The reviewed record of science sign in
Pith

arxiv: 2607.05863 · v1 · pith:M6GMI4YB · submitted 2026-07-07 · cs.LG · cs.GT

Strategic Bargaining in Multi-Buyer Markets: Reinforcement Learning from Verifiable Rewards for LLM Negotiations

Shuze Daniel Liu , Claire Chen , Jiabao Sean Xiao , Xin Chen , David Simchi-Levi This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-07-08 22:02 UTCglm-5.2pith:M6GMI4YBrecord.jsonopen to challenge →

classification cs.LG cs.GT
keywords strategiclearningsellerbuyermarketmodelsanchoringbalance
0
0 comments X

The pith

Trained 30B seller LLM out-negotiates frontier models 4.7x in multi-buyer bargaining

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper claims that a 30B-parameter language model, trained via Reinforcement Learning from Verifiable Rewards (RLVR) on a concurrent multi-buyer negotiation task, becomes a strategically competent seller that far surpasses frontier models up to 1T parameters. The core problem the authors identify is that standard LLMs — even those with advanced reasoning — act as satisficers in economic settings: they fixate on the first acceptable bid, fail to explore the buyer pool, and concede too readily due to agreeableness biases from instruction tuning. The paper's central mechanism is a reward function anchored to a single verifiable economic outcome: the fraction of available surplus captured per deal, with hard penalties for selling below cost or violating format. Through this reward signal, the agent undergoes a three-phase training evolution — first internalizing the cost floor, then learning to close deals, and finally discovering that probing all buyers with high price anchors reveals which buyer has the highest hidden budget. The trained agent achieves a 99.5% rate of closing deals with the highest-budget buyer (vs. 34.6–52.0% for baselines), extracts 70% of available surplus per deal, and reaches a mean reward of +0.580 — a 4.7-fold improvement over the strongest frontier baseline. The authors further claim robustness: under out-of-distribution conditions with five buyers, unseen buyer checkpoints, and altered budget distributions, the agent maintains reward +0.540 vs. +0.400 for the best baseline, prioritizing per-deal margin over transaction volume.

Core claim

The paper's central discovery is that when an LLM seller is trained with a reward function tied directly to verifiable economic surplus (profit above cost, capped at list price), three strategic behaviors emerge endogenously without being explicitly programmed: (1) price anchoring at the list price to test buyer elasticity, (2) diagnostic probing across all buyer channels to infer hidden budgets from how each buyer responds to the anchor, and (3) strategic patience — walking away from low-value deals to concentrate on the highest-budget counterparty. The most diagnostic metric is the Deal on Top Buyer Rate: the trained agent identifies and closes with the highest-budget buyer 99.5% of the in

What carries the argument

RLVR (Reinforcement Learning from Verifiable Rewards) applied to a concurrent multi-buyer negotiation POMDP, where the terminal reward is the capped surplus ratio (P_deal - C)/(P_list - C), with -1 penalty for instruction violations and 0 for no-deal outcomes. The agent's action space includes a private Thought field, a Target buyer selector, natural-language Talk, and a structured transactional Action ([SELL], [DEAL], or [QUIT]). Training uses the CISPO loss on a Qwen3-30B-A3B-Instruct-2507 base model over 72 optimization steps against frozen buyer checkpoints.

If this is right

  • If the result holds, firms deploying automated negotiation agents (procurement, marketplace selling, B2B contracting) should prefer small models trained on objective economic rewards over large general-purpose models, reducing compute costs while improving strategic outcomes.
  • The three-phase training trajectory (cost-floor → deal-closing → surplus-and-routing) suggests a general curriculum for economic agent training: hard constraints must be internalized before exploration strategies can emerge, which has implications for how reward functions are designed in other multi-agent economic settings.
  • The agreeableness bias identified in frontier LLMs implies that RLHF-trained models are systematically unsuitable for adversarial economic roles, and that the AI safety community's focus on helpfulness may create direct financial harm in commercial deployments.
  • The diagnostic-probing strategy the agent discovers — anchoring high and observing which counterparty escalates — mirrors classical search theory and suggests that LLMs can rediscover economically rational search behavior from reward signals alone, without being taught the underlying theory.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The generalization claim is bounded by the opponent pool: all buyers share the same base model, training pipeline, and dataset family. If the seller's probing strategy exploits idiosyncratic concession patterns of this specific buyer family (e.g., predictable escalation thresholds), it may fail against human negotiators or independently trained buyer models with different anchoring behaviors. A de
  • The narrowing performance gap in the OOD setting (from 4.7x to ~1.35x over the best baseline) is partly explained by the removal of first-offer regulation, which makes the task easier for baselines. This suggests the trained agent's advantage is largest precisely when information is most opaque — a property that may or may not hold in real marketplaces where opening offers are more informative.
  • The reward cap at 1.0 (list price) means the agent has no incentive to discover surplus beyond the list price, which in real markets may not be the true ceiling. Extending the reward to capture above-list-price deals would test whether the probing strategy generalizes to settings where the optimal price is unknown.
  • If the three-phase training trajectory is a general phenomenon, it predicts that any RLVR-trained economic agent will pass through a constraint-satisfaction phase before developing exploration strategies, which could inform training schedules and early-stopping decisions in production deployments.

Load-bearing premise

The generalization claim rests on buyer agents drawn from the same research group's prior work — three checkpoints from a single Qwen3-30B training run sharing the same base model, dataset, and pipeline. If the seller's success depends on predictable concession patterns specific to this buyer family, the routing accuracy and surplus extraction gains may not transfer to human negotiators or independently trained buyer models. The paper acknowledges this limitation in Section 6

What would settle it

Test the trained seller against buyer agents from a completely independent model family (e.g., a Llama-based or GPT-based buyer) or against human negotiators. If the Deal on Top Buyer Rate drops substantially below the 70.7% achieved in the OOD setting, or if surplus extraction falls toward baseline levels, the learned probing strategy is specific to the training-time buyer family rather than a general negotiation competence.

read the original abstract

Negotiation is a fundamental strategic interaction in management science, characterized by agents attempting to reach agreements while protecting private information, such as reservation costs and hidden valuations. A prevalent yet complex scenario involves a single seller negotiating concurrently with multiple buyers, each possessing heterogeneous, private budgets. In such settings, constrained by a limited number of communication turns, the seller must balance exploring the broader market to discover the highest valuation with concentrating sufficient turns on a single target buyer to secure the best possible outcome. Our analysis reveals a significant gap in standard Large Language Models (LLMs): while these models are linguistically proficient, they fail to act as effective economic decision-makers. Specifically, they exhibit a failure to explore the buyer pool, often fixating on the current highest bid rather than strategically investigating the market to discover latent high valuations. In this paper, we propose a specialized training recipe using Reinforcement Learning from Verifiable Rewards (RLVR). By anchoring the reward function to objective economic outcomes, the strategic balance between market discovery and surplus extraction emerges natively through the learning process. Our results demonstrate that the trained seller undergoes a multi-stage strategic evolution, learning to leverage price anchoring and strategic probing to identify more profitable counterparties. The agent extracts a substantially higher surplus than frontier models by both improving its persuasive bargaining skills and consistently closing deals with high-value buyers. Finally, we show that our seller strategies generalize robustly to unseen buyer negotiation styles and budget distributions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 7 minor

Summary. This paper proposes a Reinforcement Learning from Verifiable Rewards (RLVR) framework for training a single LLM-based seller agent to negotiate concurrently with multiple buyers who have private, heterogeneous budgets. The environment is formalized as a POMDP with sealed buyer channels, a limited total message budget T < N·K, and a verifiable reward based on deal surplus. The authors train a Qwen3-30B seller against frozen buyer checkpoints from their prior work (Liu et al. 2026) and observe a three-phase behavioral evolution: cost-floor internalization, concentrated closing, and joint surplus extraction with rank-1 buyer routing. The trained agent achieves a mean reward of +0.580 on a held-out 128-product test set (4.7× the best frontier baseline) and maintains an advantage under out-of-distribution conditions with 5 buyers, unseen buyer checkpoints, and altered budget distributions. The paper includes 12 baselines (4B–1T parameters), standard errors, full prompt templates, and qualitative transcripts.

Significance. The paper makes a solid contribution to the growing literature on LLM agents as strategic decision-makers. The concurrent multi-buyer negotiation setting with a limited communication budget is well-motivated and captures a genuine exploration-exploitation trade-off that is absent from bilateral negotiation benchmarks. The verifiable reward design (Eq. 1) is clean and parameter-free in its core formulation. The three-phase training decomposition (Section 4.3) is a genuinely interesting empirical finding about how strategic capabilities emerge in a staged hierarchy. The paper ships full prompt templates (Appendix C), hyperparameter tables (Tables 5–8), and qualitative transcripts (Appendix F), which support reproducibility. The 12-baseline panel spanning 4B–1T parameters provides a meaningful comparison axis. The central claim—that RLVR can teach a 30B model to outperform frontier models on a structured economic task—is well-supported by the in-distribution evidence.

major comments (2)
  1. Section 6.1, Table 8, and Table 12: The OOD evaluation perturbs budget distributions, buyer count, first-offer regulation, and buyer checkpoints, but all three buyer checkpoints (iter-50/60/70) share the same base model (Qwen3-30B-A3B), the same training pipeline (RLVR on bilateral negotiation from Liu et al. 2026), and the same dataset (AmazonHistoryPrice). Table 12 confirms the checkpoints differ in degree (first-offer ratio 0.31–0.37, buyer surplus 0.64–0.71) but not in qualitative response style. The seller's routing accuracy drops from 0.995 in-distribution to 0.707 OOD, which is consistent with partial overfitting to iter-60-specific concession patterns. The paper's claim that the seller 'generalizes robustly to unseen buyer negotiation styles' (abstract) is stronger than what this evaluation supports. The authors should either (a) soften the generalization claim to reflect that it
  2. Section 5.1, Table 1: The in-distribution Deal on Top Buyer Rate of 0.995 is remarkably high given that the first-offer regulator masks budget rank (Table 11 shows only 31.7% top-1 match from opening offers). The paper attributes this to 'diagnostic probing' but does not provide a mechanism analysis showing what specific dialogue signals the seller learned to extract from the iter-60 buyer's responses to list-price anchoring. Without such analysis, it is difficult to distinguish whether the seller learned a general budget-inference principle or a family-specific heuristic tuned to the Qwen3-30B buyer's concession curve. A controlled ablation—e.g., shuffling buyer response patterns across slots, or testing against a structurally different buyer (different base model or training pipeline)—would substantially strengthen the claim that 'the strategic balance between market discovery and surp
minor comments (7)
  1. Section 3.3: The 'first-offer regulator' is described as sampling from [0.25, 0.30]·P_list, but it is unclear whether this is a hard constraint enforced by the environment (programmatic interception) or a soft instruction in the buyer prompt. Appendix C.1 shows it baked into the prompt, but the enforcement mechanism should be clarified in the main text.
  2. Table 5: The KL penalty coefficient is set to 0. This means there is no regularization keeping the seller policy close to the base model. While this may be intentional, it allows substantial policy drift over 72 steps and should be discussed—particularly whether the three-phase evolution depends on this design choice.
  3. Section 4.3, Phase 3: The claim that surplus extraction and rank-1 routing 'emerge together' is supported by the co-occurrence of their rises (Figures 7 and 9), but no causal or mechanistic analysis is provided. A brief discussion of why these capabilities are coupled—beyond noting they share a training window—would strengthen the claim.
  4. Figure 3: The radar plot shows the trained agent against only two frontier baselines (DeepSeek-V3.1, Kimi-K2.6). Including gpt-5.1-high-reasoning, which is the strongest baseline in Table 1, would make the visual comparison more informative.
  5. Section 6.2: The paper notes that the OOD environment is more transparent because unregulated opening offers correlate with budgets (63.7% top-1 match per Table 11). This is offered as an explanation for the narrowed performance gap, but it also means the OOD test is in some respects easier for baselines, complicating the interpretation of the robustness result.
  6. Table 2: Under OOD conditions, the trained agent's Deal Rate drops to 70.7% while its Seller Surplus Extraction Ratio rises to 0.770 (higher than the in-distribution 0.700). The paper frames this as 'strategic selectivity,' but an alternative reading is that the agent is walking away from deals it could close. A brief analysis of the no-deal episodes in the OOD setting would clarify whether the lower deal rate reflects strategic discipline or a failure mode.
  7. Appendix E.2, Table 12: The three buyer checkpoints are characterized by first-offer ratio, buyer surplus extraction, and deal rate. It would be useful to also report each checkpoint's concession pattern (e.g., average price increase per turn in response to anchoring), since this is the signal the seller is presumably learning to exploit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for a careful and constructive report. Both major comments identify legitimate gaps in the evidence supporting our generalization claims. We agree that the OOD evaluation, while multi-axis, tests generalization across checkpoints that share a base model and training pipeline, and that the abstract's claim of robust generalization to 'unseen buyer negotiation styles' is stronger than what the current evidence supports. We also agree that the 0.995 in-distribution routing accuracy lacks a mechanism analysis distinguishing general budget-inference from family-specific heuristic use. We will revise the manuscript to soften the generalization claim and add a mechanism analysis with a controlled ablation. We cannot fully resolve the concern that all buyer checkpoints share the same base model family, as no structurally different trained buyer agent currently exists; we state this as a standing limitation.

read point-by-point responses

  1. Referee: Section 6.1, Table 8, and Table 12: The OOD evaluation perturbs budget distributions, buyer count, first-offer regulation, and buyer checkpoints, but all three buyer checkpoints (iter-50/60/70) share the same base model (Qwen3-30B-A3B), the same training pipeline (RLVR on bilateral negotiation from Liu et al. 2026), and the same dataset (AmazonHistoryPrice). Table 12 confirms the checkpoints differ in degree (first-offer ratio 0.31-0.37, buyer surplus 0.64-0.71) but not in qualitative response style. The seller's routing accuracy drops from 0.995 in-distribution to 0.707 OOD, which is consistent with partial overfitting to iter-60-specific concession patterns. The paper's claim that the seller 'generalizes robustly to unseen buyer negotiation styles' (abstract) is stronger than what this evaluation supports. The authors should either (a) soften the generalization claim to reflect that it

    Authors: The referee is correct on the substance. The three buyer checkpoints (iter-50/60/70) do share the same base model, training pipeline, and dataset; they differ in degree rather than in qualitative response style. The routing accuracy drop from 0.995 to 0.707 is indeed consistent with partial overfitting to iter-60-specific concession patterns. We will take option (a): soften the generalization claim throughout the manuscript. Specifically, we will revise the abstract to state that the seller 'maintains its advantage under out-of-distribution conditions including perturbed budget distributions, unseen buyer checkpoints, and altered market transparency,' rather than claiming robust generalization to 'unseen buyer negotiation styles.' We will add an explicit limitation paragraph in Section 6.1 noting that all buyer checkpoints share the same model family and training pipeline, and that the OOD evaluation therefore tests generalization across behavioral variations within a single model family rather than across structurally different buyer architectures. We will also add a sentence in the Discussion (Section 7) identifying evaluation against buyers trained from different base models as a necessary future-work direction. We note that the OOD evaluation does simultaneously perturb four axes (budget distribution, first-offer regulation, buyer checkpoint identity, and buyer count/message budget), and the seller does maintain the highest reward (+0.540) and surplus extraction ratio (+0.770) in that setting. However, the referee's point stands: this evidence supports a narrower claim than the abstract currently makes, and we will correct it. revision: yes

  2. Referee: Section 5.1, Table 1: The in-distribution Deal on Top Buyer Rate of 0.995 is remarkably high given that the first-offer regulator masks budget rank (Table 11 shows only 31.7% top-1 match from opening offers). The paper attributes this to 'diagnostic probing' but does not provide a mechanism analysis showing what specific dialogue signals the seller learned to extract from the iter-60 buyer's responses to list-price anchoring. Without such analysis, it is difficult to distinguish whether the seller learned a general budget-inference principle or a family-specific heuristic tuned to the Qwen3-30B buyer's concession curve. A controlled ablation—e.g., shuffling buyer response patterns across slots, or testing against a structurally different buyer (different base model or training pipeline)—would substantially strengthen the claim that 'the strategic balance between market discovery and surp

    Authors: This is a fair and important point. The 0.995 routing accuracy, combined with the 31.7% top-1 match rate from opening offers, does imply the seller is extracting budget-revealing signals from multi-turn dialogue rather than from opening offers alone. However, we agree that without a mechanism analysis, we cannot distinguish whether the seller learned a general budget-inference principle or a family-specific heuristic tuned to the iter-60 buyer's concession curve. We will address this in two ways. First, we will add a mechanism analysis to Section 5.1 that examines what dialogue signals correlate with the seller's routing decisions. Specifically, we will analyze the relationship between each buyer's response to list-price anchoring (e.g., magnitude of bid escalation after receiving a [SELL]$Plist counter) and the seller's subsequent targeting decisions, reporting the correlation between escalation magnitude and the seller's probability of closing on that buyer. This will make explicit what the trained agent appears to have learned. Second, we will add a controlled ablation: we will run the trained seller against a buyer pool where the response-generation model is shuffled across slots (i.e., a buyer with a low budget but an iter-60-style aggressive concession curve, and vice versa), to test whether the seller's routing decisions track the underlying budget or the family-specific concession pattern. If routing accuracy degrades significantly under shuffling, this would support the family-specific heuristic interpretation; if it holds, this would support the general-principle interpretation. We will report whichever result obtains honestly. We cannot, however, fully resolve the concern about structurally different buyers: no trained buyer agent from a different base model或 revision: no

Circularity Check

2 steps flagged

No significant circularity; one minor self-citation dependency that is acknowledged but not load-bearing for the central RLVR contribution.

specific steps
  1. self citation load bearing [Section 3.3, Table 3, and Section 6.1 (Table 8)]
    "The N = 3 buyer slots in each episode are comprised of a trained and frozen Qwen3-30B-A3B-Instruct-2507 model... Specifically, we utilize a buyer checkpoint that was previously trained via RLVR on a bilateral (one-on-one) negotiation task from Liu et al. (2026)."

    The buyer agents used in both training and evaluation come from Liu et al. (2026), which shares authors with this paper. The OOD evaluation (Section 6.1) perturbs budget distributions, buyer count, and first-offer regulation, but the buyer policy space is still confined to three checkpoints (iter-50/60/70) from that same training run. This creates a dependency where the seller's 'generalization' claim is tested only within one buyer model family defined by overlapping authors. However, this is a scope limitation on the generalization claim, not a circularity in the RLVR derivation itself: the reward function (Eq. 1) is defined independently of the buyer model, the seller's training objective does not reference Liu et al. (2026)'s results, and the in-distribution benchmarking against 12 bas

  2. self citation load bearing [Section 3.3 and Appendix A.1, Table 3]
    "This ensures the seller is matched against a strong opponent that has already learned to protect its own surplus and walk away from poor deals, rather than a naive or overly agreeable baseline buyer model."

    The choice of buyer agent is justified by citing Liu et al. (2026) for the claim that these checkpoints are 'strong opponents.' This is a self-citation used to establish the difficulty of the environment. However, the central contribution of the present paper — the concurrent multi-buyer RLVR training recipe and the emergence of diagnostic probing behavior — does not logically depend on this characterization being true. The reward signal is computed from objective deal economics (Eq. 1), not from any property established in the cited work. The self-citation is a design choice justification, not a load-bearing premise in the derivation chain.

full rationale

The paper's core derivation chain is self-contained. The reward function (Eq. 1) is defined purely in terms of deal price, seller cost, and list price — all objective economic quantities from the AmazonHistoryPrice dataset (Xia et al. 2024, an independent source). The RLVR training loop optimizes this reward without referencing any result from the authors' prior work. The buyer agents from Liu et al. (2026) serve as environment components, not as inputs to the seller's reward computation or training objective. The OOD generalization claim is tested against checkpoints from the same buyer family, which limits the scope of the generalization evidence but does not make the derivation circular: the seller's policy is not fitted to any quantity defined by the cited work, and the evaluation metrics (Reward, Deal Rate, Surplus Extraction Ratio, Deal on Top Buyer Rate) are all computed from the environment's ground-truth parameters, not from Liu et al. (2026)'s reported results. The 12-baseline comparison panel includes externally developed models (GPT-5.1, DeepSeek, Kimi, Llama), providing independent benchmarks. The two self-citations to Liu et al. (2026) are minor: they establish the buyer agent provenance and justify the choice of a 'strong opponent,' but neither is load-bearing for the central claim that RLVR training produces strategic negotiation behavior. Score 2 reflects these minor self-citations that do not undermine the independence of the main derivation.

Axiom & Free-Parameter Ledger

7 free parameters · 4 axioms · 2 invented entities

The environment has 7 hand-specified free parameters (N, K, T, budget intervals, first-offer range, clip thresholds, learning rate). The buyer competence axiom is the most consequential: all empirical results depend on buyers from the authors' own prior work. The first-offer regulator is an invented mechanism whose removal in OOD evaluation provides a partial falsifiability check.

free parameters (7)
  • N (number of buyers) = 3 (training), 5 (OOD)
    Environment parameter chosen by the authors, not derived from theory.
  • K (per-buyer message cap) = 3
    Chosen to create the T < N·K resource constraint. Not derived.
  • T (total message budget) = 7 (training), 9 (OOD)
    Chosen to ensure T < N·K. Not derived.
  • Budget ratio intervals = {[0.40,0.55],[0.65,0.80],[1.00,1.15]}
    Hand-specified to create low/medium/high buyer tiers. Not derived from data.
  • First-offer ratio distribution = U[0.25,0.30]
    Hand-specified to mask buyer rank in Turn 1. Not derived.
  • CISPO clip thresholds = (0.8, 6.0)
    RL optimization hyperparameter from Chen et al. (2025).
  • Learning rate = 3e-5
    Standard RL fine-tuning rate, not tuned via systematic search.
axioms (4)
  • domain assumption Buyer agents from Liu et al. (2026) are sufficiently strategic opponents for evaluating seller competence.
    Section 3.3 states buyers are 'a strong opponent that has already learned to protect its own surplus.' This is assumed, not independently verified against human negotiators or other buyer models.
  • domain assumption The reward function R = (P_deal - C)/(P_list - C) captures the seller's strategic objective adequately.
    Section 3.2, Eq. 1. The reward is a single-deal surplus ratio. Multi-deal scenarios, relationship value, and non-price attributes are excluded by construction.
  • domain assumption The AmazonHistoryPrice dataset products are representative of real-world negotiation scenarios.
    Section 4 and Appendix B. 930 products from Amazon are used, but the negotiation dynamics (single item, fixed cost, sealed channels) may not reflect real marketplace conditions.
  • ad hoc to paper 72 RL training steps are sufficient for the agent to reach a stable strategic policy.
    Section 4 reports 72 steps with metrics appearing to plateau, but no convergence analysis or multi-seed comparison is provided.
invented entities (2)
  • First-offer regulator no independent evidence
    purpose: Forces all buyers to open with bids in [0.25, 0.30]·P_list regardless of budget, masking rank information in Turn 1.
    Introduced in Section 3.3 to create the exploration challenge. It is an environment design choice, not a derived necessity. The OOD evaluation disables it (Table 8), which serves as a partial falsifiability test.
  • Standing-offers board no independent evidence
    purpose: Public state summary appended to each seller turn, listing buyer status, action history, and remaining message budget.
    Described in Appendix C.2. It is an interface design choice that structures the seller's observation space. No claim of novelty is made for this entity.

pith-pipeline@v1.1.0-glm · 37203 in / 5116 out tokens · 472120 ms · 2026-07-08T22:02:28.793251+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

300 extracted references · 300 canonical work pages · 25 internal anchors

  1. [1]

    International Conference on Learning Representations , volume=

    Towards understanding sycophancy in language models , author=. International Conference on Learning Representations , volume=

    work page

  2. [2]

    Meta Newsroom , year =

    work page

  3. [3]

    Harvard Business Review , year =

    Van Hoek, Remko and DeWitt, Michael and Lacity, Mary and Johnson, Travis , title =. Harvard Business Review , year =

    work page

  4. [4]

    Management Science , volume=

    Personalized dynamic pricing with machine learning: High-dimensional features and heterogeneous elasticity , author=. Management Science , volume=. 2021 , publisher=

    work page 2021

  5. [5]

    Operations research , volume=

    Inventory planning with forecast updates: Approximate solutions and cost error bounds , author=. Operations research , volume=. 2006 , publisher=

    work page 2006

  6. [6]

    Operations Research , volume=

    A dynamic near-optimal algorithm for online linear programming , author=. Operations Research , volume=. 2014 , publisher=

    work page 2014

  7. [7]

    Production and Operations Management , volume=

    Committed versus contingent pricing under competition , author=. Production and Operations Management , volume=. 2014 , publisher=

    work page 2014

  8. [8]

    Operations Research , volume=

    Close the gaps: A learning-while-doing algorithm for single-product revenue management problems , author=. Operations Research , volume=. 2014 , publisher=

    work page 2014

  9. [9]

    Operations Research , volume=

    The big data newsvendor: Practical insights from machine learning , author=. Operations Research , volume=. 2019 , publisher=

    work page 2019

  10. [10]

    Management Science , volume=

    Dynamic pricing of perishable assets under competition , author=. Management Science , volume=. 2014 , publisher=

    work page 2014

  11. [11]

    Manufacturing & Service Operations Management , volume=

    Modeling payment timing in multiechelon inventory systems with applications to supply chain coordination , author=. Manufacturing & Service Operations Management , volume=. 2020 , publisher=

    work page 2020

  12. [12]

    Management Science , volume=

    Gathering information before negotiation , author=. Management Science , volume=. 2023 , publisher=

    work page 2023

  13. [13]

    Let me talk to my manager

    “Let me talk to my manager”: Haggling in a competitive environment , author=. Marketing Science , volume=. 2004 , publisher=

    work page 2004

  14. [14]

    Management Science , volume=

    The effects of delay in bargaining: Evidence from ebay , author=. Management Science , volume=. 2025 , publisher=

    work page 2025

  15. [15]

    Manufacturing & service operations management , volume=

    Optimal pricing of seasonal products in the presence of forward-looking consumers , author=. Manufacturing & service operations management , volume=. 2008 , publisher=

    work page 2008

  16. [16]

    Management Science , volume=

    Optimal pricing with speculators and strategic consumers , author=. Management Science , volume=. 2010 , publisher=

    work page 2010

  17. [17]

    European journal of operational research , volume=

    Game-theoretic analysis of cooperation among supply chain agents: Review and extensions , author=. European journal of operational research , volume=. 2008 , publisher=

    work page 2008

  18. [18]

    Management Science , volume=

    Bargaining chains , author=. Management Science , volume=. 2010 , publisher=

    work page 2010

  19. [19]

    Management science , volume=

    Contracting to assure supply: How to share demand forecasts in a supply chain , author=. Management science , volume=. 2001 , publisher=

    work page 2001

  20. [20]

    2005 , publisher=

    The logic of logistics: theory, algorithms, and applications for logistics and supply chain management , author=. 2005 , publisher=

    work page 2005

  21. [21]

    Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , pages=

    Math-shepherd: Verify and reinforce llms step-by-step without human annotations , author=. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , pages=

    work page

  22. [22]

    Let's reward step by step: Step-Level reward model as the Navigators for Reasoning

    Let's reward step by step: Step-Level reward model as the Navigators for Reasoning , author=. arXiv preprint arXiv:2310.10080 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  23. [23]

    Training Verifiers to Solve Math Word Problems

    Training verifiers to solve math word problems , author=. arXiv preprint arXiv:2110.14168 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  24. [24]

    Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback

    Open problems and fundamental limitations of reinforcement learning from human feedback , author=. arXiv preprint arXiv:2307.15217 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  25. [25]

    Too Nice to Tell the Truth: Quantifying Agreeableness-Driven Sycophancy in Role-Playing Language Models

    Too Nice to Tell the Truth: Quantifying Agreeableness-Driven Sycophancy in Role-Playing Language Models , author=. arXiv preprint arXiv:2604.10733 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  26. [26]

    Findings of the association for computational linguistics: ACL 2023 , pages=

    Discovering language model behaviors with model-written evaluations , author=. Findings of the association for computational linguistics: ACL 2023 , pages=

    work page 2023

  27. [27]

    Advances in Neural Information Processing Systems , volume=

    Cooperation, competition, and maliciousness: Llm-stakeholders interactive negotiation , author=. Advances in Neural Information Processing Systems , volume=

    work page

  28. [28]

    Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing , pages=

    Be selfish, but wisely: Investigating the impact of agent personality in mixed-motive human-agent interactions , author=. Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing , pages=

    work page 2023

  29. [29]

    Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing , pages=

    Decoupling strategy and generation in negotiation dialogues , author=. Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing , pages=

    work page 2018

  30. [30]

    International Conference on Machine Learning , pages=

    Hierarchical text generation and planning for strategic dialogue , author=. International Conference on Machine Learning , pages=. 2018 , organization=

    work page 2018

  31. [31]

    Group Decision and Negotiation , volume=

    The state of the art in automated negotiation models of the behavior and information perspective , author=. Group Decision and Negotiation , volume=

    work page

  32. [32]

    International Journal of Group Decision and Negotiation , volume=

    Automated negotiation: prospects, methods and challenges , author=. International Journal of Group Decision and Negotiation , volume=

    work page

  33. [33]

    2001 , publisher=

    Strategic negotiation in multiagent environments , author=. 2001 , publisher=

    work page 2001

  34. [34]

    Companion Proceedings of the ACM on Web Conference 2025 , pages=

    Fishbargain: An llm-empowered bargaining agent for online fleamarket platform sellers , author=. Companion Proceedings of the ACM on Web Conference 2025 , pages=

    work page 2025

  35. [35]

    Findings of the Association for Computational Linguistics: ACL 2024 , pages=

    Agenttuning: Enabling generalized agent abilities for llms , author=. Findings of the Association for Computational Linguistics: ACL 2024 , pages=

    work page 2024

  36. [36]

    ReAct: Synergizing Reasoning and Acting in Language Models

    React: Synergizing reasoning and acting in language models , author=. arXiv preprint arXiv:2210.03629 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  37. [37]

    International Conference on Learning Representations , volume=

    Agentbench: Evaluating llms as agents , author=. International Conference on Learning Representations , volume=

    work page

  38. [38]

    Stockholm: Economic Research Institute , year=

    Bargaining theory , author=. Stockholm: Economic Research Institute , year=

    work page

  39. [39]

    Journal of economic Theory , volume=

    Foundations of dynamic monopoly and the Coase conjecture , author=. Journal of economic Theory , volume=. 1986 , publisher=

    work page 1986

  40. [40]

    The RAND Journal of Economics , pages=

    The Nash bargaining solution in economic modelling , author=. The RAND Journal of Economics , pages=. 1986 , publisher=

    work page 1986

  41. [41]

    The Review of Economic Studies , volume=

    A multistage model of bargaining , author=. The Review of Economic Studies , volume=. 1983 , publisher=

    work page 1983

  42. [42]

    The Review of Economic Studies , volume=

    Sequential bargaining with incomplete information , author=. The Review of Economic Studies , volume=. 1983 , publisher=

    work page 1983

  43. [43]

    Journal of economic theory , volume=

    A model of price adjustment , author=. Journal of economic theory , volume=. 1971 , publisher=

    work page 1971

  44. [44]

    Management science , volume=

    Reducing buyer search costs: Implications for electronic marketplaces , author=. Management science , volume=. 1997 , publisher=

    work page 1997

  45. [45]

    The quarterly journal of economics , pages=

    A behavioral model of rational choice , author=. The quarterly journal of economics , pages=. 1955 , publisher=

    work page 1955

  46. [46]

    Fine-Tuning Language Models from Human Preferences

    Fine-tuning language models from human preferences , author=. arXiv preprint arXiv:1909.08593 , year=

    work page internal anchor Pith review Pith/arXiv arXiv 1909

  47. [47]

    International Journal of Game Theory , volume=

    Perfect equilibria in simultaneous-offers bargaining , author=. International Journal of Game Theory , volume=. 1990 , publisher=

    work page 1990

  48. [48]

    1985 , publisher=

    The art and science of negotiation , author=. 1985 , publisher=

    work page 1985

  49. [49]

    Econometrica , volume=

    The bargaining problem , author=. Econometrica , volume=

    work page

  50. [50]

    Journal of economic theory , volume=

    Efficient mechanisms for bilateral trading , author=. Journal of economic theory , volume=. 1983 , publisher=

    work page 1983

  51. [51]

    Operations research , volume=

    Bargaining under incomplete information , author=. Operations research , volume=. 1983 , publisher=

    work page 1983

  52. [52]

    The Quarterly Journal of Economics , volume=

    Sequential bargaining in the field: Evidence from millions of online bargaining interactions , author=. The Quarterly Journal of Economics , volume=. 2020 , publisher=

    work page 2020

  53. [53]

    Training Language Models for Bilateral Trade with Private Information

    Training Language Models for Bilateral Trade with Private Information , author=. arXiv preprint arXiv:2604.16472 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  54. [54]

    MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention

    Minimax-m1: Scaling test-time compute efficiently with lightning attention , author =. arXiv preprint arXiv:2506.13585 , year =

    work page internal anchor Pith review Pith/arXiv arXiv

  55. [55]

    Instructing LLMs to Negotiate using Reinforcement Learning with Verifiable Rewards

    Instructing LLMs to Negotiate using Reinforcement Learning with Verifiable Rewards , author =. arXiv preprint arXiv:2604.09855 , year =

    work page internal anchor Pith review Pith/arXiv arXiv

  56. [56]

    OpenAI GPT-5 System Card

    Openai gpt-5 system card , author =. arXiv preprint arXiv:2601.03267 , year =

    work page internal anchor Pith review Pith/arXiv arXiv

  57. [57]

    Journal of Economic Behavior & Organization , volume =

    Selling “Money” on eBay: A field study of surplus division , author =. Journal of Economic Behavior & Organization , volume =. 2021 , publisher =

    work page 2021

  58. [58]

    Science , volume =

    Human-level play in the game of diplomacy by combining language models with strategic reasoning , author =. Science , volume =. 2022 , publisher =

    work page 2022

  59. [59]

    , author =

    First offers as anchors: the role of perspective-taking and negotiator focus. , author =. Journal of personality and social psychology , volume =. 2001 , publisher =

    work page 2001

  60. [60]

    Handbook of the fundamentals of financial decision making: Part I , pages =

    Prospect theory: An analysis of decision under risk , author =. Handbook of the fundamentals of financial decision making: Part I , pages =. 2013 , publisher =

    work page 2013

  61. [61]

    , author =

    Judgment under Uncertainty: Heuristics and Biases: Biases in judgments reveal some heuristics of thinking under uncertainty. , author =. science , volume =. 1974 , publisher =

    work page 1974

  62. [62]

    Journal of Economic Literature , volume =

    Bargaining with private information , author =. Journal of Economic Literature , volume =. 1993 , publisher =

    work page 1993

  63. [63]

    Econometrica: Journal of the Econometric Society , pages =

    Two-person cooperative games , author =. Econometrica: Journal of the Econometric Society , pages =. 1953 , publisher =

    work page 1953

  64. [64]

    The Llama 3 Herd of Models

    The llama 3 herd of models , author =. arXiv preprint arXiv:2407.21783 , year =

    work page internal anchor Pith review Pith/arXiv arXiv

  65. [65]

    2025 , eprint =

    gpt-oss-120b & gpt-oss-20b Model Card , author =. 2025 , eprint =

    work page 2025

  66. [66]

    2024 , eprint =

    DeepSeek-V3 Technical Report , author =. 2024 , eprint =

    work page 2024

  67. [67]

    Qwen2.5-1M Technical Report

    Qwen2.5-1M Technical Report , author =. arXiv preprint arXiv:2501.15383 , year =

    work page internal anchor Pith review Pith/arXiv arXiv

  68. [68]

    2025 , eprint =

    Qwen3 Technical Report , author =. 2025 , eprint =

    work page 2025

  69. [69]

    1991 , publisher =

    Game theory , author =. 1991 , publisher =

    work page 1991

  70. [70]

    American Economic Review , volume =

    Games with incomplete information , author =. American Economic Review , volume =. 1995 , publisher =

    work page 1995

  71. [71]

    Bayesian

    Games with incomplete information played by “Bayesian” players, I--III Part I. The basic model , author =. Management science , volume =. 1967 , publisher =

    work page 1967

  72. [72]

    Econometrica: Journal of the Econometric Society , pages =

    Perfect equilibrium in a bargaining model , author =. Econometrica: Journal of the Econometric Society , pages =. 1982 , publisher =

    work page 1982

  73. [73]

    Proceedings of the national academy of sciences , volume =

    Equilibrium points in n-person games , author =. Proceedings of the national academy of sciences , volume =. 1950 , publisher =

    work page 1950

  74. [74]

    Advances in neural information processing systems , volume =

    Training language models to follow instructions with human feedback , author =. Advances in neural information processing systems , volume =

    work page

  75. [75]

    Advances in neural information processing systems , volume =

    Deep reinforcement learning from human preferences , author =. Advances in neural information processing systems , volume =

    work page

  76. [76]

    arXiv preprint arXiv:2503.16252 , year =

    Fin-r1: A large language model for financial reasoning through reinforcement learning , author =. arXiv preprint arXiv:2503.16252 , year =

    work page arXiv

  77. [77]

    arXiv preprint arXiv:2407.09450 , year =

    Human-inspired episodic memory for infinite context LLMs , author =. arXiv preprint arXiv:2407.09450 , year =

    work page arXiv

  78. [78]

    arXiv preprint arXiv:2603.15255 , year =

    SAGE: Multi-Agent Self-Evolution for LLM Reasoning , author =. arXiv preprint arXiv:2603.15255 , year =

    work page arXiv

  79. [79]

    arXiv preprint arXiv:2506.24119 , year =

    Spiral: Self-play on zero-sum games incentivizes reasoning via multi-agent multi-turn reinforcement learning , author =. arXiv preprint arXiv:2506.24119 , year =

    work page arXiv

  80. [80]

    arXiv preprint arXiv:2401.04536 , year =

    Evaluating language model agency through negotiations , author =. arXiv preprint arXiv:2401.04536 , year =

    work page arXiv

Showing first 80 references.