Parallelism or Concession? Concurrency-Aware Procurement Negotiation for Agentic Commerce

Xiaolin Xu; Donghao Zhu

cs.GTOct 5, 2026

Parallelism or Concession? Concurrency-Aware Procurement Negotiation for Agentic Commerce

Authors: Xiaolin Xu, Donghao Zhu

Organizations: School of Business Nanjing University Nanjing, Jiangsu, China · Institute of Business Sciences University of Tsukuba Bunkyo-ku, Tokyo, Japan · University of Tokyo Market Design Center Bunkyo-ku, Tokyo, Japan

Abstract

Agentic buyers can cheaply fork a procurement task into many parallel negotiations, but concurrency is not free: every thread consumes resources, and simultaneous agreements create cancellation and commitment risk. We study a one-unit post-order sourcing problem with a single hard-deadline negotiation window, in which a planner jointly chooses the number of seller-facing negotiators and a common procurement price cap. The model combines a product-specific acceptance curve with fulfillment loss, per-thread cost, and excess-commitment cost. We establish three structural results. First, holding the per-thread acceptance target fixed, the marginal value of another negotiator decays geometrically, yielding a conditional concurrency threshold. Second, under a convex quantile curve, parallelism substitutes for concession: more concurrent negotiators imply a weakly lower per-thread acceptance target and price cap. Third, when prices are more dispersed, Agentic buyers benefit by searching harder for bargains, but suffer when they instead try to guarantee procurement by offering higher prices. We operationalize these results in the Concurrency-Aware Negotiation Optimizer (CANO), a deterministic optimizer that jointly determines the optimal negotiation concurrency and procurement price cap for an agentic procurement system. Across different analytic market configurations and extensive Monte Carlo, finite-data, non-Gaussian, and correlated-seller stress tests, CANO consistently outperforms common heuristic policies while validating the predicted structural properties.

Figures & tables

Panel of Figure 1 — Figure 1. Cano as the economic control layer of an agentic procurement system. The market estimator supplies the eligible-seller count $N$ and estimated acceptance curve $\widehat{F}$ . The planner selects concurrency $m^{\star}$ , acceptance target $q^{\star}$ , and procurement cap $b^{\star}$ . Seller-facing agents negotiate in parallel subject to $p_{it}\leq b^{\star}$ , and the commitment manager executes at most one binding transaction. Logged outcomes support auditing and future acceptance-curve updates. A horizontal architecture diagram with four rounded blocks: market estimator, CANO planner, parallel negotiation agents, and commitment manager. Solid arrows indicate the forward control flow. A dashed curved arrow returns outcome logs, audit information, and acceptance-curve updates from the commitment manager to the market estimator.

Symbol	Meaning
$N$	eligible sellers (market thickness)
$m$	concurrently launched negotiators
$b=C(q)$	common terminal procurement cap
$V$	net value of a fulfilled order
$L$	loss from cancellation or failed fulfillment
$\kappa$	cost per launched negotiation thread

Table 1. Core notation and operational interpretation.

Figure 2. Structural predictions for $V=1.4,\mu=1,L=.2,\kappa=.01,\delta=.05$ . (a–b) With $N=20,\sigma=.30$ , the fixed- $m$ acceptance target and cap fall as concurrency grows; the dashed line marks the joint optimum. (c) The joint policy over market thickness and dispersion. The white contour marks $q^{\star}=.5$ , the sign boundary in Theorem 4.3 . Three panels. The first plots an acceptance target decreasing with concurrent threads. The second plots a decreasing price cap. The third is a heat map in seller count and price dispersion, with higher thread counts in thicker and more dispersed markets and a white median contour.

Figure 3. Representative markets with

N\in\{3,20\}

and

\sigma\in\{.08,.35\}

, holding

V=1.4,L=.2,\kappa=.01,\delta=.05

. Joint optimization matters most in dispersed markets. Higher reliability is not free: Mean-cap and Fixed-

q

can fulfill more often while earning less. Two grouped bar charts over four market regimes. The left shows expected profit for five policies and the right shows fulfillment probability. CANO has the highest profit, especially in dispersed markets; some more reliable policies have lower profit.

Policy	Surplus ratio	Mean regret	90th-pct. regret	Near (%)	Cancel (%)	Mean $m$
Cano	1.000	0.000	0.000	100.0	0.0	7.07
Single-agent	0.614	0.160	0.425	28.8	0.0	1.00
All-parallel	0.857	0.059	0.234	62.8	10.9	10.46
Mean-cap	0.727	0.113	0.319	8.5	0.0	2.96
Fixed- $q=.8$	0.440	0.232	0.575	3.6	25.9	1.23

Table 2. Full-factorial policy summary over 1,944 analytic configurations. Surplus ratio aggregates profit above immediate cancellation. Regret is in normalized profit units; “Near” is the share within 1% of Cano ’s recoverable surplus; “Cancel” is the share choosing

m=0

$n$	Mean regret	95% interval	Mean $m$	Calibration
25	.0686	[.0528, .0860]	12.56	.0591
50	.0251	[.0197, .0309]	12.95	.0337
100	.0220	[.0171, .0273]	13.53	.0306
250	.0092	[.0070, .0115]	14.06	.0173
1000	.0033	[.0027, .0041]	13.99	.0095

Table 3. Finite-data planning for

N=20,\mu=1,\sigma=.35,V=1.4,L=.2,\kappa=.01,\delta=.05

. Each row uses 100 independent histories; intervals are percentile bootstrap intervals for mean oracle regret. Calibration is mean absolute acceptance error at the selected cap.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4. Stress tests. (a) Mean regret and 95% bootstrap interval over 100 finite-data replicates. (b) Correlation-aware planning partially recovers profit lost under shared seller shocks. (c) Policy profit under uniform, truncated-normal, lognormal, and two-component reservation-price distributions. Three panels. Mean oracle regret falls from about 0.069 with 25 observed threshold samples to 0.003 with 1,000. As the tested latent Gaussian correlation rises from 0 to 0.7, expected profit falls; at every positive tested correlation, the correlation-aware line is above the independence-planned line. Hatched grouped bars compare five policies under four mean-one, standard-deviation-about-0.30 distribution shapes.

Parameter	Values
$N$	$1,2,5,10,20,50$
$\sigma/\mu$	$.05,.15,.30,.45$
$V-\mu$	$.10,.30,.50$
$L$	$0,.10,.30$
$\kappa$	$.001,.01,.03$
$\delta$	$0,.02,.10$

Appendix

Table 4. Factorial design for the

1944{}

analytic markets.

	Uniform		Trunc. normal
Policy	$m,q$	Profit	$m,q$	Profit
Cano	$13,.161$	.465	$15,.134$	.421
Single	$1,.539$	.092	$1,.627$	.105
All	$20,.117$	.444	$20,.106$	.412
Mean-cap	$4,.500$	.269	$4,.500$	.269
Fixed-.8	$2,.800$	.025	$2,.800$	.079

Appendix

Table 5. Distribution robustness:

m

q

, and expected profit.

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Abstract

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