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Learning to Sell: Reinforcement Learning for Strategic Large Language Model Agents in Multi-Product Markets

Shuze Daniel Liu, Claire Chen, Jiuqi Wang, David Simchi-Levi, Thorsten Joachims

arXiv:2609.33289v2cs.AI

TL;DR

Concurrent multi-product bargaining requires sellers to make sequential decisions with hidden buyer valuations and limited communication. The paper formalizes this as a POMDP and trains sellers using verifiable rewards. The trained 30B seller matches or outperforms evaluated frontier models, including models with more than one trillion parameters, on surplus extraction and allocation quality.

  • Problem

    In concurrent bargaining, hidden buyer valuations, one-item-per-buyer matching, and a global communication budget make portfolio-wide seller-profit decisions sequential and interdependent.

    Source: §1 · pp. 1–2

  • Method

    The paper formalizes bargaining as a POMDP and post-trains a seller with RLVR using a verifiable reward based on portfolio-wide seller surplus.

    Source: §1 · p. 2

  • Results

    The trained 30B seller matches or outperforms evaluated general-purpose frontier models, including models with more than one trillion parameters, on seller surplus extraction and buyer-item allocation quality.

    Source: §10 · p. 23, §11 · p. 24

  • Takeaways & Limitations

    The learned behavior transfers across evaluated changes in buyer behavior, market scale, supply-demand balance, valuation correlations, and product price ranges.

    Source: §10 · p. 23

    The evaluated formulation uses a finite catalog of substitutable items, independent buyers who can each purchase at most one item, and a finite global communication budget with per-buyer turn limits.

    Source: §3 · pp. 5–6

Abstract

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Autonomous large language model (LLM) agents operating in multi-product markets must make sequential decisions under information asymmetry and resource constraints. We develop a machine learning approach for training such agents to act effectively as sellers in a multi-item bargaining environment, where a seller concurrently negotiates a catalog of substitutable assets across a pool of independent buyers. Buyers hold private, heterogeneous valuations across products, and each can purchase at most one item. Facing limits on total communication turns, the seller must dynamically match buyers with the most profitable products considering their private valuations, while strategically allocating its limited interaction budget toward combinations of greater potential value. We formalize this problem as a Partially Observable Markov Decision Process using a structured, four-part message protocol that maps natural language into a parsable and regulated decision space. Using this formalization, we design a post-training method using Reinforcement Learning from Verifiable Rewards (RLVR). To evaluate this framework, we construct a multidimensional metric suite that quantifies constraint adherence, seller surplus extraction, and allocation quality. Our trained seller agent learns to match limited inventory to buyers more effectively, matching or outperforming trillion-parameter frontier models in both seller surplus extraction and buyer-product allocation quality. Finally, these learned strategies generalize robustly to unseen market structures, correlated valuation distributions, and price ranges not encountered during training.

1 Introduction

The paper studies concurrent multi-product bargaining, where private valuations, coupled buyer-item matches, and limited communication make portfolio-wide profit difficult to optimize. It formalizes the setting and trains sellers with verifiable rewards, evaluating constraint adherence, surplus extraction, and allocation quality.

1 Introduction

  • The motivation spans commercial bargaining settings where counterparties withhold reservation values, making information gathering costly and limited attention consequential.The paper cites procurement, customized supply-chain contracting, and business-to-business sourcing as examples.Source: §1 · p. 1
  • Each buyer can purchase at most one product, so accepting a deal removes both that buyer and item from future matching opportunities.The seller must allocate limited communication turns across buyers while inferring their private valuations and coordinating matches.Source: §1 · pp. 1–2
  • The paper formalizes concurrent bargaining as a finite-horizon POMDP and introduces a Thought, Target, Talk, Action protocol for parsable, rule-bounded decisions.The protocol is designed to enforce hard action constraints and coordinate decisions under a limited interaction budget.Source: §1 · p. 2
  • RLVR optimizes the seller against strategic counterparties using a terminal economic reward for portfolio-wide surplus, without predefined matching logic.The authors report improved buyer-item matching and allocation precision as the agent maximizes surplus, although these behaviors are not explicitly rewarded.Source: §1 · p. 2
  • The evaluation suite measures instruction violations, seller surplus extraction, and matching precision through Deal on Top Buyer Rate and Optimal-Pair Offer Coverage Rate.The framework is evaluated on an empirical dataset of 6,500 functionally substitutable products.Source: §1 · p. 2

2 Related Work

The related work spans strategic language agents, bargaining under asymmetric information, and allocation under resource constraints. The paper connects them in a concurrent marketplace where natural-language valuation screening and buyer-item matching share a communication budget.

2.1 Large Language Models as Autonomous Strategic Agents

  • RLVR offers an alternative to general-purpose post-training objectives by optimizing against programmatically verifiable outcomes rather than subjective human labels.The paper applies verifier-based training to coordinate information gathering, negotiation, and allocation toward seller surplus.Source: §2.1 · pp. 3–4
  • General-purpose language agents can be shortsighted in negotiation, while this work unifies persuasive communication and concurrent market search in one surplus-optimization loop.The paper positions its approach against modular systems that separate strategy from language generation.Source: §2.1 · pp. 3–4

2.2 Negotiation and Price Discovery under Asymmetric Information

  • Negotiation research treats sequential pricing as a way to infer private valuations, while this paper studies how those choices interact with capacity-constrained allocation.The paper frames its contribution as integrating valuation elicitation and matching under a finite interaction budget.Source: §2.2 · p. 4
  • Prior language-agent work often studies isolated bilateral bargaining, whereas this paper considers concurrent screening and matching across private channels under a communication limit.The cited LLM negotiation frameworks are described as restricting their focus to bilateral settings.Source: §2.2 · p. 4

2.3 Sequential Allocation and Matching under Resource Constraints

  • Classical sequential allocation methods commonly use centralized optimization over structured numerical signals and may assume demand distributions or market priors.The paper contrasts these methods with dialogue-based preference discovery across parallel channels.Source: §2.3 · pp. 4–5, Figure 1 · p. 5

3 Problem Formulation and POMDP Framework

The framework models a seller allocating substitutable items across buyers whose valuations are hidden, while both global and per-buyer communication limits constrain negotiation. A POMDP and structured action protocol define the seller’s information and choices; a terminal reward scores surplus and rule compliance.

3 Problem Formulation and POMDP Framework

  • The seller allocates a finite catalog of substitutable items across buyers, each of whom can purchase at most one item, while buyer valuations and seller costs are private.The hidden buyer valuation matrix is generated by an environment-specific process.Source: §3 · p. 5
  • A finite global turn budget and per-buyer turn cap prevent the seller from exhausting every conversation, requiring it to choose which buyers to engage.The seller’s costs remain hidden from buyers, and buyer channels do not expose other conversations or private budgets.Source: §3 · pp. 5–6

3.1 Multi-Item Seller Negotiation as a POMDP

  • The seller problem is represented as a finite-horizon POMDP whose tuple specifies state, actions, transitions, rewards, observations, and the observation mapping.The state includes fixed episode components and evolving histories and remaining budget.Source: §3.1 · p. 6
  • At each turn the seller observes the catalog, its costs, interaction records, and remaining budget, but must infer buyers’ valuations from dialogue because those values remain hidden.The observation mapping withholds the valuation matrix from the seller.Source: §3.1 · p. 6
  • The four-part Thought, Target, Talk, Action protocol lets the seller select a buyer, communicate in natural language, and issue a structured price menu, deal, or quit command.Targeting an inactive buyer, quoting invalid or sold items, and other rule violations are disallowed.Source: §3.1 · pp. 6–7
  • After each seller action, the targeted buyer responds, the dialogue and negotiation records update, and the global and buyer-specific turn counts advance.The episode ends when inventory is sold, channels are inactive, the budget is depleted, the seller quits, or an instruction violation occurs.Source: §3.1 · p. 7

3.2 Verifiable Reward Formulation

  • For compliant episodes, the terminal reward measures the share of catalog-wide list-price margin captured, penalizing unsold items through the reward denominator.A no-deal episode receives zero, while an instruction violation receives −1; the reward also makes early low-margin deals costly because buyers leave the market.Source: §3.2 · pp. 7, 9

3.1 Multi-Item Seller Negotiation as a POMDP

  • In the illustrated three-item episode, the trained seller rejects below-cost opening bids, quotes near-list prices on two higher-margin items, and closes Item 1 at $140.The figure shows the first two seller turns; the full transcript and untrained comparison are in Appendix H.Source: §3.1 · p. 7, Figure 2 · p. 8

4 The Substitutable-Product Dataset

The paper builds an empirical dataset of functionally substitutable Amazon products, with catalog metadata and seller costs, then separates cluster-level training, test, and held-out out-of-distribution data.

4 The Substitutable-Product Dataset

  • The dataset contains 1,300 clusters of five substitutable products each, totaling 6,500 products across 13 Amazon categories.Each product includes its title, brand, list price, seller cost, and text features; each cluster includes a substitutability rationale.Source: §4 · p. 9, Figure 3 · p. 10
  • Clusters average 4.4 distinct brands, and the median within-cluster highest-to-lowest list-price ratio is 1.85.The corpus contains five products per cluster, so the seller cannot rely on a single-brand pitch.Source: §4 · p. 9

4.1 Dataset Construction

  • The construction pipeline proposes product types, retrieves best-selling Amazon listings through Keepa, and filters clusters for strict functional substitutability.Seller cost is set to the lowest recorded Amazon sale price, while list price is the posted price at collection.Source: §4.1 · pp. 9–10

4.2 Dataset Splits

  • The 12 base categories are split by cluster into 960 training and 240 test clusters, while 100 Musical Instruments clusters are held out for out-of-distribution evaluation.The held-out category has a median list price of $165.49 versus $44.10 in the other 12 categories, producing a price range unseen during training.Source: §4.2 · pp. 10–11

5 Simulation Environment and Experimental Setup

The setup trains a seller to negotiate concurrently with fixed buyer agents over substitutable products under global and per-buyer turn limits. The market randomizes buyer valuations and can decouple opening offers from those valuations.

5.1 Agent Configurations and Training Setup

  • Training updates the seller while keeping buyer models fixed, using Qwen3-30B-A3B-Instruct-2507 for both roles and a seller optimization sequence of one epoch on the in-distribution split.The seller uses CISPO without an explicit KL divergence penalty; buyers use an iteration-60 checkpoint trained on a separate bilateral negotiation task.Source: §5.1 · p. 11
  • Buyer agents are adapted to multi-product negotiations by prompts describing the catalog, offer format, private valuations, and exit after a first deal; their protocol violation rate is validated below 1%.The buyer checkpoint was trained exclusively on single-item negotiations.Source: §5.1 · p. 11

5.2 Market Settings and Information Structure

  • Episodes draw three of five substitutable items from a sampled training cluster and match them with three buyers, under seven total turns and at most three turns per buyer.The cluster-level split contains 960 training and 240 held-out test clusters across 12 product categories; test valuations are freshly sampled.Source: §5.2 · p. 11
  • With probability 0.5, each buyer’s opening prices on selected items are resampled into 0.25–0.30 times list price, breaking their correlation with true valuations.Otherwise, buyers generate opening offers freely subject to their private valuation constraint; the design requires sellers to use multi-turn dialogue to recover preferences.Source: §5.2 · p. 12

6 Evaluation Metrics and Framework

The evaluation compares realized negotiations with a centralized surplus-maximizing assignment and reports six metrics across episode outcomes, constraint adherence, surplus extraction, and allocation quality. Allocation measures distinguish realized assignments from optimal pairs merely proposed during negotiation.

6 Evaluation Metrics and Framework

  • The framework evaluates six metrics across episode outcome, constraint adherence, surplus extraction, and allocation quality, comparing realized results with a centralized assignment optimum.The pipeline samples an episode, runs negotiations, records outcomes, computes the optimum from private valuations, and overlays realized results against it.Source: §6 · p. 12, Figure 4 · p. 13

6.1 Episode Outcome

  • Reward is the terminal outcome metric, while Item Deal Rate measures the fraction of item–episode opportunities that close a deal.Reward is −1 for a violation and falls within [0, 1] on a valid episode; Item Deal Rate is bounded within [0, 1].Source: §6.1 · p. 12

6.2 Constraint Adherence

  • Instruction Violation Rate measures the share of episodes ending in a seller violation; zero indicates perfect protocol compliance.Violations incur the full −1 penalty, and the rate is computed over all episodes.Source: §6.2 · p. 12, §6 · p. 12

6.3 Surplus Extraction

  • Seller Surplus Extraction Ratio measures the episode-level fraction of catalog-wide list-price margin captured by the seller.It is aggregated over valid episodes, including no-deal episodes, which contribute a well-defined ratio of 0.Source: §6.3 · pp. 12–13

6.4 Allocation Quality

  • Allocation metrics compare realized buyer–item assignments with an oracle matching that maximizes seller surplus under a one-deal-per-buyer constraint, using hidden valuations unavailable to the seller.Deal on Top Buyer Rate measures assignment to the highest-valuation buyer among sold items; Optimal-Pair Offer Coverage Rate counts optimal pairs proposed through a SELL or DEAL action, whether or not a deal closes.Source: §6.4 · p. 14

7 Performance Benchmarking

On held-out in-distribution scenarios, the trained seller leads the tested benchmark panel on primary economic dimensions, while general-purpose models tend toward more agreements but lower margins. The trained agent also leads on allocation metrics, using dialogue to uncover buyer valuations and route items to high-valuation buyers.

7.2 Surplus Extraction and Economic Trade-offs

  • +0.407 mean Reward and +0.425 Seller Surplus Extraction Ratio: the trained seller leads the benchmark panel across primary economic dimensions.It exceeds Kimi-K2.6-thinking (+0.379 reward) and DeepSeek-V4-Pro-thinking (+0.369 reward) despite its smaller model size and without a provider-native hidden reasoning mode.Source: Table 1 · p. 15, §7.2 · p. 15

7.3 Allocation Quality

  • 0.844 Optimal-Pair Offer Coverage Rate and 0.687 Deal on Top Buyer Rate: the trained model outperforms baselines on both allocation metrics.The authors report that dialogue helps the model systematically learn buyer preferences and match items to high-valuation buyers within the turn limit.Source: Table 1 · p. 15, §7.3 · p. 16

7.1 Experimental Configuration and Baselines

  • The benchmark compares the trained Qwen3 seller with its untrained base and frontier models on the same held-out scenarios, using Reward, Item Deal Rate, violation rate, surplus extraction, and allocation metrics.Table 1 covers three buyers, three items, and T=7 turns; open-weight models are evaluated in standard and extended-reasoning configurations.Source: §7.1 · pp. 14–15, Table 1 · p. 15

7.2 Surplus Extraction and Economic Trade-offs

  • 64.7% Item Deal Rate accompanies higher realized seller surplus for the trained seller, while GPT-5.4-high-reasoning reaches a panel-leading 78.1% Item Deal Rate but a +0.315 surplus extraction ratio.The reported pattern is higher agreement volume but lower economic margin among evaluated general-purpose models.Source: §7.2 · p. 15

8 Empirical Training Dynamics

Across training, the seller improved protocol compliance, surplus extraction, and allocation accuracy; its final reward exceeded the frontier-model benchmarks. The trajectories also show a trade-off between transaction volume and margin, with gains in matching emerging without explicit matching incentives.

8 Empirical Training Dynamics

  • Training trajectories show simultaneous improvements in protocol compliance, surplus extraction, and allocation accuracy on both training rollouts and held-out assets.The reward measures seller surplus rather than oracle matching quality, so the improvements in optimal-pair coverage and buyer-item matching emerge without explicit matching incentives.Source: §8 · p. 16, §8.4 · p. 19

8.1 Episode Outcome

  • +0.407 final reward for the trained 30B seller agent, versus +0.309 for GPT-5.4-high-reasoning and +0.369 for DeepSeek-V4-Pro-thinking.The reward rose from −0.329 for the untrained base model; Figure 5 tracks training and held-out performance.Source: §8.1 · p. 16, Figure 5 · p. 17

8.2 Constraint Adherence

  • 1.3% Instruction Violation Rate at convergence, down from 43.3% for the untrained model as the rate fell sharply in the first 15 steps.The reward assigns R = −1 for any rule breach, providing a direct penalty signal.Source: Figure 7 · p. 17, §8.2 · p. 18

8.1 Episode Outcome

  • Item Deal Rate initially falls as the seller rejects low-margin opening offers, then recovers as it learns effective later-turn counter-offers.GPT-5.4-high-reasoning has the highest baseline Item Deal Rate but lower terminal reward, consistent with accepting some suboptimal offers.Source: §8.1 · pp. 16–17, Figure 6 · p. 17

8.3 Surplus Extraction

  • Seller Surplus Extraction Ratio rises during training, with the terminal trained-agent ratio exceeding both generalist baselines.The increase becomes more pronounced after protocol compliance stabilizes; selective rejections and counter-proposals help avoid inefficient deals that remove buyers and assets from the market.Source: Figure 8 · p. 17, §8.3 · p. 18

8.4 Allocation Quality

  • Optimal-Pair Offer Coverage Rate rises and exceeds generalist baselines late in training, while realized allocation accuracy also improves despite episode-level variance.A Deal on Top Buyer Rate below 1.0 does not necessarily imply suboptimal routing because one buyer may value multiple items most highly under the one-deal-per-buyer constraint.Source: Figure 9 · p. 18, Figure 10 · p. 18, §8.4 · p. 19

9 Out-of-Distribution Generalization

The section tests whether the seller’s learned negotiation strategy transfers beyond its training environment, where shifts can change both market opportunities and coordination demands.

9.1 Out-of-Distribution Environment

  • The six OOD tests combine scale and horizon expansion, buyer–item imbalance, correlated valuations, an unseen product category, and varied buyer checkpoints.The unseen Musical Instruments category also shifts list-price ranges beyond those encountered in training.Source: §9.1 · pp. 20–21

9.2 Out-of-Distribution Results

  • Across all six OOD environments, the trained seller beats the highest-scoring baseline on reward, surplus extraction, and offer coverage.The reward and surplus figures show the comparisons; the reported result also covers offer coverage.Source: §9.2 · pp. 21–22, Figure 11 · p. 22, Figure 12 · p. 23
  • Reward margins over the best baseline range from +0.089 in Item Heavy to +0.135 in Expanded Musical and Item Correlation.Because attainable reward ceilings differ across market structures, compare reward levels within each environment, not across environments.Source: §9.2 · p. 22, Figure 11 · p. 22

10 Discussion

The discussion contrasts general-purpose models’ tendency toward early deals with the trained seller’s portfolio-wide optimization, then considers the transfer of its strategic behavior.

10 Discussion

  • General-purpose baselines favor early agreements and higher deal volume at the expense of portfolio-wide seller surplus, while the trained seller develops valuation screening and matching behaviors.The surplus reward does not explicitly encode a matching heuristic, yet the trained agent improves coverage of high-value pairs.Source: §10 · p. 23
  • The trained 30B seller outperforms evaluated frontier models, including models exceeding one trillion parameters, on seller surplus extraction and buyer–item allocation quality.Its behavior transfers across changes in buyer behavior, market scale, supply–demand balance, valuation correlations, and product price ranges.Source: §10 · p. 23
  • The seller’s learned information-gathering, negotiation, and allocation behaviors remain effective across changing market structures.The discussion presents transferable strategic behavior as valuable for language agents in dynamic multi-agent environments.Source: §10 · p. 23

11 Conclusion

The conclusion summarizes a seller-agent approach to multi-item bargaining under private valuations and a global communication budget, and reports gains in surplus, allocation quality, and generalization.

11 Conclusion

  • A single seller negotiates substitutable products with multiple buyers under information asymmetry and a global communication budget, with each buyer limited to one item.The problem is framed as multi-item concurrent bargaining.Source: §11 · p. 24
  • RLVR training with a verifiable seller-surplus reward improves valuation screening, buyer–item matching, and surplus extraction without predefined matching heuristics.The conclusion reports that the resulting 30B seller matches or outperforms evaluated frontier models, including models exceeding one trillion parameters, on surplus extraction and allocation quality.Source: §11 · p. 24
  • The trained seller generalizes across shifts in buyer behavior, market scale, supply–demand balance, valuation correlations, and product price ranges.The conclusion identifies verifiable-reward training as having potential for long-horizon strategic decision-making in partially observable multi-agent environments.Source: §11 · p. 24

AI Use Statement

The appendices state AI-tool use, organize notation, and formalize allocation metrics against an oracle matching benchmark.

AI Use Statement

  • AI tools assisted with proofreading, grammar correction, and visual pipeline diagrams; the authors reviewed the AI-assisted content and take responsibility for the final content.Source: AI Use Statement · p. 24

A Notation

  • The notation table groups symbols by framework component, with full definitions given at each symbol’s first use in the main text.Source: A Notation · p. 28, Table 3 · p. 28

B Formal Definitions of Evaluation Metrics

B.1 Oracle Matching Model

  • The oracle matching model assigns each item to at most one buyer and each buyer to at most one item, maximizing clipped surplus at list price.The empty matching is optimal when no positive clipped surplus exists.Source: §B.1 · pp. 28–29

B.2 Primary Allocation Metrics

  • Optimal-Pair Offer Coverage Rate measures the fraction of oracle-optimal buyer–item pairs proposed at least once with a SELL or DEAL action.A pair counts as offered regardless of whether a deal closes; the episode’s selected optimal matching maximizes overlap with the seller’s proposals.Source: §B.2 · p. 29
  • Deal on Top Buyer Rate measures the fraction of sold items assigned to a buyer with the highest private valuation for that item.Ties count, and a value below one does not by itself imply routing error because each buyer can close at most one deal.Source: §B.2 · p. 29

C In-Distribution Benchmarking Figure

Figure 14 visualizes in-distribution rankings across ten seller models on identical held-out instances. The appendix also specifies the seller and buyer models and the training and evaluation configurations.

C In-Distribution Benchmarking Figure

D.1 Multi-Item Seller Setting — Model Specifications

  • The seller is the only learning agent; all buyer checkpoints remain frozen during the one-sided training setup.The seller and buyers share the Qwen3-30B-A3B-Instruct-2507 base model; in-distribution buyers use an iteration-60 bilateral negotiation RLVR checkpoint.Source: §D.1 · pp. 30–31
  • The held-out benchmark compares the trained seller with nine other seller models, forming a ten-model panel with the buyer held fixed.Three open-weight models are evaluated in thinking and no-thinking modes; the panel also includes DeepSeek-V4-Pro and DeepSeek-V4-Flash.Source: Table 5 · p. 31, §D.1 · p. 31

D.2 Training and Evaluation Hyperparameters

  • Training uses the reported CISPO configuration, with no systematic hyperparameter search and no held-out or OOD evaluation data used for selection.Training valuations are sampled independently as fractions of list prices, with first-offer noise applied independently to each buyer with probability 0.5; the held-out test uses 240 clusters with unseen product contexts.Source: §D.2 · p. 31, Table 7 · p. 32, Table 8 · p. 32

D.3 Out-of-Distribution Evaluation Setup

This section describes the out-of-distribution evaluation setup, including its environments, data, prompts, procedures, and shared-instance comparison. It also summarizes catalog economics and realized allocations in two episodes.

D.3 Out-of-Distribution Evaluation Setup

  • OOD tests vary buyer and item counts, valuation correlations, and price scale, while sampling each buyer slot per episode from iter-50, iter-60, and iter-70 checkpoints.The reference uses 3 buyers, 3 items, and T=7 with a fixed iter-60 buyer; OOD settings include a held-out Musical Instruments category with a higher list-price range.Source: §D.3 · p. 33, Table 9 · p. 33

E Dataset Details

  • The dataset contains 1,300 clusters and 6,500 products, with 100 clusters of five substitutable products contributed by each of 13 categories.Across clusters, the average is 4.4 distinct brands, and 59% of clusters contain five distinct brands; median within-cluster price spread is 1.85×.Source: Table 10 · p. 34, §E.2 · p. 34

F. Prompt Templates

  • The seller prompt requires four XML tags and regulates targeting and actions, while the buyer prompt permits at most one item purchase and constrains bids to private budgets.The seller’s reward uses list-clipped deal prices and assigns −1 for violations; buyers can see only public list prices, not seller costs.Source: §F.1 · p. 38, §F.2 · p. 39

F.2 Buyer System Prompts

  • OOD buyer slots are sampled per episode from the same training trajectory’s iter-50, iter-60, and iter-70 checkpoints, while only seller parameters update during training.In-distribution evaluation instead uses the frozen iter-60 buyer checkpoint.Source: §F.2 · p. 39

G Extended Benchmarking Results

  • Seller metrics in the extended results are estimated from direct episode rollouts, and the appendix supplies point-estimate and standard-error tables for OOD environments.The supplied table captions identify environments and metrics but do not provide cell values, so they do not establish comparative results.Source: G Extended Benchmarking Results · p. 40

H Qualitative Example: Untrained versus Trained Seller on an Identical Instance

  • The qualitative example compares an untrained and trained seller on the same catalog, seller costs, and hidden valuation matrix, with independently sampled buyer rollouts.No buyer opening offer was resampled by first-offer noise in this instance.Source: H Qualitative Example: Untrained… · pp. 41–42

H.1 Episode Information

  • Episode information covers catalog economics and realized allocations for two episodes, including a video recorder listed at $55.99 with a stated cost of $100.00.The listed product is ZOSI H.265+ 8 Channel 5MP Lite 1080p CCTV DVR Recorder Without HDD.Source: §H.1 · p. 43

H.2 Untrained Baseline

The appendix contrasts an untrained seller that misallocates buyers and leaves the highest-margin item unsold with a trained seller that realizes the surplus-maximizing assignment in the illustrated instance.

H.3 Trained Seller

  • The trained seller realizes the surplus-maximizing assignment, while the untrained seller leaves the highest-margin item unsold after misallocating two buyers.The assignment routes Item 1 to Buyer 1, Item 2 to Buyer 2, and Item 3 to Buyer 3; Buyer 2 can close at most one deal despite holding the top valuation on both high-value items.Source: Table 24 · p. 45, §H.3 · p. 50

H.2 Untrained Baseline

  • The untrained seller earns a $3.59 margin on Buyer 1’s $45.66 purchase, then sells Item 1 to Buyer 2 while Lorex remains unsold.Buyer 2’s hidden Lorex valuation was $252.12; the remaining Buyer 3 could not afford the $150 quote.Source: §H.2 · pp. 46–47
  • The untrained seller’s reward is 0.171, calculated from $47.60 in realized margin against $277.91 in available margin.The item-level margins are shown in the reward calculation.Source: §H.2 · p. 47

H.3 Trained Seller

  • The trained seller closes all three items for $140, $240, and $43.99, yielding reward 0.813 in the illustrated instance.The last price equals Buyer 3’s valuation; Item 2 sells for 96% of list price.Source: §H.3 · p. 50

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