Does Multi-Agent Collaboration Pay When Agents Serve Users? Testing Agent Scaling in Dual-Control Settings

Ethan Yang; Xiangcheng Shi

cs.AIOct 20, 2026

Does Multi-Agent Collaboration Pay When Agents Serve Users? Testing Agent Scaling in Dual-Control Settings

Authors: Ethan Yang, Xiangcheng Shi

Organizations: University of Pennsylvania

Abstract

Multi-agent systems (MAS) built from language models are deployed on the premise that collaboration beats a single-agent system (SAS), yet when it pays is unclear. The most systematic study to date gives a capability-saturation rule: coordination helps while the SAS is weak and hurts once it is strong, with the crossing near 45% single-agent accuracy. That rule was derived on autonomous benchmarks, where no user takes part. We test it where agents now work: in conversation with a user under a written policy, on $τ^2$ -bench, the dual-control benchmark. On its airline, retail and telecom domains we compare the stock SAS with a centralized MAS built from the same model for six models from three families, over about 7,950 simulated conversations, with one completion-token ledger per episode per system. The study was pre-registered with a public change log; the MAS is reported as built, with one validity bar unmet (its planner never saw the tool schemas). Under a fixed simulated user no cell shows a MAS benefit: the MAS is worse in 12 of the 13 valid cells and tied in the thirteenth, and the fitted gain is negative across the observed capability range (weighted mean -28 points, 95% CI [-44, -12]). On the two cells where the rule predicts a benefit, the MAS loses by 13 and 22 points, and without a budget ceiling it at best draws level at 5.5 times the SAS's token spend. The one gain appears on the cell nearest 45%, under a second simulator. Whether the gain declines with capability is unresolved (slope -0.41, 95% CI [-1.51, +0.68]), because model-by-domain effects dominate. The MAS does not detectably reduce wrongful database writes; it converts other failures into budget exhaustion and inaction. For agents that serve people, the SAS is the default; a multi-agent design must show compute-matched evidence from the setting itself. We release all trajectories, ledgers, prompts and code.

Figures & tables

Study	Architectures	Capability varied	Compute matched (what, level)	User (tools)	Sim.	Rule
Kim and others (2026)	SAS + 4 generic MAS	3 families $\times$ 3 tiers	reasoning tokens, per system, reported as a matched mean; matched maximum iterations	no	n/a	fitted
Tran and Kiela (2026)	SAS + 5 MAS variants	4 models	thinking tokens, per call, split	no	n/a	no
Jwalapuram and others (2026)	CoT-SC vs automated MAS	several	USD, post hoc	no	n/a	no
Yu and others (2026)	SAS vs MAS	3 scales	max. total steps (experiments); relay bandwidth (theory)	no	n/a	no
Gao and others (2025)	SAS vs MAS	several	cost reported	no	n/a	no
LangChain (2025)	single, swarm, supervisor	1 model	no	yes (no)	no	no

Table 1: Position against the closest prior work. No prior study has all six properties at once. “User” means a user takes part in the episode, with “tools” when the user also holds tools (dual control in the sense of Barres et al. (2025) ). “Rule tested” means an existing selection rule is applied unchanged to a new setting.

Panel of Figure 1 — Figure 1: The systems. (a) Single-agent systems: the stock SAS, whose uncapped episodes calibrate the budget, and S2, one agent that runs the MAS’s plan-and-review cycle in one context under the same ledger. (b) The centralized MAS built from the same model: only the orchestrator talks to the customer, only the database agent calls tools, and all calls draw on one completion-token ledger (Eq. 2 ); in M2 the policy advisor becomes a checker that can veto an order or a message (outlined, not evaluated here). On telecom the customer also acts on the device (dashed).

Protocol	Adopted	Deviation here
Kim and others (2026)	per-system ceiling; coordination paid from the same pool; exhaustion is a legal termination	they report matched reasoning-token budgets as a mean per trial and matched maximum iterations, with no per-episode token ceiling described as enforced at call time; here a per-episode token ceiling, enforced
Tran and Kiela (2026)	the SAS spends the whole budget in one trajectory; a MAS divides it	they keep planner and aggregator near budget-neutral, here every component is charged; they count thinking tokens, here completion tokens with reasoning-only as sensitivity; they split statically ( $B/k$ ), here a shared pool with reservations, which is more generous to the MAS, so a null MAS result is conservative
Wang and others (2024)	performance-at-tokens curves	their cap is input plus output per question; here input is reported as a deployment account outside the scientific budget
Kapoor et al. (2024)	accuracy-versus-USD frontier for deployment claims	not used for the main contrast, where compute and architecture would co-vary

Table 2: Relationship to prior budget protocols.

Domain	Model	SAS mean	$B_{1\times}$ ( $P_{75}$ )	$B=4B_{1\times}$	$c$	per-call $P_{95}$
airline	gpt-5-nano	40,839	51,297	205,188	51,297	11,566
retail	gpt-5-nano	29,783	35,313	141,252	35,313	8,897
telecom	gpt-5-nano	60,570	75,032	300,128	75,032	6,100
airline	gpt-5-mini	20,808	27,477	109,908	27,477	8,312
retail	gpt-5-mini	14,432	18,294	73,176	18,294	5,389
telecom	gpt-5-mini	26,165	31,514	126,056	31,514	5,273

Table 3: Calibration per cell from the 150 uncapped SAS episodes: mean and 75th percentile of episode completion tokens (

B_{1\times}

), the ceiling

B=4B_{1\times}

, the per-call cap as run (

c=B_{1\times}

) and the SAS per-call 95th percentile for reference. The wrap-up threshold is

w=\max(0.15B_{1\times},2\,\text{median})

and the minimum allowance

a_{\min}=\text{median}

of SAS per-call completion tokens (full values in the released budgets.json ).

$x$	Scenario	$b=0$	$-0.10$	$-0.20$	$-0.30$	$-0.40$	acc. @ $-0.3$	inform. @ $-0.3$
naive	27 cells, 50 tasks, 3 seeds	0.19	0.78	1.00	1.00	1.00	0.84	0.39
naive	18 cells, 50 tasks, 3 seeds	0.20	0.67	0.99	1.00	1.00	0.87	0.49
split seed	27 cells, 50 tasks, 3 seeds	0.07	0.48	0.87	0.99	1.00	0.82	0.32
split seed	18 cells, 50 tasks, 3 seeds	0.07	0.35	0.80	0.97	1.00	0.86	0.42
leave-one-domain-out	27 cells, 50 tasks, 3 seeds	0.07	0.40	0.77	0.95	1.00	0.84	0.38
leave-one-domain-out	27 cells, 50 tasks, 5 seeds	0.10	0.51	0.93	0.99	1.00	0.86	0.47

Table 4: Power of the H1 slope test by form of

x

and grid size (simulation). acc.: expected sign accuracy at

b=-0.3

; inform.: share of informative cells.

Model	Domain	SAS	SAS 95% CI	MAS	Gain [95% CI]	Exh.	Util.	Fin./exh.	Tokens
gpt-5-nano	airline	42.7	[31.3, 54.0] ∘	45.3	$+2.7$ [ $-6.7$ , $+12.7$ ]	23%	0.50	50% / 31%	2.9 $\times$
	retail	68.0	[58.7, 77.3]	44.7	$-23.3$ [ $-32.7$ , $-13.3$ ]	16%	0.63	52% / 8%	3.1 $\times$
	telecom	32.7	[22.7, 43.3] ↓	19.3	$-13.3$ [ $-20.7$ , $-6.0$ ]	15%	0.54	20% / 13%	2.8 $\times$
gpt-5-mini	airline	74.7	[64.7, 84.0]	58.0	$-16.7$ [ $-27.3$ , $-6.7$ ]	34%	0.83	68% / 39%	5.2 $\times$
	retail	76.0	[66.7, 84.0]	48.0	$-28.0$ [ $-40.0$ , $-17.3$ ]	43%	0.90	68% / 22%	4.9 $\times$
	telecom	77.3	[68.0, 86.0]	66.0	$-11.3$ [ $-18.7$ , $-4.0$ ]	18%	0.70	79% / 7%	4.2 $\times$

Table 5: No cell shows a MAS benefit. The grid in the cost-bounded arm (

B=4B_{1\times}

c=B_{1\times}

r=4

; 150 episodes per system), pass 1 in percent with task-cluster bootstrap CIs. Exh.: MAS episodes ending budget exhausted; util.: median share of the ceiling spent; fin./exh.: pass rates of MAS episodes that finished and that were exhausted; tokens: median MAS completion tokens per episode over the SAS median (the ceiling bounds this ratio at

B

over the SAS median, 5.0 to 6.3 across cells).

\dagger

: fails the mechanical bars, sensitivity only; SAS values computed by a collaborator.

\ddagger

: local route; per trial the MAS passed 15, 11 and 9 of 50, with the third trial affected by the route’s fixed sampling seed (Appendix B ).

Model	Domain	Cut calls	Cut tokens	2-cut (exh./other)	Advisor	Plan fail (n)	Forced	As issued	Bars
gpt-5-nano	airline	0.3%	0.3%	0 / 0	17	3.5% (48)	31	16%	met
	retail	0.4%	0.5%	0 / 0	13	1.1% (15)	43	10%	met
	telecom	0.3%	0.5%	0 / 0	9	1.6% (30)	51	20%	met
gpt-5-mini	airline	0.9%	0.9%	0 / 0	21	3.9% (46)	40	31%	met
	retail	1.3%	1.4%	0 / 0	7	4.8% (58)	54	39%	met
	telecom	0.5%	0.5%	0 / 0	8	1.9% (32)	25	41%	met

Table 6: G1 indicators per MAS cell at

4\times

, computed from logs. Bars: calls cut at the cap

\leq 5\%

; tokens in cut calls

\leq 10\%

; no turn with two or more cut calls outside the final exhaustion turn (shown as exhaustion / other); no JSON or cut text sent to the customer. Reported indicators: episodes (of 150) that consulted the advisor; plan calls that did not parse (share and count); forced customer messages; and the share of unique write orders executed exactly as issued under the stricter audit (a refused or diverted order counts as not executed). The fidelity bar (

\geq 90\%

as issued) fails in every cell. Last column: whether the mechanical bars are met. “–”: not available from the collaborator’s files.

Model	Domain	Gain	Exhausted	Finished	Share	Tasks better / equal / worse
gpt-5-nano	airline	$+2.7$	$+2.0$	$+0.7$	–	13 / 26 / 11
	retail	$-23.3$	$-6.2$	$-17.1$	27%	2 / 23 / 25
	telecom	$-13.3$	$-3.6$	$-9.8$	27%	3 / 28 / 19
gpt-5-mini	airline	$-16.7$	$-11.8$	$-4.9$	71%	6 / 27 / 17
	retail	$-28.0$	$-22.9$	$-5.1$	82%	5 / 19 / 26
	telecom	$-11.3$	$-8.7$	$-2.7$	76%	5 / 25 / 20

Table 7: Where the loss arises, per cell meeting the mechanical bars, at

4\times

(points). The exhausted and finished parts sum to the gain up to rounding; share: part of the loss carried by exhausted episodes, shown where the gain is negative. Tasks: number of the 50 tasks on which the MAS pass rate is above, equal to or below the SAS pass rate.

SAS 95% CI relative to 45%	Cells	Principle predicts	Observed	Sign matches
entirely above	10	MAS loses	10 losses	10 of 10
entirely below	2	MAS gains	2 losses	0 of 2
straddles	1	(uninformative)	1 tie	–
all informative cells	12			10 of 12 (binomial $p=0.039$ )

Table 8: Where the principle predicts a MAS benefit, the MAS loses under the ceiling and at best ties without one. Top: the 45% rule applied to each of the 13 cells’ own SAS pass 1 . Bottom: the three cells at or below 45%, with and without a ceiling (uncapped arm). Index: SAS pass 1 on the model’s other two domains; tokens: median MAS completion tokens per episode over the SAS median, without a ceiling.

Figure 2: (a) Principle map: each of the 13 cells’ own SAS pass 1 against its gain with the paired task-cluster 95% interval; the principle predicts a gain left of the dashed 45% line and a loss right of it; the hollow marker is the one cell whose interval covers zero; grey crosses are the three qwen3.5-9b cells that fail the mechanical bars. No regression is drawn on this axis. (b) H1: the same gains against the leave-one-domain-out index for the 12 cells of the primary fit, with the weighted fit at the mean family and domain effect and its 95% band. The two telecom cells left of 45% in (a) move right of it. Colour marks the domain and shape the family.

Form	Cells	Slope [95% CI]	Perm. $p$
leave-one-domain-out index (primary)	12	$-0.41$ [ $-1.51$ , $+0.68$ ]	0.43
split seeds	12	$-0.44$ [ $-0.95$ , $+0.07$ ]	–
logit gain a	12	$-1.61$ [ $-4.96$ , $+1.75$ ]	–
relative gain a	12	$-0.35$ [ $-1.40$ , $+0.70$ ]	–
primary with the qwen3.5-9b cells	15	$-0.28$ [ $-1.26$ , $+0.69$ ]	0.59
own SAS score (naive, biased)	12	$-0.55$ [ $-1.16$ , $+0.06$ ]	–

Table 9: The gain shows no detectable dependence on capability, and its fitted level is negative across the observed range. Left: the H1 slope (points of gain per point of index) under each form; the primary form carries the test (minimum detectable slope in our power analysis

0.20

). a Other units. Right: the primary fit at the mean family and domain effect.

Outcome	SAS	MAS	Change per episode [95% CI]	Cells down / up
pass	1,362	768	$-30.5$ [ $-43.6$ , $-18.6$ ]	12 / 1
wrongful write (WW)	55	43	$-0.6$ [ $-2.6$ , $+1.2$ ]	5 / 5
budget exhausted (BX)	0	666	$+34.2$ [ $+24.5$ , $+44.3$ ]	0 / 13
inaction (IN)	126	268	$+7.3$ [ $+3.7$ , $+11.8$ ]	1 / 10
other failure	407	205	$-10.4$ [ $-17.0$ , $-4.3$ ]	10 / 3
FP, commission (airline)	27 of 415 passes	17 of 332 passes	$-1.7$ (4 clusters, no CI)	4 / 0

Table 10: The MAS does not detectably reduce wrongful writes and converts other failures into exhaustion and inaction. Pooled over the 13 cells (1,950 episodes per system); paired change per episode in points, cell-cluster bootstrap CI; classes assigned in the order WW, BX, IN, other. FP (airline only; 600 episodes per system) counts judge flags among passes; “all flags” adds omission flags, which were not adjudicated by hand, and is an upper bound.

		SAS					MAS
Model	Domain	PASS	WW	BX	IN	OTHER	PASS	WW	BX	IN	OTHER
gpt-5-nano	airline	64	28	0	10	48	68	14	23	22	23
	retail	102	0	0	16	32	67	0	22	23	38
	telecom	49	12	0	8	81	29	5	19	51	46
gpt-5-mini	airline	112	5	0	12	21	87	0	31	24	8
	retail	114	0	0	8	28	72	0	51	17	10

Table 11: Failure taxonomy per cell meeting the mechanical bars (episodes out of 150): passes, wrongful writes, budget exhausted, inaction, other.

Model	Domain	SAS	MAS at $4\times$	Ratio	Agent only
gpt-5-nano	airline	4.66	9.15	2.0	2.9
	retail	3.74	7.49	2.0	3.1
	telecom	8.71	12.57	1.4	2.5
gpt-5-mini	airline	8.77	27.54	3.1	3.9
	retail	6.82	20.83	3.1	4.0
	telecom	16.94	34.45	2.0	3.4

Table 12: Recorded cost per cell in USD at list prices (agent plus simulator; tau2’s own cost field). Ratio: MAS over SAS; agent only: the same ratio without the simulator. The local 4-billion model has no per-call price, so its cells show the simulator cost only.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Row	Unit; contrast; test	Reading rule	Result
H1 slope (primary)	cells meeting the mechanical bars; gain on leave-one-domain-out index, family and domain effects, inverse-variance weights; permutation $p$	supported if slope $<0$ with CI excluding zero; null read as $\|b\|<0.20$	$-0.41$ $[-1.51,+0.68]$ , $p=0.43$ ; not supported; CI far wider than the minimum detectable slope of 0.20
H1 crossing	same fit; $x_{0}=-\text{intercept}/\text{slope}$ ; bootstrap CI	transfers if CI covers 45%; shifts if not; no crossing if slope CI covers zero	no crossing (fitted gain $<0$ over the whole index range)
Sign match	cells not straddling 45%; predicted vs observed sign; binomial vs 0.5	$X/N$ beside 15/16; informative and within-noise cells apart	10 of 12 informative ( $p=0.039$ ); right on all 10 above 45%, wrong on both below
H2a (primary)	SAS cells; WW/failures and FP/passes on the index	WW/failures slope $<0$ , FP/passes slope not $<0$	WW half: $-0.15$ $[-0.64,+0.34]$ , $p=0.78$ ; not supported; FP half (airline, 4 cells, descriptive): commission flags per pass fall from 15.6 to 2.5%
H2b (primary)	paired MAS $-$ SAS WW, pooled, cluster CI	grid over WW, IN, BX, FP	WW $-0.6$ pts $[-2.6,+1.2]$ : no detectable change; BX $+34$ , IN $+7$ pts; FP commission 6.5 to 5.1% of passes
R1	2 cells, gain across budget levels	dependence only if its CI excludes zero	$\text{gain}_{4\times}-\text{gain}_{1\times}$ $+5.3$ $[-2.7,+14.0]$ and $+8.0$ $[-1.3,+18.0]$ : not claimed

Appendix

Table 13: Tests and results. Each row gives a test, the rule used to read it and the result.

Cell	Build	MAS pass / exhausted (trial 0, 1, 2)			Gain, pooled	Trials 0 and 1	Trial 2
		0	1	2
telecom (grid)	registered	15 / 26	11 / 27	9 / 41	$-71.3$ $[-80.0,-62.7]$	$-69.0$ $[-78.0,-59.0]$	$-76.0$ $[-88.0,-62.0]$
	SAS passes	48 of 50	47 of 50	47 of 50
retail (appendix)	October	16 / 19	14 / 12	5 / 43	$-50.7$ $[-60.7,-40.7]$	$-46.0$ $[-58.0,-34.0]$	$-61.2$ $[-73.5,-46.9]$
	SAS passes	40 of 48	34 of 48	35 of 49
airline (collaborator)	registered	28 / 15	30 / 14	26 / 42	–	–	–

Appendix

Table 14: The three local 4-billion MAS cells per trial: MAS passes and exhausted episodes out of 50, SAS passes out of the evaluated episodes of the same trial, and the paired gain (points, task-cluster bootstrap CI) pooled, on trials 0 and 1, and on trial 2. The airline SAS on the registered build does not exist beyond 10 episodes, so that row has no gain.

Prompt	Seed	Cut on first repeat	Calls	Median tokens	Cut	Empty
trial 2	361454 (trial 2’s)	5 of 6	12	5,369	8	7
trial 2	373753 (trial 1’s)	0 of 6	12	404	1	1
trial 2	none	0 of 6	12	629	0	0
trial 1	361454	1 of 6	12	2,798	2	2
trial 1	373753	0 of 6	12	371	0	0
trial 1	none	0 of 6	12	538	0	0

Appendix

Table 15: Seed replay on the October build (17 October 2026; 120 calls, 86 minutes of model time, no errors). For each condition: trial-2 or trial-1 first plan prompt of the six cut tasks; first-repeat cuts at the cap; and over both repeats the number of calls, median completion tokens, calls cut at the cap and calls with no visible text.

Pairing	Tasks	MAS	SAS	Gain [95% CI]	Tasks better / equal / worse
SAS as recorded (crashes score 0)	50	56.0%	39.7%	$+16.3$ $[+4.7,+27.7]$	20 / 24 / 6
SAS crashed episodes excluded	38	63.2%	70.2%	$-7.0$ $[-20.2,+5.3]$	5 / 26 / 7
By trial, SAS as recorded: trial 0	49	57.1%	38.8%	$+18.4$ $[+2.0,+34.7]$	13 / 32 / 4
trial 1	48	58.3%	41.7%	$+16.7$ $[0.0,+33.3]$	12 / 32 / 4
trial 2	47	51.1%	38.3%	$+12.8$ $[-2.1,+25.5]$	9 / 35 / 3

Appendix

Table 16: Airline

\times

qwen3.5-4b sensitivity: the collaborator’s MAS (registered build, 150 episodes) paired with the collaborator’s September SAS (other stack, 144 evaluated episodes). Task-mean pass 1 ; paired gain with task-cluster bootstrap CI (seed 300, 2,000 draws); tasks on which the MAS pass rate is above, equal to or below the SAS’s.

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