuration-dependent bills under sharing, increasing differences must be checked for the full profit αB_π−C_π, not just cost savings.The identity separates cost savings from bill drift across configurations.Source: §A.3 · p. 9

A.4 Flexible retail and upstream terms

  • The flexible retail and upstream-term benchmarks allow prices or upstream payments to adjust, retaining acceptance at zero surplus or profit.Source: §A.4 · p. 10

A.4.1 Retail pricing.

Under pointwise retail pricing, the appendix identifies when model-controlled participation can still support a higher budget and limits those conclusions to that schedule. For upstream payments, cost-covering capacity fees and flexible transfers can recover the integrated supplier objective.

A.4.1 Retail pricing.

  • The overprovision region is empty under the pointwise schedule, although model-controlled participation can still support the high budget under the stated cloud-cost condition.The cloud accepts the high budget when Cπ(kH) ≤ α(VH − u0); the welfare change remains ΔV − ΔC1 + sL under Proposition 3.5’s remaining conditions.Source: §A.4.1 · p. 10
  • These conclusions use a pointwise schedule, not unrestricted menu pricing, where prices at other budgets can also steer the cloud.Source: §A.4.1 · p. 10

A.4.2 Upstream payments.

  • A capacity fee equal to the integrated-optimal budget’s cost supports that budget at zero cloud profit and lets the firm maximize social welfare with pointwise retail extraction.This applies when all considered budgets satisfy user participation and the integrated maximum is nonnegative.Source: §A.4.2 · p. 10
  • With a signed fixed transfer, sharing can support either user-accepted budget meeting Bk ≥ Ck and make the integrated supplier objective attainable.Setting α = ΔC/ΔB and F = CL − αBL makes cloud profit zero at both budgets when 0 < ΔC/ΔB < 1.Source: §A.4.2 · p. 10

B Experimental and Price Calibration

The experimental section describes five deployments, their service accounting, and resource-cost and tariff calibration. Matched comparisons and service profiles supply inputs for the later pricing and welfare calculations, whose scope and protocol are documented.

B.1 Deployments and service accounting

  • Five deployments use frozen generation settings, and service-window accounting includes online selection while excluding offline correctness audits and idle harness roles.The service results are descriptive for fixed tasks and observed allocations.Source: §B.1 · p. 10, Table 5 · p. 10

B.2 Matched pooling comparisons

  • All 18 matched pooling contrasts are positive, with the measured GPU-resource reduction covering generation and answer delivery.The contrasts compare the increase in GPU seconds per request from one to eight candidates under serial versus pooled execution.Source: §B.2 · p. 10, Table 6 · p. 11

B.3 Tariff anchors and reference prices

  • Archived tariffs provide calibration anchors for three deployments, while the controlled comparison sets bills to equal average charges on the reference workload.Coder and Nemotron lack durable matching tariff anchors, and hosted-weight identity is unverified for the quoted rates.Source: §B.3 · p. 10

B.4 Resource-cost conversion

  • Per-request resource costs combine cohort GPU, CPU, and energy costs under declared central-rate scenarios, with sensitivity analyses varying energy assumptions and startup treatment.Public prices provide context rather than observed supplier costs.Source: §B.4 · p. 11

B.5 Protocol timeline

  • The protocol timeline records later changes to hardware variants, call limits, cost grids, and analyses; the original primary bootstrap was withheld by its pause rule.Supplemental pipeline diagnostics are not intervals for the service comparisons.Source: §B.5 · p. 11

C Numerical Checks and Price Thresholds

C.1 Service profiles and welfare thresholds

  • Service profiles across five deployments provide quality and cost inputs, while welfare-threshold coefficients express how added error loss and waiting costs affect the required answer value.The threshold coefficients and profiles are presented in Tables 7 and 8; Coder and Nemotron also provide social thresholds without matching retail quotes.Source: §C.1 · pp. 11–12, Table 7 · p. 11, Table 8 · p. 12

C.2 Supplier participation

The participation comparisons show that supplier control and payment structure can determine whether a service is provided. For models without quoted tariffs, the paper reports price and social thresholds, while scans find no admissible share for a specified pooling-induced participation switch.

C.2 Supplier participation

  • The model firm rejects the low metered budget and the cloud rejects the high one, while both profit from the low fixed-price service over a common 20.3–34.7 USD per 1,000 requests interval.The reference capacity fee is 28.9 USD per 1,000 requests, and exact boundary ties are retained.Source: §C.2 · p. 12

C.3 Models without quoted tariffs

  • For Coder and Nemotron, complete bills include delivered, reasoning, and unselected output, and strict purchase imposes a price bound alongside a social-provision threshold.Table 11 reports price-bound coefficients by budget; the social comparison is against exit.Source: §C.3 · p. 12, Table 11 · p. 12

C.4 Pooling admission scans

  • No admissible share satisfies the separate pooling-induced cloud-participation switch in any of the 1,400 pipeline or 896 service scenario rows under complete non-delivered-token billing.For serial bills and costs, the high-budget cost-to-bill ratio is below the low-budget ratio in every service row, excluding the required initial acceptance pattern.Source: §C.4 · p. 12
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