Why more procurement threads can perform worse at the same acceptance probability
In our internal model experiment, a fourteen-thread procurement policy has expected profit of 0.518956 when acceptances are independent. Making those outcomes perfectly dependent, while preserving each thread's acceptance probability and price cap, changes profit to −0.283656. The value of additional branches depends on whether they diversify risk, not only on their individual reliability. Engineers designing procurement agents need to examine fulfillment and excess acceptances together.
Equal acceptance rates do not imply equal diversification
The Cano paper studies single-unit procurement within one hard-deadline negotiation window and a common price cap. Its objective includes failure loss, per-thread cost and excess-acceptance cost. A commitment manager is assumed to retain at most one final binding transaction. Sections 2.3 and 3 describe a model and allocation of responsibilities, rather than demonstrated transaction enforcement.
Let m be launched threads, q their individual acceptance probability, and K the number of acceptances. Under independence, the probability of at least one acceptance is S=1−(1−q)^m. If every thread shares one acceptance event, S=q. Expected acceptance count remains mq in both cases, but expected excess acceptances are mq−S and therefore change.
Using value V, failure loss L, thread cost κ, excess-acceptance cost δ and common cap b(q), the objective reimplemented in the admitted analysis is:
Expected profit = (V + L + δ − b(q)) S − L − κm − δmqPerfect dependence is a deliberately constructed boundary control, not an estimate of real seller risk. It exposes the independence assumption while holding marginal acceptance fixed. Retaining only one final transaction also does not make every other tentative acceptance costless: cancellation or opportunity costs may remain.
Three policies answer three different questions
The same-day analysis used a normalized market with V=1.4, L=0.2, κ=0.01, δ=0.05 and at most twenty threads. Uniform prices have mean 1 and standard deviation 0.35. It reimplemented the source equation, searched q on a 0.0001 grid, enumerated binomial outcomes exactly, and simulated 100,000 orders with seed 20261103. Production reports those completed results; it adds no experiment.
| Condition | Threads m | Per-thread acceptance q | Expected profit | Evidence role |
|---|---|---|---|---|
| Grid plan under independent acceptance | 14 | 0.151 | 0.518956 | Internal equation reimplementation |
| Original policy under perfect dependence | 14 | 0.151 | −0.283656 | Internal constructed counterexample; other parameters unchanged |
| Replanned under perfect dependence | 1 | 0.4974 | 0.090008 | Internal discrete search; both concurrency and acceptance target change |
Source: same-day internal experiment output, linked below. The third row is not a fixed-q comparison, so its difference from the second cannot be attributed solely to reducing threads.
Under independence, the simulated mean is 0.520128 with standard error 0.000924. Exact enumeration gives 0.5189564216185868, consistent with the analytic objective. The simulated fulfillment frequency is 0.89999, the frequency of at least two acceptances is 0.646, and mean excess acceptances are 1.21375. These are internal normalized-market results, not seller observations or independent reproduction.
The fixed policy loses diversification while continuing to pay thread and excess-acceptance costs. Replanning shows that the model changes its choice; it does not show that an operational system can identify that dependence.
Faster information synthesis cannot establish commitment safety
AutoMARS describes parallel retrieval, report merging and reflection-based revision. Its authors report ten runs per setting, with total time falling from 622.11±59.84 seconds sequentially to 327.49±64.70 seconds in parallel. These are source-reported results from Sections 4 and 5.3.4. We did not rerun them, and raw traces or isolated timing provenance were not established in the admitted input.
Information-producing branches can merge their reports. Branches that may create external obligations must also account for excess acceptances. Lower latency cannot establish effective cancellation, a single final obligation, or procurement profitability. This comparison separates responsibilities; it does not rank performance across papers.
What a thread budget still needs
The internal calculation supports a counterexample within the specified objective. The paper's correlation-0.7 stress test is a separate author experiment; our perfectly dependent construction does not reproduce it. A discrete grid optimum is not a proof of a continuous global optimum. Real sellers need not be perfectly dependent, and dependence or costs can change with price, time or policy.
A resulting research check is to identify which branches only return information and which can create obligations, state the joint-acceptance assumption behind the thread budget, and name who bears excess-acceptance cost. Observed acceptance data can then test sensitivity, while actual cancellation, final commitment and deduplication require separate execution tests. These are model-derived research directions, not verified product operating instructions.
No language model, seller interaction, payment, cancellation or commitment enforcement ran in this experiment. The unresolved question is how to choose a usable thread budget when dependent acceptances are observable and cancellation rules are implemented.
Evidence and sources
Published designs are public primary-source facts about what the papers specify; performance numbers remain author reports. Neither automatically supplies independent validation. Our internal experiment is a bounded calculation, not third-party reproduction. Publication and citation establish provenance, without establishing general validity.
- Xu and Zhu, Parallelism or Concession? Concurrency-Aware Procurement Negotiation for Agentic Commerce, 5 October 2026, preprint v1. Model and appendices. We use its single-window objective rather than claiming full-paper reproduction.
- AutoMARS, October 2026, preprint v1. Design and timing report. Used to distinguish information synthesis from procurement commitments.
- Research Center, 3 November 2026, internal experiment data and equation reimplementation source. The data retain grid, seed, sampling error and limits. The source includes other bounded checks from the same analysis; this article uses only the procurement results.