From Preference to Reciprocity: Decentralized Matching with Empirically Grounded LLM-agent Based Modeling

Wangxuan Fan; Xiaoyu Nie; Zhoutian Shi; Xiangcheng Meng; Shipei Zeng; Pin Gao; Yan Hu; Zhongxiang Dai

cs.LGSep 28, 2026

From Preference to Reciprocity: Decentralized Matching with Empirically Grounded LLM-agent Based Modeling

Authors: Wangxuan Fan, Xiaoyu Nie, Zhoutian Shi, Xiangcheng Meng, Shipei Zeng, Pin Gao, Yan Hu, Zhongxiang Dai

Organizations: The Chinese University of Hong Kong, Shenzhen

Abstract

Bipartite matching is a fundamental problem in game theory and market design. Classical approaches such as Gale--Shapley assume complete preferences and centralized computation, whereas many real-world matching processes are decentralized, asynchronous, and shaped by sequential interaction under limited information. We propose a dynamic bipartite matching framework that combines large language model (LLM) agents with contextual bandits. In a simulated Chinese marriage market, economically grounded LLM agents evaluate locally encountered candidates, while agent-specific Logistic-UCB models learn reciprocal acceptance from realized proposal outcomes. The mechanism therefore separates two decisions---\emph{whom do I like?} and \emph{who is likely to like me back?}---without requiring ex ante market-wide preference rankings. We first validate LLM-induced mate preferences against the empirical conditional-logit reference across multiple LLM backbones. In the $50\times50$ matching experiment, Bandit-UCB achieves the highest mean mutual welfare (56.01 versus 54.87 for Gale--Shapley), a smaller gender rank gap than the classical baselines, and the fewest blocking pairs among the LLM-ABM policies. Learned acceptance models show economically interpretable gender-differentiated associations, while counterfactual setups reveal no systematic unilateral advantage from prior search knowledge. Overall, these results support the advantages of decentralized matching with LLM-based behavioral modeling and online learning under incomplete information for economic simulation and computational social science research.

Figures & tables

Figure 1: Empirical-reference alignment in the 10

\times

10 validation task. Bars show means across five seeds and error bars show standard deviations.

Figure 2: Dimension-consistency heatmap for agents in the 10 $\times$ 10 validation. Entries report Pearson correlations between overall desirability and dimension-level scores, averaged across five seeds.

	Method	Info required	Mutual welfare $\uparrow$	Rank gap $\downarrow$	#Blocking $\downarrow$	Proposals $\downarrow$
Baselines	Gale–Shapley	Whole	54.87 $\pm$ 0.29	2.74 $\pm$ 0.53	0.00 $\pm$ 0.00	873.14 $\pm$ 20.24
	LLM-solver	Whole	54.63 $\pm$ 0.50	2.57 $\pm$ 1.18	9.40 $\pm$ 10.71	N/A
	Axtell–Kimbrough	Partial	54.73 $\pm$ 0.39	2.43 $\pm$ 0.83	19.90 $\pm$ 14.02	31504.70 $\pm$ 4280.30
LLM-ABM	Random eligible	Local	55.24 $\pm$ 0.62	1.54 $\pm$ 0.68	38.00 $\pm$ 17.42	13781.90 $\pm$ 2349.29
	Utility-only	Local	55.92 $\pm$ 0.48	1.84 $\pm$ 0.75	17.58 $\pm$ 12.26	16753.14 $\pm$ 2876.91
	Bandit-UCB	Local	56.01 $\pm$ 0.59	2.11 $\pm$ 0.73	16.28 $\pm$ 12.76	16591.78 $\pm$ 2376.70

Table 1:

50\times 50

market size matching results. Values are means

\pm

standard deviations over 50 seeds; bold, underlined, and italic mean values denote first, second, and third place among methods for which each outcome metric is defined. The “Info required” column summarizes the information regime, including both ex ante preference access and whether pairwise valuations are generated only after local encounter.

Panel of Figure 3 — Figure 3: Learned reciprocal-acceptance structure under Bandit-UCB. Panel (a) reports aggregated coefficients from private proposer-specific models; Panel (b) reports a pooled receiver-perspective diagnostic fitted after simulation and used only for interpretation.

Figure 4: Individual warm-start effects across the 50 male focal agents. Effects are same-seed treatment–control mean differences over ten held-out seeds and are oriented so that positive values indicate improvement. The upper panel classifies focal agents by the sign of the effect; the lower panels report the corresponding effect distributions.

Method	Initial knowledge	Mutual welfare $\uparrow$	M rank $\downarrow$	F rank $\downarrow$	Rank gap $\downarrow$	#Blocking $\downarrow$	Proposals $\downarrow$
Gale–Shapley (men-proposing)	Complete rankings	54.87 $\pm$ 0.29	16.74 $\pm$ 0.39	19.48 $\pm$ 0.32	2.74 $\pm$ 0.53	0.00 $\pm$ 0.00	873.14 $\pm$ 20.24
Cold-start Bandit-UCB	Local	55.84 $\pm$ 0.33	16.48 $\pm$ 0.47	18.56 $\pm$ 0.46	2.08 $\pm$ 0.70	16.70 $\pm$ 8.21	15829.50 $\pm$ 2462.34
All-male warm-start Bandit-UCB	Pooled male $\theta$	55.71 $\pm$ 0.44	16.56 $\pm$ 0.73	18.68 $\pm$ 0.47	2.12 $\pm$ 0.76	15.80 $\pm$ 4.66	15136.70 $\pm$ 2210.78

Table 2: Market-level counterfactual results for male-side information advantage. M rank and F rank denote the average ranks of matched male and female agents for their realized partners, respectively.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Dimension	Values or scale	Sampling and dependency structure
Age	20–50	Sampled from marriage-market-active age groups according to the target population distribution.
Income	Monthly RMB income	Generated conditional on educational attainment around a reference monthly income of 1830 RMB.
Education	Middle school or below; high school; university and above	Sampled from population education proportions and aggregated into three experimental categories.
Family background	Urban; rural	Sampled from the corresponding urban/rural population composition.
Housing	Owns house; no house	Sampled conditionally on age, gender, and family background.
Appearance	Below average; average; attractive	Sampled from an approximately bell-shaped distribution, with most probability mass assigned to average appearance.

Appendix

Table 3: Persona dimensions and sampling structure.

Attribute	Male (n=50)	Female (n=50)	Overall (n=100)
Mean age	36.60	34.62	35.61
Mean monthly income	1881.24 RMB	1712.88 RMB	1797.06 RMB
Middle school or below	70%	72%	71%
High school	10%	14%	12%
University and above	20%	14%	17%
Urban family background	58%	56%	57%

Appendix

Table 4: Realized composition of the 100-agent synthetic marriage market.

Model	Male $\tau$	Female $\tau$	Male WPVR	Female WPVR
DeepSeek CoT	0.692 $\pm$ 0.076	0.572 $\pm$ 0.082	0.064 $\pm$ 0.025	0.122 $\pm$ 0.027
Qwen CoT	0.708 $\pm$ 0.115	0.646 $\pm$ 0.072	0.055 $\pm$ 0.035	0.089 $\pm$ 0.022
GPT-OSS CoT	0.666 $\pm$ 0.103	0.502 $\pm$ 0.092	0.073 $\pm$ 0.042	0.158 $\pm$ 0.030
No-CoT baseline	0.286 $\pm$ 0.065	0.400 $\pm$ 0.085	0.298 $\pm$ 0.055	0.236 $\pm$ 0.053

Appendix

Table 5:

10\times 10

reference-alignment results across LLM backbones. Values are means

\pm

standard deviations across five random seeds.

Metric	Male evaluators	Female evaluators
Kendall’s $\tau$	0.703 $\pm$ 0.054	0.607 $\pm$ 0.082
WPVR	0.054 $\pm$ 0.018	0.105 $\pm$ 0.039
Overlap@3	0.460 $\pm$ 0.187	0.473 $\pm$ 0.232
Overlap@5	0.684 $\pm$ 0.133	0.448 $\pm$ 0.186

Appendix

Table 6: DeepSeek alignment with the empirical preference reference in the

50\times 50

validation market.

Figure 5: DeepSeek validation in the $50\times 50$ market. Panel (a) reports reference-alignment metrics by evaluator gender; Panel (b) reports dimension-consistency correlations.

Feature	Interpretation
Age gap	Age mismatch between proposer and candidate
Income gap	Relative income difference
Education gap	Relative education difference
Same background	Indicator for shared family background
Housing advantage	Relative housing-status advantage
Appearance gap	Relative appearance difference

Appendix

Table 7: Features in the local reciprocal-acceptance context. Gap and advantage variables follow the proposer-oriented encoding used in the implementation.

Parameter	Value
Market size	50 male agents and 50 female agents
Repeated runs	50 random seeds
Main matching LLM scorer	DeepSeek V4 Pro, temperature $=0.5$ , CoT prompt
Matching horizon	$T=500$ periods
Candidate set size	25 candidates per activation when more are available
Reservation utility	$r=0.25$ on the normalized utility scale

Appendix

Table 8: Main LLM-ABM parameter configuration used in Table 1 .

Metric	Improved	Unchanged	Worsened	Avg. gain	Avg. loss	Mean effect
Own rank	11	26	13	0.95	0.46	-0.15
Own score	11	26	13	0.95	0.55	-0.22
Proposals	22	3	25	8.20	15.37	-5.00

Appendix

Table 9: Distribution of individual warm-start effects across male focal agents.

Figure 6: Sensitivity of market-level outcomes to exploration strength

\beta

and lock probability

\rho

. The blue curve varies

\beta

with

\rho=0.05

fixed, while the orange curve varies

\rho

with

\beta=1

fixed. Shaded regions indicate 95% confidence intervals across 50 seeds; stars mark the main experimental setting.

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Abstract

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