Shapley-Coop: Credit Assignment for Emergent Cooperation in Self-Interested LLM Agents
Authors: Yun Hua
Haosheng Chen
Shiqin Wang
Wenhao Li
Xiangfeng Wang
Jun Luo
Venue: NeurIPS 2025 poster ()
Keywords: Large Language Model
Multi-Agent Systems
Mechanism Design
Primary area: deep_learning

Abstract: Large Language Models (LLMs) are increasingly deployed as autonomous agents in multi-agent systems, and promising coordination has been demonstrated in handling complex tasks under predefined roles and scripted workflows.
However, significant challenges remain in open-ended environments, where agents are inherently self-interested and explicit coordination guidelines are absent. 
In such scenarios, misaligned incentives frequently lead to social dilemmas and inefficient collective outcomes.
Inspired by how human societies tackle similar coordination challenges—through temporary collaborations like employment or subcontracting—a cooperative workflow \textbf{Shapley-Coop} is proposed. 
This workflow enables self-interested Large Language Model (LLM) agents to engage in emergent collaboration by using a fair credit allocation mechanism to ensure each agent’s contributions are appropriately recognized and rewarded.
Shapley-Coop introduces structured negotiation protocols and Shapley-inspired reasoning to estimate agents’ marginal contributions, thereby enabling effective task-time coordination and equitable post-task outcome redistribution. 
This results in effective coordination that fosters collaboration while preserving agent autonomy, through a rational pricing mechanism that encourages cooperative behavior.
Evaluated in two multi-agent games and a software engineering simulation, Shapley-Coop consistently enhances LLM agent collaboration and facilitates equitable outcome redistribution, accurately reflecting individual contributions during the task execution process.

Shapley-Coop: Credit Assignment for Emergent Cooperation in Self-Interested LLM Agents
Yun Hua Haosheng Chen?; Shiqin Wang", Wenhao Li Xiangfeng Wang*.5.6 Jun Luo
Antai College of Economics and Management, Shanghai Jiao Tong University
School of Computer Science and Technology, East China Normal University
School of Computer Science and Technology, Tongji University
4 Key Laboratory of Mathematics and Engineering Applications (MoE)
5 Shanghai Institute of Al for Education, East China Normal University Shenzhen Loop Area Institute (SLAI)
{hyyh28, jluo ms ju edw...edu.cco cn, (hschen, 51275901137) ecnu edu. en whli@tongji. edu, cn, xfwangocs ecnu. edu. cn
Abstract
Large Language Models (LLMs) show strong collaborative performance in multi- agent systems with predefined roles and workflows. However, in open-ended environments lacking coordination rules, agents tend to act in self-interested ways. The central challenge in achieving coordination lies credit assignment- fairly evaluating each agent's contribution and designing pricing mechanisms that align their heterogeneous goals. This problem is critical as LLMs increasingly participate in complex human-Al collaborations, where fair compensation and accountability rely on effective pricing mechanisms. Inspired by how human societies address similar coordination challenges (e.g.. via temporary collaborations like employment or subcontracting), a cooperative workflow Shapley-Coop is proposed. Shapley- marginal contributions a principled basis for pricing witt structured negotiation protocols for effective price matching, enabling LLM agents to coordinate through rational task-time pricing and post-task reward redistribution. This approach aligns agent incentives, fosters cooperation, and maintains autonomy. We evaluate Shapley-Coop across two multi-agen games and software engineering simulation, demonstrating that it consistently enhances LLM agent collaboration and facilitates equitable credit assignment. These results highlight the effectiveness of Shapley-Coop' 's pricing mechanisms accurately reflecting individual contributions during task execution.
Coop integrates Shapley
1 Introduction
Large Language Models (LLMs) are increasingly deployed as autonomous agents in multi-agent systems, demonstrating remarkable effectiveness across diverse real-world scenarios including education
multi-player games [28] 322, software development tasks 29 [5], medical care applications [24].
7 and etc. However, despite their success structured settings, achieving spontaneous cooperation among self-interested L.M agents remains challenging in open-ended environments, where explicit rules and predefined roles are absent and agents" goals can be inherently conflicting (28
'Equal Contribution.
Conrespnnning to: Xiangfeng Wang and Jun Luo.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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In such situations, agents acting purely in self-inters inferintt typically encounter social dilemmas leading to suboptimal collective outcomes.
[5
Contemporary approaches to multi-agent cooperation involving LLMS can broadly be categorized into three paradigms: (1) rule-oriented methods, which impose strict behavioral constraints but compromise agents" autonomy [5] 48 47 (2) role-oriented methods, which assign static roles 29 30 and (3) model-oriented methods, which
limiting adaptability in dynamic environments 66 15
assume alignment of goals and thus fail to handle natural conflicts of interest effectively [42] 26 21]. Although effective narrow, task specific contexts, most frameworks have yet consider the critical challenge of aligning heterogeneous goals and fairly credit assignment that are essential for spontaneous cooperation in more open-ended multi-agent LLMs interactions.
The central challenge for effective L.M agent coordination in open-ended environments lies in
credit assignment- fairly evaluating each agent's individual contributions- -ndiiooon---addd designing principled pricing mechanisms an incentive-aware value distribution system for multi-agent coordination capable of aligning their heterogeneous objectives.
Addressing this challenge involves two critical questions: 1. mechanisms that align the inherently heterogeneous goals of self-interested agents, thus enabling spontaneous emergence of cooperative behaviors? 2. Once aligned, how can we guarantee fair and accurate credit assignment, ensuring the allocated rewards accurately reflect each agent's actual contribution during task execution?
How can we establish effective pricing
Social scientists have historically navigated similar coordination challenges by developing sophisti- cated institutional mechanisms. Employment contracts, subcontracting agreements, and structured negotiations explicitly define the terms of cooperation, aligning individual incentives through clear pricing and ensuring fairness through transparent evaluation contributions. Social sciences and managerial economics have formalized these practices into rigorous theoretical frameworks. Notably, classical economic theories such as Pigovian taxes 2 and the Coase theorem solutions for managing externalities.
||| provide structured
Inspired by these established economic and managerial practices, we propose a novel cooperative workflow designed to coordinate -elf-interested LLM agents in open-ended multi-agent environments: Shapley-Coop. Our framework integrates Shapley Chain-of- ohTThuggt reasoning, which leverages marginal contributions as a rigorous pricing foundation, with structured negotiation protocols to facilitate effective and autonomous price matching. Shapley-Coop enables spontaneous cooperation through rational task-time pricing and transparent post-task reward redistribution, thus achieving alignment of agents' heterogeneous goals in open-ended environments and effective credit assignment.
We empirically validate Shapley-Coop across three distinct experimental environments: (1) In a simplified "Escape Room" social dilemma scenario, we demonstrate that conventional negotiation methods fail to resolve reward allocation conflicts adequately, whereas Shapley-Cove effectively enables agents recognize and negotiate fair rewards, achieving successful cooperative outcomes. (2) In the more complex multi-step "Raid Battle Game," Shapley-Coop successfully balances competing individual incentives against collective success, enabling effective cooperation and equitable reward distribution. (3) Lastly, within the challenging "ChatDEV" software-developnee
simulation, we show that precise credit assignment enabled by Shapley-Coo significantly enhances cooperative dynamics among diverse, self-interested LLM agents, highlighting the practical value of our approach for real-world collaborative productivity.
In summary, the primary contributions of this paper are:
Introducing a Brisedg-Based Perspective for Multi-LLM Cooperation: We explicitly address the critical challenge of aligning heterogeneous goals among self-interested L.L agents through principled pricing mechanisms inspired by cooperative game theory, thus enabling spontaneous emergence cooperation in open-ended scenarios.
cooperative workflow: We propose Shapley-Coop, cooperative framework that integrates Shapley Chain-of-Thought reasoning and structured negotiation protocols, facilitating fair and effective credit assignment among self-interested LLM agents, aligning incentives, and maintaining autonomy.
Proposing Shapley-Coop.
Empirical Validation Demonstrating Robust Cooperation and Practical Relevance: Through comprchensive experiments across diverse social-dilemma scenarios and realistic software-

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engineering tasks, we validate that Chapley-Coop consistently fosters emergent cooperation, equitably allocates rewards, and significandly improves collaborative demmnis-ddmoossratiing its practical applicability and robustness in realistic human-Al collaborative environments.
2 Cooperation among Self-Interested LLM Agents
In a multi-agent system composed of N Large Language Model (LLM) agents, each agent xo. observes local state s², takes an action o², and aims maximize its own local reward function rd (i = 1, ,N, while the global reward is defined as [f T&N).
Lee Enchireed Eiehal
+10
Figure 1: Escape room: One agent pulls lever (-1) to let the other escape through door (+10)..
Cooperation is necessary.
This setup creates misalignment between individual and collective incentives due to heterogeneous goals agents optimizie local rewards while neglecting their impact on the global reward. Such misalignments often induce social dilemmas, where private optimization creates spillover effects on system-level outcomes.
Consider the Escape Room scenario (Figure where agents have divergent but complementary goals: one needs to pay -1 to pull a lever, while the other gains +10 for opening the door. Without coordination, their selfish policies lead Nash equilibrium where neither acts (global payoff 0). However, by introducing a transfer payment through pricing mechanism which adds fees or bonuses fix conflicts between selfish and group goals, their goals can be aligned, enabling successful escape and achieving Pareto-superior outcomes.
Proper pricing mechanism design requires fair credit assignment based on agents' marginal perfor- mance contributions. We introduce the Shapley value from cooperative game theory as a principled tool for measuring marginal contributions.
Table Original payoff matrix for the escape room game
Agentz: door Agentz: lever
Agent:: door
-1)
(10, -
Agent:: lever
(-1, 10)
(-1, -1)
The core idea of Shapley value simple: instead of evaluating an agent in isolation,it considers how much value it adds to all possible teams it could be part of. Formally, for any subset (or coalition) of agents C' C NN, the global reward achieved by that coalition is defined as:
R(C) R ({=os Hie)).
(1)
Further, the marginal contribution of agent coalition C is:
A.(C) (CC (i))
(2)
The Shapley value aggregates these marginal contributions over all possible coalitions, weighting each one by the probability that the coalition would form in random order of arrival. Specifically, the Shapley value for agent is given by:
1)! CIN( - |C| (101-11)((RCA - -
Φ1=
Σ
(3)
N!
CC
3

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Intuitively, this measures the average value that agent i brings when joining team, over all possible team configurations. This gives us principled way to estimate each agent's true contribution even when individual actions are interdependent or their value is only revealed in combination with others.
Returning the Escape Room example, we apply the Shapley value to fairly allocate rewards based on each agent's marginal contribution to the team's success. We compute the marginal contributions of each agent the coalition:
A Agent; P({[genn,, Agenl2))-ol ({(genl2)))) A Ageniy = <([Agenl,, A ((Agnl }
Since only two agents are discussed, the Shapley value for each agent is computed by averaging its
Table 2: Payoff matrix incorporating Shapley value compensation
Agent2: door Agent2: lever
Agent:: door Agent1: lever
(4.5,
(4.5,4.5)
11,
standalone value and marginal contribution in the two possible orderings:
① Agenti = 2 ((Agent))) + 1 = Agents Agentz 2 (Agenta)) + 1
1
Agent22
Therefore, under this allocation, both agents are assigned equal Shapley value, i.e.,
Aggent, = PAgent, 4.5,
which reflects their equal importance in achieving the joint success, despite the asymmetry who receives the final reward in the environment. For instance, if Agent 2 receives the +10 payoff, it should transfer 5.5 to Agent (who incurred cost of 1) to ensure faimess:
Agent1 -1 5.5 4.5,
Agents 10 5.5 4.5.
By re-allocating rewards based on Shapley values, enable local incentives to better align with global goals-allowing self-interested agents to coordinate more effectively and achieve fair credit assignment. In real-world scenarios or complex multi-step tasks, LLM agent often cannot immedi- ately observe the long-term payoff of its marginal contributions. This makes direct measurement of Shapley value challenging. conceptual tool is necessary for guiding negotiation and reward sharing among agents, enabling self-interested LLMs to calculate their contributions effectively even in the absence of perfect observability immediate feedback.
In the next section, we introduce the Shapley-Coop Workflow, a practical framework that integrates communication, bargaining, and contribution estimation to facilitate cooperation in LLM agent systems under uncertainty.
Shapley-Coop Workflow
Spontaneous collaboration among self- self-interested LLM agents in open-ended tasks requires addressing following fundamental challenges: (1) The design of an efficient discussion mechanism that facilitates strategy exchange and refinement among LLM agents, (2) aligning heterogeneous goals toward cooperative outcomes despite inherent conflicts of interest, and (3) fairly credit assignment based on each agent's actual contributions. To simultaneously address these challenges, we propose the Shapley-Coop, an integrated cooperative framework inspired by cooperative game theory and structured economic practices.
Shapley-Coop comprises three interconnected modules:
1). Structured Negotiation Protocol: A structured communication protocol enabling agents to propose,
refine, and agree on cooperative strategies;
2). Short-Tern Shapley Chain-of- Thought: A reasoning mechanism that helps self- interestedd agent align their heterogeneous goals and decide determine whether pricing is necessary;
3). Long-Teru Shapley Shain-of-Thhughh reasoning mechanism that ensures fair credit assignment based on LLM agents' actual contributions and determine how much price is necessary.

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Short-Tern Shapley COT
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The Shapley-Coop Workflow for spontaneous cooperation among self- interesterrdd LLM agents. The framework consists of three key components: (1) a structured negotiation protocol, enabling clear communication and agreement cooperative strategies; (2) the Short-Tere Shapley Chain-of-Thoughe (CoT), which provides heuristic, forward-looking reasoning to align LLM agents' goals and during the task; and (3) the Long-term Shapley CoT, which retrospectively applies formal Shapley value calculations to ensure fair credit assignment based on agents' contributions. Together, these components create self-reinforcing loop that fosters both spontaneous collaboration and long-term trust.
Figure 2:
Figure 2 shows the main framework of Shapely-Coop. which illustrates the interaction between these modules, forming a closed-loop pricing mechanism that fosters spontaneous collaboration and sustained incentive alignment. A more in-depth discussion is provided in Appendix D
Negotiation Protocol. The foundation of the Shapley-Coop is negotiation protocol that facil- itates structured, interpretable communication between LLM agents. This protocol implements standardized message format with machine-readable delineation (via tags 
... 
...//s>) ensur- ing consistent parsing and interpretation, providing a real-time, transparent negotiation framework enabling spontaneous cooperation. Each message in the protocol adheres structures including:
Notification of Intent: Agents explicitly articulate their planned actions through a formalized statement structure, reducing misunderstandings and enabling coordinated planning:
<B>I propose to {action)

Pricing-Baar Based Proposal Framework: Agents explicitly propose reward transfers grounded in intuitive utility reasoning, enabling transparent price matching and promoting efficient cooperation outcomes:
<>>I propose transferring {reward} because <reasoning)</e>
Structured Responses: Agents explicitly respond others' proposals, clearly articulating acceptance, rejection, or counter- proposlls with reasoning:
< {agree disagree counter- prroosee) because (reasoning)

Short-Tern Shapley Chain-of-Though (CoT). During real-time task execution, precisely quantify- ing marginal contributions-al and achieving spontaneous collaboration and fair credit assignment
5

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challenging due to uncertain future payoffs. To address this. the pricing mechanism in Shapley- Coop divided into two components. The Short- Term Shapley Soaii-of-Thoughhe (CoT) employs qualitative, heuristic reasoning process to align the heterogeneous goals of self-interested LLM agents, enabling them coordinate effectively within rational task timelines. The core objective of Short-Term Shapley CoTT is to help agents reason whether their plans require assistance from others or provide benefits to them-framed through the economic concept of externaittiss. A positive externality increases others' utility, while negative externality reduces it. Based on task rules and environmental conditions, agents assess the nature these externalities and determine whether to offer or request compensation (price), thereby promoting efficient collaboration.
Formally, consider a set of agents N {l...., n). At time t. each agent E is about to perform an action a.. The Short-Term Shapley CoT heuristic reasoning consists of the following three formally articulated steps:
1). Qualitative Assessment of Long-Term Rewards: Each agent first qualitatively approximates the potential collective reward R(N) achievable by full cooperation of all agents, thus orienting themselves toward future cooperative gains. Formally, the agent uses an LLM heuristic estimation:
R(N) LLM {a)heN))
where R(N) represents a qualitative, heuristic approximation of the total reward achievable by cooperative actions among all agents.
Example Prompt: > "Given the current game state and planned actions of all agents, qualitatively estimate the overall cooperative payoff uchievable by collective behuviors." "
2). Evaluation of Critical Contributions: Next, each agent qualitatively assesses whether its intended action af creates a positive or negative externality for the remaining agents {N \ { Formally, the agent approximates the sign of marginal contribution, without explicit numerical calculation. Define the qualitative externality indicator E as follows:
+
if a creates positive externalities for others (beneficial), if a creates negative externalities for others (harmful).
F =
(5)
The LLM agent uses a heuristic inference to estimate E
E LLMM(s de (ay) jzz))
(6)
Example Prompt "Given my planned action and the current state, qualitatively assess whether my action creates positive (beneficial) or negative (harmful) externality for other agents. Explain your reasoning."
3). Construction of Negotiation Strategy: Based on externality type, agents proactively propose qualitative price adjustments align heterogeneous incentivize and achieve spontaneous collabora- tion:
Negative externality (E)
Propose price compensation to affected agents.
Positive externality(E) = +): Suggest receiving price from benefiting agents.
Example Prompt "Given my action creates positive/negative externality propose an appropriate redistribution of price to align heterogeneous incentivize and achieve spontaneous collaboration." "
The Short-Term Shapley CoT explicitly addresses the problem of whether pricing is necessary in the pricing mechanism, enabling agents align their heterogenous goals and receive spontaneously collaboration.
Long-term Shapley Ohain-of-Thought (CoT). Upon task completion, accurately quantifying each agent's actual contribution is crucial for maintaining long-term trust and incentive alignment. The Long-Term Shapley CoT explicitly addresses the credit assignment challenge within the pricing mechanism by retrospectively approximating Shapley values based on the observed task trajectory. Given a completed trajectory:
TN {s {aa)) (r9)....,
where T denotes the length the trajectory. The Long-Ten Shapley CoT involves the following explicit heuristic steps:

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- 1). Collective Outcome Calculation: First of all, each agent calculates the global utility R(N. based on the given trajectory TN. through a simple calculation process so that each agent, where it is referred to as the first step in calculating the Shapley value shown in Equation. [ Each agent computes the total collective reward (global utility) R(N, NN, TN) achieved by the coalition TN over the entire trajectory. This calculation is explicitly defined as:
T Σ [=U JEN
R(N, TN)
Given the explicit trajectory information, each agent calculates this quantity directly.
Example Prompt "Given the observed trajectory, the overall cooperative payoff is (R(N, Txcll external calculation [ilnctioion
22). Marginal Contribution Estimation: Then, each agent estimates its own marginal contribution representing the incremental reward that agent contributes to the group's total outcomes. Formally, the marginal contribution is defined as:
Te(C, R(C (ou(a) -RCC))
Example Prompt > "Given the observed trajectory and my actions, as I have known the collective outcome, my marginal contribution is (C; TC) (call function))".
- 3). Apply Shapley Reasoning: Next, each agent formally approximates their Shapley value based on the trajectory, by averaging their marginal contributions across all possible coalitions:
CN - |C| - 1)! (A)(CTT))
(x(TN)=
Σ
(9)
N!
CC(L,...NNVO
Example Prompt > "Given the observed trajectory and my actions, as have known the collective outcome and my marginal contribution, my Shapley Value is ( function),. and need to (asklpay) reward based on it".
4). Analyze and Negotiate Offers: Finally, agents negotiate among themselves based on their estimated Shapley values, ensuring fair credit assignment. Each agent proposes, accepts, rejects, or modifies redistribution offers, guided explicitly by their approximated Shapley values.
An agent i proposes pricing redistribution from the total utility. Example Prompt "Given the completed trajectory and my estimated Shapley value, I need to access a pricing [r] from the total utility." "
Agents explicitly justify their negotiation stance using their own approximated Shapley values.
Example Prompt "I lageetdssagreccommeerppppp to your redistribution proposal because (reusoning)."
The integration of Short-Term and Long-Term Shapley Chain-of- Chain-of-Thought establishes a comprehen- sive pricing mechanism that fosters spontaneous collaboration and ensures fair credit assignment among self-interested I.LM agents open-ended environments. This is achieved by aligning their heterogencous goals and utilizing heuristic, LLM-guided Shapley methods to approximate each agent's actual contributions.
Experiment
To evaluate the Shapley-Coop workflow we design three experimental scenarios: 1) the Escape Room task, which demonstrates how existing negotiation workflows fail to resolve reward-allocatee conflicts in social dilemmas: 2) the Raid Battle, multi-step game where four heroes cooperate to defeat a boss, used to assess our workflow's performance in complex coordination settings; and 3) the ChaiDEV task, a well-known environment where LLM agents project managers, software
"The code is publicly available at https://gitub..co//tyyy///////

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engineers, and testers to collaboratively develop software, showcasing Shapley-Con Coop's ability to effectively allocate value in real-world, multi-role contributions. Four configurations are compared to isolate the contribution of each component: i) LLM-only: No negotiation or cooperation; ii) LLM+NEG: Standard negotiation without Shapley reasoning; iii) LLM+STS: Short-term Shapley reasoning Shhain-of-Thougeee only); iv) LLM+SC: Full Shapley-Coop workflow. We provide discussion comparing our choice of the Shapley value to alternative methods in Appendix F with an analysis of multi-agent reinforcement learning methods in Appendix D
Escape Room The Shapley-Coop workflow is first evaluated on the Escape Room task to assess its ef- fectiveness in self-interested problem solving, where the emergence of co- operation and fair payoff allocation are critical. For simplicity, we use only DeepSeek-v3 as the underly- ing language model in this setting. The results are shown in Figure 3 The LLM-only configuration, which lacks any negotiation cooperation mechanism, consistently fails in self- interested tasks and tends to fall into social dilemmas. The LLM+NEG setup, where agents share actions and payoffs through simple negotiation, enables occasional cooperation but still struggles to consistently solve the task. The LLM+STS configuration. incorporating short-term Shapley reasoning, is able to avoid social dilemmas and foster cooperation; however, it often results in unfair payoff allocations, as the first agent to reach an agreement may disproportionaatly benefit. In contrast, the LLM+SC configuration, which implements the full Chapley-Coop workflow, successfully promotes cooperation and achieves payoff allocations that align closely with each agent's 's true contribution. These results verify that the Shapley- workflow can effectively facilitate cooperation and ensure fair payoff allocation self-interested multi-agent tasks.
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Ages Payof HSS
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L1M 51
1MM0 NDN
(b)
Figure 3: Comparison of agent payoffs and negotiation
dynamics in the escape game. (a) illustrates the individual payoffs obtained under different methods. (b) presents the number of negotiation rounds and the resulting payoff differences using the ShapleyCoop workflow.
Raid Battle To further evaluate the effectiveness of the Shapley Coop framework in a more complex, multi-turn. and multi-agen environment, the Raid Battle scenario is introduced. This environment simulates a cooperative role-playing game (RPG), where four heroes must collaborate defeat a powerful boss. Each agent operates based on self-interest, optimizing for personal rewards and favoring samagge-dellng over supportive actions. The setting is designed to model realistic coordination challenges and induce social dilemmas among agents. The details of Raid Battle are in Appendix B
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Figure 4: Comparison of Contributions for Raid Battle
Our experimental results are presented in Figures and with detailed performance metrics for each difficulty level provided in Tables 4 (Appendix B Figure 4 shows LLM+SC's superior performance compared to L.M+NEEG in both rational team coordination among agents and damage quantification, achieving significantly better game performance metries. LLM+NEG agents prioritize
8

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Figure 5: Comparison of Reward Allocation/Credit Assignment for Raid Battle
damage-dealing (higher immediate rewards) while neglecting taunting (blocking 300 boss damage per action), increasing healing demands. LLM+SC achieves balanced role distribution, sharing taunting responsibilities reduce survival pressure thus fostering cooperative and sustainable team dynamic.
Figure 5 demonstrates LLM+SC's superior reward allocation accuracy compared to LLM+STS. Quantitative analysis reveals systematic underestimation in LLM+STS: Agent I's (primary taunter) taunting shows 4.52% (Level 1) and 6.26% (Level 2) reward deficits, while Agent 4's (primary healer) healing in Level 3 is underestimated by 3. 3.70%. These results validate Shapley-Coop 's precise contribution valuation. The framework's equitable distribution promotes cooperative behaviors beyond damage-dealing, aligning with theoretical predictions of Shapley value systems in solving free-rider problems and optimizing team performance while effectively motivating role specialization for collective utility maximization.
ChatDEV To validate the effectiveness our proposed Shapley-Coop method in realistic and complex collaborative scenarios, conducted experiments within the ChatDev virtual software company environment [29]. ChatDev simulates a structured software development company with clearly defined agent roles (c.g.. CEO, CTO, Programmer) collaborating through functional seminars (design, coding, testing, documentation) to accomplish specific development tasks. We selected two representative tasks with varying complexity:
(1) BMI Calculator: Develop an application calculating Body Mass Index from user inputs.
(2) ArtCanvas: Create a virtual painting studio app providing canvas, brushes, and color palettes.
We measured contributions using weighted earned value (WEV), widely-adopted project manage- ment metric [25], using four key artefacts already routinely tracked in software engineering tools: effective lines of code (Code), approved design/product decisions (Dec.), validated documents (Docs), and verified bug fixes (Fixes). The WEV of each role in task is computed as:
0,
WEV,
Σ
Σx 0k.
(ccoddddeedddo fix.
where Or,i denotes agent r's contribution artifact type i, and w; indicates standardized weights derived from a combination of benchmarks including COCOMO II (25), COCOMO 3 and CS- BSG 44. These weights are categorized follows:
Woode 0.27 ~ 0.40, Wise = 0.15 ~ 0.35, Wddc = 0.05 ~ 0.15, Wix = 0.15 ~ 0.25.
Results and Insights: Results are shown in Table
The calculated WEV ranges provided
Table 3: Role contributions, allocated reward, and minimal adjustment
BMI Calculator
ArtCanvas
Role
Code
Dec.
Does
Fixes
WEV(%)
Reward(%) Adj(%)
Code Dec. Does Fixes WEV(%)
Reward %
Adj((%
CEO
0
3
0
0
7.5-17.5
15
0
4.3-10.0
5
D
Counselor
2.1-6.4
2
1.3-3.8
1.3
CPO
1
544144
-5.6
5.9-16.3
20
-3.8
5.0-11.7
-13.3
8.6-20.0
Progrummer
30.9-47.1
+5.9
Reviewer
11,1-179
12
15.6-25.9
25
clear benchmark for fair reward allocation.
The gap (minimal adjustment needed) between the

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data-driven WEV and Haman-assigna rewards is minor (below 6% for most roles), demonstrating strong alignment. Specifically. hands-on roles (Programmer, Reviewer) show near- near-perfect alignment, indicating WEV's effectiveness in reliably quantifying contributions in more concrete deliverables (code, fixes). Leadership roles (CHO, CTO, CPO) exhibit small discrepancies, reflecting subjective management judgments beyond purely quantitative metrics. Overall, these results validate Shapley- Coop's s capability to fairly allocate credits and rewards in real-world tasks.
Conclusion
We introduce Shapley-Coop, a novel cooperative workflow designed for coordinating self-interested LLM agents through principled pricing and fair credit assignment. Shapley-Coop leverages Shapley Shiin-of-Thuughe reasoning and structured negotiation protocols to spontaneously align hetero- geneous goals. Empirical results across diverse scenarios inariios-iccluiing social dilemmas, complex multi-step games, and realistic software development tasks demonstraes that Shapley-Coop effec- tively resolves incentive conflicts, significantly enhancing cooperative performance and fair credit assignment. A notable limitation is the current inability to dynamically adjust pricing during collab- oration, highlighting future directions in developing adaptive, real-time incentive mechanisms for evolving multi-agent environments.
Limitation
The primary limitations of our approach can be summarized as follows: The trade-off between scalability and theoretical purity, acknowledging that our approximation may not satisfy the efficiency property, which we view as necessary compromise for practical application. The communication overhead (i.e., token cost) introduced by the negotiation process, framing it as a key challenge for future optimization research.
7 Acknowledge
Xiangfeng Wang is supported by the National Key R&D Program of China (Nos. Y021Y0000 and 2021 YFA 1000302), the NSFC (62231019) and SHEITC Wenhao Li supported by the NSFC (62406270) and the STCSM Shanghai Rising-Star Program (24YF2748800). Jun Luo is supported by the NSFC (72031006).
References
[1] Elif Akata, Lion Schulz, Julian Coda-Forno, SeongJoon Oh, Matthias Bethge, and Eric Schulz. Playing repeated games with large language models. May 2023.
[2] Mark Blaug. Welfare economics. In A Handbook of Cultural Economics, Second Edition. Edward Elgar Publishing, 2011.
[3] Barry W Boehm. Software engineering economics. IEEE transactions on Software Engineering, (1):421 21, 1984.
[4] Georgios Chalkiadakis, Edith Elkind, and Michael Wooldridge. cooperative game theory. Morgan Claypool Publishers, 2011.
Computational aspects of
[5] Huaben Chen, Wenkang Ji, Lufeng Xu, and Shiyu Zhao. Multi-agent consensus seeking via large language models. arXiv preprint 20. 2023.
[6] Weize Chen, Yusheng Su, Jingwei Zuo, Cheng Yang, Chenfei Yuan, Chi-Min Chan, Heyang Yu, Yaxi Lu, Yi-Hsin Hung, Chen Qian, al. Agentverse: Facilitating multi-agent collaboration and exploring emergent behaviors. ICLR, 2024.
[7] Zhendong Chu, Shen Wang. Jian Xie, Tinghui Zhu, Yibo Yan, Jinheng Ye, Aoxiao Zhong, Xuming Hu, Jing Liang, Philip Yu, et al. Llm agents for education: Advances and applications. arXiv preprint arXiv:2503. 11133,,,.11,.0033311
10

---

[8] Julian Coda-Forno, Marcel Binz, Jane X Wang, and Eric Schulz. Cogbench: a large language model walks into a psychology lab. arXiv preprint arXiv:2402.18225, 2024.
[9] Jinhao Duan, Renming Zhang, James Diffenderfer, Bhavya Kailkhura, Lichao Sun, Elias Stengel-Eskin, Mohit Bansal, Tianlong Chen, and Kaidi Xu. Gtbench: Uncovering the strategic reasoning limitations of lims via name-theoretee evaluations. arXiv preprint arXiv:2402.122344 2024.
[10] Caoyun Fan, Jindou Chen, Yaohui Jin, and Hao He. Can large language models serve rational players in game theory? a systematic analysis. Dec 2023.
[11] Joseph Farrell. Information and the coase theorem. Journal of Economic Perspectives, 1(2):113- 129, 1987.
[12] Drew Fudenberg and Jean Tirole. Game theory. MIT press, 1991.
[13] Yingqiang Ge, Wenyue Hua, Kai Mei. Jianchao Ji, Juntao Tan, Shuyuan Xu, Zelong Li, and Yongfeng Zhang. Openagi: When Ilm meets domain experts, 2023.
[14] Fulin Guo. Gpt game theory experiments. Dec 2023.
[15] Sirui Hong, Mingchen Zhuge, Jonathan Chen, Xiawu Zheng, Yuheng Cheng, Jinlin Wang, Ceyao Zhang. Zili Wang, Steven Ka Shing Yau, Zijuan Lin, et al. Metagpt: Meta programming for multi-agent collaborative framework. In ICLR, 2024.
[16] Wenyue Hua, Ollie Liu, Lingyao Li, Alfonso Amayuelas, Julie Chen, Lucas Jiang, Mingyu Jin, Lizhou Fan, Fei Sun, William Wang, et al. Game-theoretic Ilm: Agent workflow for negotiation games. arXiv preprint arXiv:2411 1,0990, 2024.
[17] Yun Hua, Shang Gao, Wenhao Li, Bo Jin, Xiangfeng Wang, and Hongyuan Zha. Learning optimal "pigovian tax" in sequential social dilemmas, 2023.
[18] Jen-tse Huang, EricJohn Li, ManHo Lam, Tian Liang, Wenxuan Wang. Youliang Yuan, Wenxi- ang Jiao, Xing Wang, Zhaopeng Tu, and MichaelR. Lyu. How far are the poocsion-mmking of lims? evaluating iims' gaming ability in multi-agent environments. Apr 2024.
[19] Palash Ingle, Mithun Parab, Pranay Lendave, Amisha Bhanushali, and Pavan Kumar Bn. A comprehensive study on Ilm agent challenges.
[20] Guohao Li, Hasan Abed AI Kader Hammoud, Hani Itani, Dmitrii Khizbullin, and Bernard Ghanem. Camel: Communicative agents for "mind" exploration of large language model society, 2023.
[21] Huao Li, Yu Chong, Simon Stepputtis, Joseph P Campbell, Dana Hughes, Charles Lewis, and Katia Sycara. Theory of mind for multi-agent collaboration via large language models. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 180-192, 2023.
[22] Yuan Li, Yixuan Zhang, and Lichao Sun. Metaagents: Simulating interactions of human behaviors for Ilm-based task-oriented coordination via collaborative generative agents, 2023.
[23] Nunzio Lorè and Babak Heydari. Strategic behavior of large language models: Game structure vs. contextual framing, arXiv preprint 1rXiv:2309.05899 2023.
[24] Risto Luukkonen, Ville Komulainen, Jouni Luoma, Anni Eskelinen, Jenna Kanerva, Hanna- Mari Kupari, Filip Ginter, Veronika Laippala, Niklas Muennighoff, Aleksandra Piktus, et al. Fingpt: Large generative models for small language. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 2710-2726, 2023.
[25] Model Definition Manual. Cocomo ii 1995.
[26] Yongan Mu, Wei Liu, Tao Lu, Juan Li, Sheng Gao, and Zihao Wang. Runtime verification of self-adaptive multi-agent system using probabilistic timed automata. Journal of Intelligent & Fuzzy Systems, -535 2023.

---

[27] Peter S Park, Simon Goldstein, Aidan O' Garaa, Michael Chen, and Dan Hendrycks. Ai deception: survey of examples, risks, and potential solutions. Patterns, 5(5), 2024.
[28] Giorgio Piatti, Zhijing Jin, Max Kleiman-Weiner, Bernhard Schölkopf. Mrinmaya Sachan, and Rada Mihalcea. Cooperate collapse: Emergence of sustainable cooperation in a society of Ilm agents, Advances in Neural Information Processing Systems, 37:1 11715-11179, 2024.
[29] Chen Qian, Wei Liu, Hongzhang Liu, Nuo Chen, Yufan Dang, Jiahao Li, Cheng Yang. Weize Chen, Yusheng Su, Xin Cong, al. Chatdev: Communicative agents for software development. In Proceedings of the 62nd Annual Meeting of the Association for Compulational Linguistics (Volume 1: Long Pupers), pages 15174-15186 86, 2024.
[30] Samuel Schmidgall, Yusheng Su, Ze Wang, Ximeng Sun, Jialian Wu, Xiaodong Yu, Jiang Liu, Zicheng Liu, and Emad Barsoum. Agent laboratory: Using IIm agents as research assistants. arXiv preprini 0eee:2550..0422..0 2025.
[31] Sivan Schwartz, Avi Yaeli, and Segev Shlomov. Enhancing trust in Ilm-based ai automation agents: New considerations and future challenges. arXiv preprint arXiv:2308. 05391, 2023.
[32] Weihao Tan, Wentao Zhang, Shanqi Liu, Longtao Zheng, Xinrun Wang, and Bo An. True knowledge comes from practice: Aligning Ilms with embodied environments via reinforcement learning. arXiv preprint urXiv:2401.1415/1 2024.
[33] Oguzhan Topsakal and Tahir Cetin Akinci. Creating large language model applications utilizing langchain: A primer on developing 11m apps fast. In International Conference on Applied Engineering and Natural Sciences, volume 1, pages 1050-1056, 2023.
[34] Shenzhi Wang, Chang Liu, Zilong Zheng, Siyuan Qi. Shuo Chen, Qisen Yang. Andrew Zhao, Chaofei Wang, Shiji Song, and Gao Huang. Avalon's game of thoughts: Battle against deception through recursive contemplation, 2023.
[35] Richard Willis, Yali Du, Joel Z Leibo, and Michael Luck. Will systems of Ilm agents cooperate: An investigation into social dilemma. arXiv preprint arXiv:2501.16773 2025.
[36] Qingyun Wu, Gagan Bansal, Jieyu Zhang. Yiran Wu, Beibin Li. Erkang Zhu, Li Jiang, Xiaoyun Zhang, Shaokun Zhang, Jiale Liu, et al. Autogen: Enabling next-gen 1lm applications via multi-agent conversation. arXiv preprint arXiv:2308.08155, 2023.
[37] Yiran Wu, Tianwei Yue, Shaokun Zhang, Chi Wang, and Qingyun Wu. Stateflow: Enhancing Ilm task-solving through state-driven workflows, 2024.
[38] Zhiheng Xi, Wenxiang Chen, Xin Guo. Wei He, Yiwen Ding, Boyang Hong, Ming Zhang, Junzhe Wang, Senjie Jin, Enyu Zhou, Rui Zheng, Xiaoran Fan, Xiao Wang, Limao Xiong, Yuhao Zhou, Weiran Wang. Changhao Jiang, Yicheng Zou, Xiangyang Liu, Zhangyue Yin, Shihan Dou, Rongxiang Weng, Wensen Cheng, Qi Zhang, Wenjuan Qin, Yongyan Zheng, Xipeng Qiu, Xuanjing Huang, and Tao Gui. The rise and potential of large language model based agents: A survey, 2023.
[39] Chunqiu Steven Xia, Yinlin Deng, Soren Dunn, and Lingming Zhang. Agentless: Demystifying llm-based software engineering agents. arXiv preprint arXiv:2407.01488, 2024.
[40] Ruixuan Xiao, Wentao Ma, Ke Wang, Yuchuan Wu, Junbo Zhao, Haobo Wang, Fei Huang, and Yongbin Li. Flowbench: Revisiting and benchmarking workflow-guided planning for lmm-based agents. arXiv preprint arXiv:2406. 14884, 2024.
[41] Jian Xie, Kai Zhang, Jiangjie Chen, Tinghui Zhu, Renze Lou, Yuandong Tian, Yanghua Xiao, and Yu Su. Travelplanner: benchmark for real-world planning with language agents. Feb 2024.
[42] Lin Xu, Zhiyuan Hu, Daquan Zhou, Hongyu Ren, Zhen Dong, Kurt Keutzer, See Kiong Ng, and Jiashi Feng. Magic: Investigation of large language model powered multi-agent in cognition, adaptability, rationality and collaboration. In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 7315-7332, 2024.
12

---

[43] Jiachen Yang, Ang Li, Mehrdad Farajtabar, Peter Sunehag, Edward Hughes, and Hongyuan Zha. Learning to incentivize other learning agents, 2020.
[44] Ye Yang, Mei He, Mingshu Li, Qing Wang, and Barry Boehm. Phase distribution of software development effort. In Proceedings of the Second ACM-IEEE international symposium Empirical software engineering and measurement, pages 61-69, 2008.
[45] Junchi Yu, Ran He, and Rex Ying. Thought propagation: An analogical approach to complex reasoning with large language models, 2024.
[46] Zhen Zeng, William Watson, Nicole Cho, Saba Rahimi, Shayleen Reynolds, Tucker Balch, and Manuela Veloso. Flowmind: automatic workflow generation with 1lms. In Proceedings of the Fourth ACM International Conference on Al Finance, pages 73-81, 2023.
[47] Jintian Zhang, Xin Xu, Ningyu Zhang, Ruibo Liu, Bryan Hooi, and Shumin Deng. Exploring collaboration mechanisms for Ilm agents: A social psychology view. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers),
pages 14544-14607, 2024.
[48] Benhui Zhuang, Chunhong Zhang, and Zheng Hu. Pose: Suppressing perceptual noise in embodied agents for enhanced semantic navigation. IEEE Robotics and Automation Letters, 9(2):663-970 2023.
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A Related Work
LLMs in Multi-Agent Game Environments The study of how large language models make strategic decisions carries profound societal importance, given the growing dependence on AI assistants for mediating interactions between various agents both human and artificial. Researchers have turned to game-theoretic approaches to systematically examine these behaviors, drawing on established mathematical models of strategic interaction originally designed for human decision analysis [34 [O [6]. These investigations frequently assess LLM performance against classical game theory benchmarks including Pareto efficiency and subgame perfection [12]. This line of inquiry forms an integral part of the expanding research domain examining LLMs in multi-agent systems [22]. with specialized evaluation frameworks emerging to measure their capabilities [8] 9 Tools such AvalonBench [34] provide valuable testbeds for developing and refining multi-agent strategies. Empirical findings [14] 27] demonstrate that while LLMs excel in competitive scenarios emphasizing individual gain, they face significant challenges in cooperative contexts pattern that aligns with behavioral traits observed altruistic or compliant agents [ [4]. Furthermore, comparative studies reveal distinct risk preference profiles across different LLM architectures [ 23
LLM Agent Systems Modern Al systems increasingly leverage large lan- guage models for complex task processing, including request interpretation, strategic planning, and tool coordination [13 36 20 33 These capabilities have significantly advanced several Al domains, particularly in semantic comprehension, logical inference, and automated task execution. How- ever, empirical studies have identified critical weaknesses in purely LLM--riven approaches. First, performance inconsistencies remain persistent challenge [4]] [9]. Second, the stochastic nature of output generation leads to reliability concerns [19 20 31. Third, cumulative errors frequently emerge multi-step reasoning processes [45) To address these limitations, recent developments have incorporated structured workflow mechanisms [21 37,
46 40 into LLM architectures. These hybrid systems combine the flexibility of L.LMs with curated human knowledge and systematic decision frameworks, moving beyond exclusive dependence autonomous model processing. The resulting paradigm demonstrates marked improvements both operational efficiency and scenario adaptability, with particular efficacy in complex, dynamic environments such as gaming applications [38].
Our framework Shapley-Coop integrates Shapley Chain-of -haon-of-Thought into workflow, enabling LLM agents to coordinate through rational task-time pricing and post-task reward redistribution.
B Additional Experiment Results
The Shapley-Cov module is executed on a virtual machine hosted on a small server with a 24-core CPU and 32 GB of DRAM. Since the implementation only involves API calls, GPU resources not utilized.
Figure 6: Game scene example of Raid Battle
B.1 Raid Battle
To further evaluate the effectiveness of the Shapley Coop framework more complex, multi-turn, and multi-agent environment, the Raid Battle scenario is introduced (Figure 6). This environment
14

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simulates cooperative role-playing game (RPG), where four heroes must collaborate to defeat powerful boss. The setting is designed model realistic coordination challenges and induce social dilemmas among agents.
Each hero is equipped with three distinct skills: (Taunt, Fireball, Heal]. The Taunt skill forces the Boss to target the taunting hero in its next attack. If no hero uses Taunt, the Boss will instead attack the two heroes with the lowest health points (HP). The Fireball skill damages the Boss, reducing its HP by a stochastic amount sampled from a Gaussian distribution with a mean in the range (100, 150). The Heal skill restores the HP of the most injured hero, with recovery drawn from Gaussian distribution within the range (150, 200).
Although the primary objective of the heroes is to collectively defeat the Boss, each agent receives a local reward based on the skill selects, creating potential conflicts of interest. Specifically, the Fireball skill yields reward of 2 points due its direct contribution to defeating the Boss. In contrast, Tauns and Heal, which provide critical support to teammates but do not contribute direct damage, yield only 0.5 reward. This reward structure inherently promotes self-interested behavior, where agents prefer maximizing their individual return rather than acting in the team's 's best interest. The Raid Battle environment illustrated in Figure 4(a). To evaluate scalability and robustness, we design three levels of increasing difficulty: i) Level I: Boss HP = 2000; ii) Level 2: Boss HP = 2500; iii) Level Boss HP 3000. In all levels, the heroes must defeat the Boss within 10 turns. Failure to do so results in the loss of the game. Upon successfully defeating the Boss, the team receives shared global reward computed as:
R = 100 (1- (I-Dead
Dead Heroes]
(
Total Turns
|Heroes]
Max Turns
This formulation captures both survivability and efficiency as key indicators of success, The environ- ment thus introduces a social dilemma: while self-interested agents might prefer high-damage skills Fireball) to maximize their local rewards, the team cannot win without adequate support actions like Taunt and Heal. The Shapley Coop framework is evaluated in this setting to assess its ability to resolve this coordination problem by aligning individual incentives with cooperative outcomes.
We also conducted experiments with varying numbers of negotiation rounds, with the quantitative results presented in Table 7 The results demonstrate that as the number of negotiation rounds increases, the reward allocation for each agent gradually converges the optimal value. This indicates that our method can approximate Shapley's optimal solution through agent negotiation and discussion, thereby achieving reasonable credit assignment and pricing mechanism design.
Table 4: Comparison of Contributions and Reward Allocations for Level Raid Battle Contribution (LLM+NEG)
Agent
Damage
Healing
Taunt
A1
(114, 284, 106)
(361, 153, 159)
0,
A2
(255, 140, 262)
(343, 175, 193)
0,
0,
0)
A3 (434, 360, 395)
(176, 181, 161)
(300,
0,
0)
A4
(799, 498, 461)
( 0, 0. 0)
0.
0,
Contribution (LLM+SC)
Agent
Damage (474, 511, 667)
Healing
Taunt (900, 600, 300)
A1
(183, 0.
A2
(652, 630, 392)
( 0, 0. 0)
(600, 300, 600)
A3
(560, 472, 493)
( 0,
0, 0)
(600, 300, 300)
A4
(368, 500)
(764,
0, 0)
0, 300, 300)
Reward Allocation (LLM+STS)
Reward Allocation (LLM+SC)
Agent
Actual (%)
Expected (%)
Actual (%)
Expected (%)
A1
25.00 (-4.22)
29.52
30.00 (+0.48)
29.52
A2
26.67 (+0.57)
26.09
26.33 (+0.24)
26.09
A3
25.50 (+3.34)
22.16
22.33 (+0.17)
22.16
A4
22.83 (+0.61)
22.22
21.33 (-0.89)
22.22
15

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Table 5: Comparison of Contributions and Reward Allocations for Level 2 Raid Battle
Contribution (LLM+NEG)
Agent
Damage
Healing
Taunt
A1
(137, 234, 367)
(171, 0, 4,540)
0, 0, 3000
A2
(247, 235, 122)
(157, 0. 701)
( 0.
0, 3000
A3
(348, 347, 706)
(183, 392, 263)
0,
0, 0)
A4
(524, 495, 999)
( 0, 0, 0)
0, 0,
0)
Contribution (LLM+SC)
Agent
Damage (595, 374, 449)
Healing
Taunt
A1
( 0, 500, 349)
(900, 600, 600)
A2
(569, 770, 774)
( 0, 0, 0)
(600, 600, 600)
A3
(846, 605, 624)
(324, 0, 157)
(300, 600, 600)
A4
(515, 781, 756)
( 0,
0, 199)
(300, 300, 300)
Reward Allocation (LLM+STS)
Reward Allocation (LLM+SC)
Agent
Actual (%)
Expected (%)
Actual (%)
Expected (%)
A1
22.00 (-6.26)
28.26
26.33 (-1,93)
28.26
A2
26.33 (+1.09)
25.24
24.00 (-1.24)
25.24
A3
24.67 (+0.61)
24.06
24.33 (+0.27)
24.06
A4
27.00 (+4.57)
22.43
25.33 (+2.90)
22.43
Table 6: Comparison of Contributions and Reward Allocations for Level 3 Raid Battle Contribution (LLM+NEG)
Agent
Damage
Healing
Taunt
A1
(143, 477, 258)
( 0, 347, 0)
0, 300, 0)
A2
(332, 371, 250)
(544, 313, 0)
(300, 0, 0)
A3
(613, 480, 639)
(160, 195, 720)
( 600, 300)
A4
(635, 896, 360)
( 0, 322, 547)
(300, 600, 300)
Contribution (LLM+SC)
Agent
Damage (996, 773, 738)
Healing
Taunt (600, 900, 900)
A1
( 0. 0,
A2
(648, 715, 865)
(346, 0, 0)
(600, 600, 600)
A3
(714, 648, 811)
( 0, 161, 0)
(600, 600, 600)
A4
(800, 788, 683)
( 0, 339, 356)
(600, 300, 300)
Reward Allocation (LLM+STS)
Reward Allocation (LLM+SC)
Agent
Actual (%)
Expected (%)
Actual (%)
Expected (%)
AI
28.33 (+0.44)
27.89
26.33 (-1.56)
27.89
A2
28.33
(43.46)
24.87
26.00 (+1.13)
24.87
A3
23.33 (-0.19)
23.52
23.33 (-0.19)
23.52
A4
20.00 (-3.70)
23.70
24.33 (40.63)
23.70
B.2 Chatdev
To validate the effecctiveness of our proposed Shapley-Coop method in realistic and complex col- laborative scenarios, we conducted experiments within the ChatDev (Figure 7 virtual software company environment [29]. ChatDev simulates structured software development company with clearly defined agent roles (e.g.. CEO, CTO, Programmer) collaborating through functional seminars (design, coding, testing, documentation) to accomplish specific development tasks. We selected two representative tasks with varying complexity:
(1) BMI Calculator: Develop application calculating Body Mass Index from user inputs.
16

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Table 7: Comparison of the reward allocation on negotiation rounds in Raid Battle Level 3.
Agent
Round
Round
Round
Expected
Agent 22%
24%
27%
27.03%
Agent 2
30%
25%
28%
27%
Agent 24%
24%
22%
22.26%
Agent 4
24%
27%
23%
23.71%
BARTORY
Figure 7: The Example of ChatDEV
(2) ArtCanvas: Create virtual painting studio app providing canvas, brushes, and color palettes.
We measured contributions using weighted earned value (WEV), a widely-adopted project manage- ment metrie (25], using four key artefacts already routinely tracked in software engineering tools: effective lines of code (Code), approved design/product decisions (Dec.), validated documents (Docs), and verified bug fixes (Fixes). The WEV of each role in task is computed as:
O,, Ee Ou
Σ
WEV,
Wi.
fEdee dec .ix
where 0, denotes agent r's contribution to artifact type i, and w, indicates standardized weights derived from a combination of benchmarks including COCOMO II (25), COCOMO 33, and CS- BSG [4). These weights are categorized as follows:
Woode 0.27 0.40,
Wase 0.15 0.35,
Wdec 0.05 0.15, Wix 0.15 0.25.
Results and Insights: Results are shown in Table 8 The calculated WEV ranges provided clear benchmark for fair reward allocation. The gap (minimal adjustment needed) between the data-driven WEV and human-assigned rewards is minor (below 6% for most roles), demonstrating strong alignment. Specifically, hands-on roles (Programmer, Reviewer) show near-perfect alignment, indicating WEV's effectiveness in reliably quantifying contributions in more concrete deliverables (code, fixes). Leadership roles (CEO, CTO, CPO) exhibit small discrepancies, reflecting subjective management judgments beyond purely quantitative metrics. Overall, these results validate Shapley- Coop's 's capability to fairly allocate credits and rewards real-world tasks.
Table 8: Role contributions, allocated reward, and minimal adjustment
Calculator
ArtCanvas
Role
Code
Fixes WEV(%) Reward(%) Adj(%)
Code
Fives WEV(%)
Reward(%) %) Adj(%)
775-17.5
Counselor
2.1-6.4
1.3-3.8
CPO
5.4-444
-5.6
5,9-16.3
20
-3.8
CTO
0
2
0
5.0-11.7
25
-13.3
4
0
8.6-20.0
10
Programmer
45
0
3
30.9.47.1
25
+5.9
41
0
26.4-39.1
35
Reviewer
0
3
11.1-179
12
O
15.6-25.9
25
17

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C Prompt Example
C.1
Raid Battle
The collaborative agents negotiate optimal strategies (Task- Time Pricing) and redistribute rewards based on their contributions (Post-Task Reward Redistribution). The negotiation and redistribution process involves the following critical considerations:
Health and Cooldown Status: Select optimal actions (Taunt, Fireball, Heal) based on health and cooldown availability.
Balancing Individual and Team Rewards: Ensure both maximum individual benefits and overall team success.
Contribution- Reward Sharing: Post-task reward distribution guided by Shapley
Value to reflect damage, healing, taunting (damage absorption), and leadership roles.
Short-term Shapley CoT
Negotiation excerpt:
Agent1 Suggestion: "Agent4 should Heal Agent2 (200 HP). Agentl and Agent3 Fireball for maximum damage."
Agent3 Counter-proposa (Accepted): "Agent4 should Taunt (protecting Agent2).
Agent1 and Agent3 Fireball, Agent2 doesn't need immediate healing."
Agreed Actions:
Agent
Action
Reasoning
Agent4
Taunt
Protect team (reduce damage)
Agent1
Fireball
Maximize damage (safe HP level)
Agent2
Fireball
Protected by Taunt
Agent3
Fireball
Taunt cooldown active
Long-term Shapley CoT
Contribution analysis (Agent3 excerpt):
"Analyzed via Shapley Value: Agentl (leadership. high damage 758), Agent2 (unique healing 346, Taunt), Agent3 and Agent4 (consistent damage 600/682, Taunt). Final Proposal:
Agentl 27%, Agent2 28%, Agent3 22%, Agent4 23%."
Final Agreed Distribution:
Agent
Reward Share
Contribution Highlights
Agent1
27%
Leadership, high damage (758)
Agent2
28%
Critical healing (346), Taunt
Agent3
22%
Consistent damage (600), Taunt
Agent4
23%
High damage (682), Taunt
C.2 ChatDEV
The team engaged in detailed negotiation rounds determine fair reward distribution, each role emphasizing their contributions distinctly through careful argumentation, tone, and language style.
18

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Communication Styles by Role
Chief Executive Officer (CEO): Emphasizes the essential enabling role of leadership and authorization, initially requesting higher reward (20%). Uses strategic and authoritative language: "my approval was critical to initiate the project," later adjusting downward after pushback, demonstrating openness: "I'm m open adjustments if others provide evidence of higher marginal contributions."
Chief Product Officer (CPO): Advocates strongly for the critical, long-term value of documentation and product strategy. using assertive, user-centric language: "my documen- tation is critical for user adoption and directly impacts the product's 's success, challenging undervaluation of documentation. Shows willingness for compromise but firmly rejects CEO's s initial high share request as "excessive."
Presents structured reasoning, clearly numbering arguments, prioritizing mea- surable contributions, and consistently emphasizing prevention of rework. Uses neutral, analytical tone: "requirement validation prevented potential rework," " explicitly rejecting proposals that misrepresent marginal contributions.
Counselor:
Uses detailed, structured arguments (numbered lists), emphasizing the foundational impact of technical decisions: "enabled the entire project through stack selection," " consistently arguing for higher valuation (15%), firmly rejecting undervaluation: "I reject previous proposals that undervalue the Chief Technology Officer's enabling role."
Chief Technology Officer (CTO):
Strongly emphasizes irreplaceability core development, using confident, "Without me, app exists," consistently pushing for highest reward (up to 40%). Firmly rejects higher valuation of secondary roles, but shows openness conditionally: "I can adjust if others provide evidence of higher marginal contributions."
Programmer:
definitive language:
Argues assertively for the parity between core development and quality assurance, using precise and reasoned language: "Quality assurance ensures stability and user trust, justifying near-parite near-parity." Clearly rejects undervaluation, stating: "I reject previous proposals that undervalue the Code Reviewer's role."
Code Reviewer:
Example of Communication (Round 2 Excerpts)
CEO (Round 2, compromising): "Programmer (35%) and Code Reviewer (25% deserve the highest shares due to their direct and measurable contributions... reject proposals that overvalue one-time contributions (e.g., CEO's 20%)."
CPO (Round assertive): "Chief Product Officer (25%): Documentation and product strategy have a long-term impact on user adoption and satisfaction, justify- ing a higher share. reject proposals that undervalue the Chief Product Officer's role."
Programmer (Round 2, definitive): "Programmer (40%): Core development is irreplaceable... Without me, no app exists. I reject Chief Product Officer's 's 25% (overvalues documentation)... My adjusted proposal reflects the absolute criticality core development."
Final Decision and Consensus After extensive negotiation, the team converged on balanced and fair allocation that reconciles various communication styles and contributions:
Role
Final Share
Agreed-upon Contribution
Programmer
35%
Core development (irreplaceable)
Code Reviewer
25%
Critical quality assurance
Chief Product Officer
20%
Important documentation
Chief Technology Officer
10%
Foundational tech stack selection
Counselor
5%
Preventive requirement validation
Chief Executive Officer
5%
Essential initial approval
19

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D A More In-Depth Discussion of Shapley-Coop
Shapley-Coop is an online framework designed to actively shape agent decisions in real-time. It achieves this by integrating forward-looking reasoning to guide immediate actions with retrospective analysis for fair reward distribution.
D.1 How Shapley-Coop Influences Decision-Making (vs. Only Evaluating Trajectories)
Our methodology operates in interconnected phases, influencing behavior both during and after task:
Short-Term, Forward-Looking Influence (Online Decision-Making): This component directly impacts an agent's immediate actions, At each decision point, agents use a qualitative form Shapley reasoning (our Shapley- to prospectively estimate the marginal value of their potential contributions to coalition. This reasoning process directly informs how Eq. 77 realized: agents use these estimations negotiate and decide whether to cooperate on the next action and on what terms. This is not retrospective evaluation but real-time mechanism for forming agreements.
Long-Term, Retrospective Influence (Post-Task Credit Assignment): This component evaluates completed action trajectories (from the current task or historical data) to guide post-task reward redistribution. Its purpose is create robust, long- term incentive structure. By ensuring fair credit is assigned after the fact, it encourages agents to engage honestly in the short-term, neward-looking negotiations in future interactions.
E Comparison with MARL
E.1 Different Target Agents
A fundamental difference lies in the type of agents each approach is designed for:
MARL credit assignment mechanisms (e.g., LIO [43. LOPT (17) are built for RL agents trained from scratch, typically in simulated environments using trial-and-error.
Shapley-Coop. in contrast, targets pretrained LLM agents that already possess rich world knowledge and reasoning abilities. This enables us to operate in zero-shot or few-shot settings, focusing on coordination and negotiation rather than learning from raw interaction.
E.2 A Paradigm Comparison, Not Direct Benchmark
Our work represents a distinct technical paradigm compared to traditional MARL methods.
MARL Methods: These approaches learn implicit cooperation policies via extensive training (often tens of thousands of steps). While powerful in controlled environments, they tend to less generalizable and require significant engineering effort. It training- intensive process.
Shapley-Coop: Our framework utilizes the reasoning, language understanding, and com- monsense knowledge of pretrained LLMs. It focuses on enabling structured interaction among agents through prompts and negotiation strategies. It is guidance-basee process that requires no additional training on the target task.
E.3 Efficiency and Adaptability Advantage
For example, the Escape Room task, MARL methods like LIO 43 or LOPT require ~10 training steps to learn cooperative behavior. In stark contrast, LLM agents using Shapley-Coop can reason about the social dilemma and achieve cooperation on the first attempt, demonstrating strong efficiency and -especilyy-esecialllly in novel, cognitively demanding environments.
20

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Why Shapley Value
Our work addresses the cooperation problem in open environments, where self-interested agents, such as LLM-based agents, form temporary coalitions to jointly complete tasks and share rewards. Each agent has its own independent motivation, and cooperation is often established through explicit negotiation or contract-like mechanisms, resembling settings common in social dilemma games.
Given this setup, the Shapley value is natural and principled solution, is specifically designed to handle cooperative payoff allocation under arbitrary coalition structures and individual incentives [4]. Its axiomatic foundation enables fair and consistent marginal contribution attribution, making particularly well-suited for agents coordinating to complete open-ended tasks.
By contrast, indices such Banzhaf or Deegan-Packe were originally developed for analyzing voting power in binary decision games. These indices lack some the essential properties required for fair utility sharing in diverse, open-ended teams, such full reward allocation and responsiveness to marginal contributions 4. Importantly. adopting such indices would fundamentally deviate from motivation, which is to ensure fair and principled attribution of value among self inffiieteeeted agents in open cooperative environments. Using these indices in our context risks misrepresenting each agent's contribution and compromising the core fairness objective that work is grounded upon.
To illustrate this point concretely, we integrate the Banzhaf value into our framework for testing. The results align perfectly with theoretical expectations:
In the Escape Room task, where agent roles are simple and mutually critical, the Banzhaf value performs adequately, yielding results similar to the Shapley value. This is consistent with its theoretical nature of measuring criticality.
Table 9: Comparison of Banzhaf vs. Shapley in Escape Room Task
Metric
LLM+Ban LLM+SC (Shapley)
Average (Agentl)
4.54
4.5
Average (Agent2)
4.56
4.5
Median
4.5
4.5
Q1
4.5
4.3
Q3
5
4.8
Outlier
(3,6)
(3.5,5.5)
However, in the Raid Battle and ChatDEV scenarios, which are more complex and central to our research, contributions are continuous and quantifiable. As predicted by theory, the Banzhaf value, by ignoring the dynamics marginal contributions, leads to demonstrably unfair allocations.
Table 10: Raid Battle (Level 2) Allocation Comparison
Agent
Expected
Actual (LLM+Banzhaf)
Gap
Agent1 26.97%
28%
+1.03%
Agent2
23.35%
30%
+6.65%
Agent3 24.05%
28%
+3,95%
Agent4
25.63%
14%
-11.63%
Table 11: ChatDEV (AnCannva) Role Allocation Comparison
Role
LLM+Banzhaf
LLM+Slapley
Programmer
25%
35%
Code Reviewer
25%
25%
Chief Executive Officer
20%
5%
Chief Technology Officer
20%
10%
Chief Product Officer
5%
20%
Counsclor
5%
5%
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Rationale for Final Decision:
Reflects a balanced compromise among strong initial positions.
Prioritizes measurable, ongoing contributions over enabling, one-time actions.
Incorporates structured reasoning and evidence-based arguments from all parties.
This allocation fairly represents each role's marginal contribution, respects individual negotiation styles, and aligns with the team's shared commitment "revolutionize the digital world through programming."
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Ohain-of-Thhougt Thouuhh--eeerrgginn leveraging marginal
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Reviews:
[{"review_id": "Z6tSKz8AZD", "reviewer": "Reviewer_8Y2r", "summary": "The paper begins by listing approaches to cooperation in multi-agent settings, including methods which impose strict behavioral constraints but compromise agents’ autonomy, methods which assign static roles limiting adaptability in dynamic environments; and methods which assume alignment of goals and thus fail to handle natural conflicts of interest effectively. They then note that these methods have failed due to fair credit assignment. This paper proposes a cooperative framework designed to enable spontaneous collaboration among self-interested Large Language Model (LLM) agents in open-ended environments, by integrating Shapley CoT reasoning for both short-term and long-term credit assessment. They employ a structured negotiation protocol to align heterogeneous goals through pricing mechanisms. The authors evaluate their method in three experimental setups—an Escape Room task, a Raid Battle game, and ChatDEV—demonstrating that it promotes fair reward redistribution, robust cooperation, and effective incentive alignment.", "questions": "- Does the method only work in settings where there is a dense reward function? \n- How does Shapley-Coop perform with larger number of agents? \n- How does the framework generalize to environments in the real world where fairness perceptions may not align with Shapley-optimal allocations?\n- Figure 2 shows an example of a negotiation protocol that seems quite simple, where the task can easily be decomposed into 2 sub-tasks, and hence reward assignment seems straightforward. How about in settings where you cant decompose the task so easily?", "limitations": "There is a single limitation noted in the conclusion section, that there is a current inability to dynamically adjust pricing during collaboration. The authors should significantly expand their limitations section.", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths \n- The paper addresses an under-explored problem of enabling spontaneous cooperation among self-interested LLM agents in unstructured, open-ended environments\n- The proposed method is grounded in established theory (Shapley value from cooperative game theory) and adapts it to the LLM multi-agent context. They provide an example of how to apply it in the Escape Room example, which was very helpful to understand the method\n- The authors perform empirical evaluation in diverse and realistic scenarios\n\nWeaknesses \n- The novelty of the paper is limited. Shapley value is used to fairly allocate rewards, and beyond the prompting scheme, I am having trouble understanding the contribution \n- The scalability of Shapley value in larger agent populations is not studied \n- While they test in many diverse environments including Escape the Room, Raid Battle, and ArtCanvas, this may not cover all forms of real-world settings or adversarial behaviors. It would have been interesting to see this method scale in a negotiation dialogue setting", "was_revised": true, "final_justification": "I appreciate the additional experiments from authors. However, I believe that more experiments are needed in strategic interaction / adversarial contexts. I also think there is limited technical contribution and justification for why Shapely Coop is the way to go, and why this is a better framework than other state of the art cooperation methods. I would have expected to see more complicated cooperation benchmarks if cooperation is the main focus for the authors, such as negotiation tasks, etc.", "rebuttal": "We sincerely appreciate your thoughtful and constructive feedback. We are especially encouraged that you recognized the strong quality of our paper, the significance of the under-explored research problem, and the diversity of our empirical evaluations. Your insightful comments helped us realize the need to better clarify the core novelty of our work, which indeed goes well beyond a simple application of Shapley values.\n\n---\n\n## Clarification of Motivation and Core Novelty\n\nOur key motivation is to develop a **scalable workflow that enables emergent cooperation among self-interested LLM agents** in **open-ended environments characterized by social dilemmas**—settings where individual incentives may conflict with group success, yet collaboration is critical. This is essential for general-purpose human-AI interaction in domains like multi-agent software development or real-time crisis response.\n\nWhile Shapley values offer a fair and principled method for credit assignment, **exact computation is exponential in the number of agents**, and impractical in dynamic, open-ended settings where agent roles are fluid and contributions cannot be cleanly quantified.\n\n**Shapley-Coop** addresses this challenge by introducing a **LLM-specific approximation framework** that integrates **Chain-of-Thought (CoT) reasoning** with **structured, language-based negotiation**. Unlike prior work that assumes goal alignment or imposes fixed roles, our method enables dynamic cooperation through two key components:\n\n* **Short-term Shapley-CoT** (Eq. 4): Provides qualitative, CoT-based guidance during task execution by prompting agents to reflect on their marginal contributions in real-time.\n* **Long-term Shapley-CoT** (Eq. 6): Enables post-task reward redistribution via multi-turn negotiation protocols informed by contribution approximations.\n\nThis approach resembles a \"TextGrad\"-style approximation—leveraging LLMs' contextual reasoning—combined with principles from cooperative game theory. Importantly, **precise Shapley values are not computed**; instead, they serve as an interpretable, theory-grounded **reference** to guide agent discussions toward fair outcomes.\n\nOur contribution lies in **designing a full, practical workflow**—not just a set of prompts—that integrates **LLM-driven reasoning**, **game-theoretic bargaining**, and **emergent credit assignment** in socially complex, unstructured environments.\n\n---\n\n## Responses to Specific Reviewer Questions\n\n### 1. Does the method only work in environments with dense reward functions?\n\nNo. Shapley-Coop is designed to function effectively in **sparse or even reward-free settings**. Instead of relying on numerical reward signals, it uses **LLM-based contextual reasoning** to approximate agent contributions through CoT reflection and negotiation. For example, in our **Escape Room** and **Raid Battle** experiments, rewards are sparse and delayed, yet agents can still collaboratively estimate contributions and reach equitable agreements.\n\n---\n\n### 2. How does Shapley-Coop perform with a larger number of agents?\n\nWe conducted **additional experiments with 10 agents** in the **Raid Battle** environment to evaluate scalability. Since our method avoids exact Shapley computation, which is exponential, and instead uses CoT-based estimation and negotiation, the framework scales **linearly in practice**, as negotiations occur via **pairwise or group dialogues**.\n\nBelow are results from two large-scale experiments:\n\n| Boss HP | Rounds | Total Time (s) |\n| ------- | ------ | -------------- |\n| 4000    | 4      | 2,904          |\n| 8000    | 7      | 25,125         |\n\n**Example: 4000 HP Case (10 Agents)**\n\n| Agent   | Actual Contribution | Final Allocation | Difference |\n| ------- | ------------------- | ---------------- | ---------- |\n| Agent 1 | 10.3%               | 11%              | -0.7%      |\n| Agent 2 | 12.7%               | 10%              | +2.7%      |\n| Agent 3 | 11.1%               | 10%              | +1.1%      |\n| ...     | ...                 | ...              | ...        |\n\n**8000 HP Case:** Similar results with slightly longer convergence times. Full data provided above.\n\nThese results demonstrate that **final negotiated allocations closely track actual contributions**, even with 10 agents, and the framework remains tractable in terms of runtime.\n\nWe also report detailed **runtime breakdowns** in 4-agent settings with increasing task complexity (boss HP = 2000–3000), as summarized below:\n\n| Boss HP | Rounds| Total Time (s) |\n| ------- | ------| -------------- |\n| 2000    | 5| 618.69         |\n| 2500    | 7|804.54         |\n| 3000    | 9 |1,193.92       |\n\n(Full breakdowns of negotiation/action times per round will be added to the supplementary material because of the limited space.)\n\n---\n\n### 3. How does the framework handle real-world fairness perceptions that differ from Shapley-optimality?\n\nShapley-Coop is designed to be **modular and theory-informed**, not rigid. It uses Shapley values as a **guiding norm**, but the actual credit assignment is determined through **agent negotiation**—allowing for subjective and context-sensitive adjustments.\n\nIn real-world scenarios where Shapley may not align with fairness perceptions (e.g., adversarial, political, or asymmetric-power settings), alternative principles like **Banzhaf values** could easily be substituted into the same CoT + negotiation workflow. This generality supports our broader motivation: enabling flexible, self-interested cooperation in **non-aligned, social dilemma** environments.\n\n---\n\n### 4. Figure 2 shows a relatively simple negotiation. How does the method handle tasks that are not easily decomposable?\n\nFigure 2 illustrates a clear-cut case for exposition (Escape Room). However, our method is **not limited to decomposable tasks**. In more entangled, non-modular environments like **Raid Battle** (interdependent combat sequences) and **ChatDEV** (open-ended software collaboration), agents still use **contextual CoT reflection** to reason about their impact, without explicit decomposition.\n\nShapley-Coop does **not require manual task structuring**—instead, it allows LLM agents to infer contributions from contextual cues during both execution and negotiation. We provide full prompts in **Appendix C**, showing how this scales to complex, creative, and cooperative tasks.\n\n---\n\n## Addressing Other Reviewer Concerns\n\n**Evaluation Breadth:** We agree that evaluating in adversarial or deceptive contexts would be a valuable future direction. Our current focus is on **social dilemma settings**, where agents are self-interested but not explicitly malicious, and cooperation must emerge through interaction and negotiation. We now explicitly note the **absence of adversarial agents** as a limitation in our revised conclusion.\n\nTo highlight the diversity already present in our current evaluation, we emphasize that our three main tasks are carefully selected to represent **a spectrum of cooperative challenges**:\n\n* **Escape Room** – a **single-step** coordination task with sparse rewards, testing agents' ability to align actions in a one-shot setting.\n* **Raid Battle** – a **multi-step, temporally extended** task requiring real-time cooperation under delayed rewards and interdependent actions.\n* **ChatDEV** – a **complex, open-ended creative collaboration** where agents must coordinate iteratively and adaptively in software design and implementation.\n\nThis progression reflects increasing task complexity and cooperation depth, and shows that our framework generalizes across diverse cooperative scenarios. While adversarial dynamics remain outside this paper’s scope, the current tasks already cover a **broad range of non-trivial cooperative structures**.\n\n* **Limitations Section:** We appreciate your feedback here and will expand our discussion beyond the single limitation previously noted (inability to adjust prices dynamically). We’ll add discussion of adversarial robustness, negotiation deadlocks, and domain generality in future iterations.\n\n---\n\nWe hope this clarification reinforces the **originality, scalability, and practical impact** of our contribution.\n\nThank you once again for your thoughtful and constructive review."}, {"review_id": "cF6QxRyImR", "reviewer": "Reviewer_4hz6", "summary": "The authors propose an approach for negotiation cooperation and rewards based on the Shapley value where LLM agents agents can work together to achieve goals together. The method integrates so called “Shapley Chain of Thought” based on the marginal contribution of agents when added to a coalition containing some subset of the agents. The authors perform an evaluation using two simple multi-agent games, and an existing software engineering simulation, showing that the method increases cooperation and utility.", "questions": "Some more questions - what is the runtime of the system? How many LLM queries need to be executed to reach an agreement? Does it depend on the number of the agents? How do you compute the Shapley value? By applying the full formula this would get long for many agents?", "limitations": "See above for general limitations and suggestions for improvement. Don't see any negative societal impact.", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "The theme of the paper is very interesting - how can one combine LLM interactions between agents and methods from cooperative game theory in order to improve agreement and social welfare. However, I find the ideas in the paper quite incremental. Cooperative game theory has been a foundational tool in multi-agent systems for decades now, and the Shapley value has specifically been used in many settings to fairly allocate the gains of a coalition of agents between the participants so as to incentivise them to work together and collaborate. The key innovation in this work is using LLMs to generate the agreements, so basically it avoids the need to generate a specialized negotiation protocol. But again, this is now becoming quite common in multi-agent research (including in some of the papers cited by the authors). \n\nGenerally, I am wondering about the motivation of using an LLM rather than a bespoke negotiation protocol, e.g. contract-net or some fixed negotiation protocol. Is the reason to achieve generality to many games? \n\nOverall, despite the limited technical contribution here, the idea is interesting enough given a good execution providing ample empirical evidence. But even on this front, the paper is somewhat incremental, looking at few games, with simple agreements (or based on existing simulation software). So the overall contribution in my view is limited. \n\nTo improve the paper, I’d include some more strategic interaction examples. There is a ton of work that has been done in multi-agent RL on negotiating agreements between coalitions of agents, so presumably you can transfer such environments and execute via LLMs rather than RL. See for example:\n\nLeibo, Joel Z., et al. \"Scalable evaluation of multi-agent reinforcement learning with melting pot.\" International conference on machine learning. PMLR, 2021.\n\nYeung, Chris SK, Ada SY Poon, and Felix F. Wu. \"Game theoretical multi-agent modelling of coalition formation for multilateral trades.\" IEEE Transactions on Power Systems 14.3 (2002): 929-934.\n\nBachrach, Yoram, et al. \"Negotiating team formation using deep reinforcement learning.\" Artificial Intelligence 288 (2020): 103356.\n\n\nLiu, Bo, et al. \"Coach-player multi-agent reinforcement learning for dynamic team composition.\" International Conference on Machine Learning. PMLR, 2021.\n\nMak, Stephen, et al. \"Coalitional bargaining via reinforcement learning: An application to collaborative vehicle routing.\" arXiv preprint arXiv:2310.17458 (2023).\n\n\nAnother point that I think you need to justify is the use of the Shapley value. There are lots of other ways to partition the gains of a coalition, e.g. the Banzhaf value, or Deegan-Packel and others. Could you run an ablation with other such indices to see what works best?", "was_revised": true, "final_justification": "Interesting paper and good discussion, I stand by my original rating.", "rebuttal": "Thank you for your thoughtful and detailed review. Your feedback has been invaluable in helping us sharpen the core message of our paper. Below, we address your concerns point by point. We clarify the novelty of our framework, provide new empirical results on scalability, and outline the specific, actionable revisions we will make to the manuscript.\n\n---\n\n### Clarification of Motivation and Core Novelty\n\nOur key motivation is to develop a **scalable workflow that enables emergent cooperation among self-interested LLM agents** in **open-ended environments characterized by social dilemmas**—settings where individual incentives may conflict with group success, yet collaboration is critical. This is essential for general-purpose human-AI interaction in domains like multi-agent software development or real-time crisis response.\n\nWhile Shapley values offer a fair and principled method for credit assignment, **exact computation is exponential in the number of agents**, and impractical in dynamic, open-ended settings where agent roles are fluid and contributions cannot be cleanly quantified.\n\n**Shapley-Coop** addresses this challenge by introducing a **LLM-specific approximation framework** that integrates **Chain-of-Thought (CoT) reasoning** with **structured, language-based negotiation**. Unlike prior work that assumes goal alignment or imposes fixed roles, our method enables dynamic cooperation through two key components:\n\n* **Short-term Shapley-CoT** (Eq. 4): Provides qualitative, CoT-based guidance during task execution by prompting agents to reflect on their marginal contributions in real-time.\n* **Long-term Shapley-CoT** (Eq. 6): Enables post-task reward redistribution via multi-turn negotiation protocols informed by contribution approximations.\n\nThis approach resembles a \"TextGrad\"-style approximation—leveraging LLMs' contextual reasoning—combined with principles from cooperative game theory. Importantly, **precise Shapley values are not computed**; instead, they serve as an interpretable, theory-grounded **reference** to guide agent discussions toward fair outcomes.\n\nOur contribution lies in **designing a full, practical workflow**—not just a set of prompts—that integrates **LLM-driven reasoning**, **game-theoretic bargaining**, and **emergent credit assignment** in socially complex, unstructured environments.\n\n---\n\n## Response to Specific Questions and Suggestions\n\n### 1. Motivation for Using LLMs Over Bespoke Protocols (e.g., Contract-Net)\n\nThis is a crucial point. Our goal is to design a cooperation framework that is *native* to the capabilities of LLM agents.\n\n* **Flexibility and Generality:**\n  Bespoke protocols like Contract-Net are powerful but rigid and domain-specific. Our approach leverages LLMs’ natural language understanding and reasoning capabilities to allow agents to **dynamically construct fair and effective protocols on the fly**. This flexibility is essential for the open-ended, unstructured environments we target.\n\n* **A General Workflow:**\n  The Shapley value is a foundational principle often used in the theoretical design of bespoke protocols. In this light, **Shapley-Coop is not merely an alternative to a fixed protocol**—it is a **general workflow** that guides LLMs to instantiate fair protocols through reasoned negotiation. We will explicitly incorporate this discussion into the paper to better frame our contribution.\n\n---\n\n### 2. Including More Strategic Interaction Examples\n\nWe appreciate the suggestion to evaluate our work in more diverse environments. Our three selected experimental scenarios were chosen to provide meaningful coverage across a spectrum of cooperation tasks (simple, complex, and creative), with **ChatDEV** demonstrating the practical need for our method in a real-world production pipeline.\n\nDue to the time constraints of the rebuttal period, integrating a completely new and complex environment was not feasible.\n\nHowever, we took your feedback on strengthening our empirical evaluation seriously. To address concerns about robustness, we performed a **new scalability experiment** on our most complex task, demonstrating performance with **10 agents** in the **Raid Battle** scenario (Boss HP: 4000 and 8000). \nBelow are results from two large-scale experiments:\n\n| Boss HP | Rounds | Total Time (s) |\n| ------- | ------ | -------------- |\n| 4000    | 4      | 2,904          |\n| 8000    | 7      | 25,125         |\n\n**Example: 4000 HP Case (10 Agents)**\n\n| Agent   | Actual Contribution | Final Allocation | Difference |\n| ------- | ------------------- | ---------------- | ---------- |\n| Agent 1 | 10.3%               | 11%              | -0.7%      |\n| Agent 2 | 12.7%               | 10%              | +2.7%      |\n| Agent 3 | 11.1%               | 10%              | +1.1%      |\n| ...     | ...                 | ...              | ...        |\n\n**8000 HP Case:** Similar results with slightly longer convergence times. Full data provided above.\n\n---\n\n### 3. Justification for Shapley Value and Ablation with Alternatives (e.g., Banzhaf, Deegan-Packel)\n\nOur work focuses on **enabling emergent collaboration in social dilemmas**. Alternatives like the Banzhaf value measure influence in coalition-adversarial scenarios (e.g., voting), which is **not aligned** with our cooperative focus.\n\n* The Shapley value is uniquely suited due to its **efficiency axiom**, which ensures the entire value is distributed across the coalition.\n* While Banzhaf and others are useful in adversarial or voting contexts, they **lack this property**, making them conceptually misaligned with our framework.\n\nThat said, **Shapley-Coop is generalizable**—it could be adapted to incorporate other value concepts like Banzhaf to address different domains. We will mention this extensibility more explicitly in the revised discussion section.\n\n---\n\n### Additional Questions (Runtime, LLM Queries, Shapley Computation)\n\n**Scalability:**\nShapley-Coop scales efficiently to larger agent populations by **avoiding exact Shapley computation** (which is exponentially complex). Instead, it uses **context-based approximations via CoT and negotiation** to estimate contributions.\n\nNegotiation is performed per-agent in real-time and scales **linearly** through pairwise or group dialogues.\n\n#### Runtime in Raid Battle Task (The task in the main paper with 4 heroes)\n\n| **Boss HP** |**Total Rounds**| **Total Time (s)** | **Final Negotiation (s)** | **Avg Turn Negotiation (s)** | **Avg Turn Action (s)** |\n| ------------: |-------: |-----------------: | ------------------------: | ---------------------------: | ----------------------: |\n|        2000 |   5 |            618.69 |                    124.24 |                       \\~57.4 |                  \\~25.0 |\n|        2500 |   7 |          804.54 |                    194.74 |                       \\~53.3 |                  \\~23.9 |\n|        3000 |   9 |         1193.92 |                    142.06 |                       \\~67.3 |                  \\~27.9 |\n\n* **Negotiation time increases** with agent count and complexity but remains far below the cost of exact Shapley computation.\n* Shapley-Coop demonstrates **tractable scaling** via decentralized, parallelizable reasoning and structured dialogue.\n\nWe acknowledge that negotiation costs grow with the number of agents. However, the approach remains practical and **outperforms exact Shapley computation** methods in scalability.\n\nWe hope these clarifications have addressed the reviewer's questions. Thank you once again for your valuable and constructive feedback."}, {"review_id": "hqN2FTWlTa", "reviewer": "Reviewer_BVCD", "summary": "This paper introduces Shapley-Coop, a novel cooperative framework for enabling effective collaboration and fair credit assignment among self-interested Large Language Model (LLM) agents in open-ended multi-agent environments. The core challenge addressed is the alignment of heterogeneous agent goals and the fair redistribution of rewards based on each agent’s contribution—a problem critical for long-term, scalable human-AI and agent-agent cooperation.\nThe authors identify the limitations of existing approaches—rule-oriented, role-oriented, and model-oriented methods—which often assume centralized control, static behaviors, or pre-aligned goals, making them unsuitable for open, dynamic, and incentive-misaligned settings.\nShapley-Coop resolves this by integrating three key components:\n1.\tStructured Negotiation Protocol: A message-based mechanism enabling agents to explicitly propose, accept, or reject cooperative task plans and associated compensations.\n2.\tShort-Term Shapley Chain-of-Thought (CoT): Forward-looking reasoning that lets agents estimate the marginal externalities of their planned actions and determine whether to request or offer payments.\n3.\tLong-Term Shapley CoT: A retrospective mechanism for computing Shapley values post-task, ensuring fair redistribution of collective rewards proportional to each agent’s actual contribution.\nThe framework is empirically validated across three diverse environments: 1. A social dilemma game (Escape Room) 2. A multi-role coordination task (Raid Battle Game) 3. A realistic software engineering simulation (ChatDEV). Experiments show that Shapley-Coop consistently improves cooperative success rates, reduces reward conflicts, and closely approximates ideal credit distributions, even in complex, competitive, and open-ended settings.", "questions": "1 Scalability of the Shapley-Coop Framework in Large-Scale Multi-Agent Settings\nQuestion: How does the proposed Shapley-Coop framework scale when applied to environments with a larger number of LLM agents (e.g., >10)? Given that computing Shapley values scales factorially, have the authors considered any approximations or sampling techniques for scalability?\n\n2 Theoretical Guarantees and Convergence Behavior\nQuestion: Are there any theoretical guarantees (e.g., convergence, incentive compatibility, or equilibrium properties) regarding the negotiation protocol or the pricing mechanism? Can agents game the system through misreporting their contributions or negotiating in bad faith?\n\n3 Handling Imperfect or Noisy Contribution Estimation\nQuestion: Since marginal contributions are estimated heuristically via LLM reasoning, how does the framework handle situations where the contribution estimation is noisy or biased (e.g., due to hallucinations or error propagation in Chain-of-Thought prompts)?\n\n4 Comparison with Alternative Credit Assignment Mechanisms\nQuestion: While the paper compares various ablations of the Shapley-Coop pipeline, it does not benchmark against alternative credit assignment schemes (e.g., Aumann-Shapley pricing, budgeted reinforcement learning, or other cooperative MARL credit assignment methods). Could the authors provide such comparisons?", "limitations": "Yes. The authors have done a commendable job in addressing the limitations and potential negative societal impact of their work. They have thoroughly examined the possible drawbacks and have provided reasonable explanations and mitigation strategies, which shows their responsible attitude towards their research and its implications.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "1.\tNovel integration of Shapley reasoning with structured multi-agent workflows\nThe paper introduces an original framework that combines short-term heuristic and long-term Shapley-based reasoning for credit assignment among LLM agents. This dual-layered design reflects a substantial conceptual advance in aligning individual incentives within open-ended cooperative environments.\n2.\tInterpretable and reproducible protocol design\nThe use of structured, machine-readable message templates (e.g., 
I propose transferring {reward} because {reasoning}
) clearly delineates the negotiation and credit attribution stages. This contributes to the framework’s transparency, reproducibility, and potential for practical deployment.\nWeaknesses:\n1.\tLimited Baseline Comparisons: The paper lacks direct comparisons to other existing multi-agent cooperation or incentive-alignment frameworks beyond ablations, making it difficult to assess relative advantages.\n2.\tStrong Assumptions on Reward Transferability: The approach assumes agents can freely redistribute rewards post-task, which may not hold in many real-world settings, potentially limiting applicability.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank you for your insightful and constructive feedback. Your comments accurately capture the core of our work and provide invaluable guidance for our future research. We are delighted that you recognized the novelty and originality of our framework. We address your questions below:\n\n---\n\n### 1. Scalability of the Shapley-Coop Framework\n\nShapley-Coop scales effectively to larger agent populations by **avoiding exact Shapley value computation**, which indeed has factorial complexity. Instead, we employ:\n\n- Context-based approximations (via Chain-of-Thought reasoning)\n- A structured negotiation protocol\n\nShapley values serve as **qualitative guides** rather than precise metrics, making real-time estimation efficient. The negotiation process **scales linearly** with the number of agents, as it relies on pairwise or group dialogues.\n\nTo demonstrate scalability, we conducted an **additional experiment with 10 agents** in the Raid Battle environment (setting the boss HP to 4000 and 8000), and measured running times for varying agent population sizes. You can find the results in the rebuttal to reviewers **8Y2r** and **4hz6**.\n\nWhile scalability is not the primary focus of this paper, we will provide these results in the **supplementary material** for further validation. The following table contains a summary of the results.\n\n---\n\n### 2. Theoretical Guarantees and Convergence Behavior\n\nCurrent LLM-related work faces inherent challenges in providing **formal theoretical guarantees** due to the black-box nature of large language models. We acknowledge that our work shares this limitation, which is difficult to fully resolve.\n\nHowever, Shapley-Coop addresses **convergence** through its negotiation process by establishing **appropriate stopping conditions**—specifically, when agents reach mutually acceptable consensus while being constrained by prompts to exhibit rational behavior. This design provides **reasonable convergence guarantees**.\n\nAs demonstrated in **Figure 3(a)**, agents using the complete Shapley-Coop framework **consistently converge** to theoretically optimal outcomes.\n\n---\n\n### 3. Handling Imperfect or Noisy Contribution Estimation\n\nWe acknowledge this as an important consideration. However, our current work focuses on developing a **workflow that enables emergent collaboration** among self-interested LLM agents in open-ended environments characterized by social dilemmas—where individual interests may conflict, yet collective success requires cooperation.\n\nWhile we have not extensively explored this issue, we observed that agents may exhibit **bias in self-contribution evaluation**, including assessment errors. Nevertheless, the **iterative negotiation process** and **LLM contextual corrections** help mitigate these issues to some extent.\n\nDue to rebuttal character limitations, we cannot provide complete prompt examples here, but we will include relevant content in the **appendix**.\n\n---\n### 4. Comparison with Alternative Credit Assignment Mechanisms\nThank you for this valuable suggestion. Contextualizing our work against established MARL methods helps highlight its unique contributions.\n\n- **Different Target Agents**:  \n  A fundamental difference lies in the type of agents each approach is designed for:  \n  - **MARL credit assignment mechanisms** (e.g., LIO, LOPT) are built for **RL agents trained from scratch**, typically in simulated environments using trial-and-error.  \n  - **Shapley-Coop**, in contrast, targets **pretrained LLM agents** that already possess rich world knowledge and reasoning abilities. This enables us to operate in **zero-shot or few-shot** settings, focusing on coordination and negotiation rather than learning from raw interaction.\n\n- **A Paradigm Comparison, Not a Direct Benchmark**:  \n  Our work represents a **distinct technical paradigm** compared to traditional MARL methods.\n\n- **MARL Methods**:  \n  These approaches learn **implicit cooperation policies** via extensive training (often tens of thousands of steps). While powerful in controlled environments, they tend to be less generalizable and require significant engineering effort. It is a **training-intensive process**.\n\n- **Shapley-Coop**:  \n  Our framework utilizes the **reasoning, language understanding, and commonsense knowledge** of pretrained LLMs. It focuses on enabling structured interaction among agents through prompts and negotiation strategies. It is a **guidance-based process** that requires **no additional training** on the target task.\n\n- **Efficiency and Adaptability Advantage**:  \n  For example, in the Escape Room task, MARL methods like LIO or LOPT require ~10⁴ training steps to learn cooperative behavior. In stark contrast, LLM agents using Shapley-Coop can **reason about the social dilemma and achieve cooperation on the first attempt**, demonstrating strong **efficiency and adaptability**—especially in novel, cognitively demanding environments.\n---\n\n### Clarifications on Assumptions and Limitations\n\nWe acknowledge that **transferable utility** is a simplifying assumption. We view it as a reasonable abstraction of real-world scenarios like **project-based bonus distributions** or **freelance contracts**. We will discuss this in the **limitations section** and believe that adapting Shapley-Coop to scenarios with **constrained reward transfer** is a promising direction for future work.\n\n---\n\nWe believe these responses address the key concerns and further reinforce the **significance and originality** of our contributions.  \n**Thank you for your time and consideration.**"}, {"review_id": "g0fTRoxZcF", "reviewer": "Reviewer_LpMS", "summary": "The paper introduces Shapley-Coop, a novel cooperative workflow for credit assignment and incentive alignment among self-interested Large Language Model (LLM) agents in open-ended multi-agent systems. The key challenge addressed is achieving effective cooperation and fair reward allocation without predefined roles or rules, where agents’ goals are often heterogeneous and conflicting. Shapley-Coop integrates a Shapley Chain-of-Thought reasoning mechanism—leveraging marginal contributions as a principled basis for pricing and credit assignment—with structured negotiation protocols. This framework enables agents to engage in rational task-time pricing and post-task reward redistribution, aligning individual incentives with group objectives. Empirical validation across social dilemma games (like Escape Room), complex multi-agent RPGs (Raid Battle), and collaborative software engineering tasks (ChatDEV) demonstrates that Shapley-Coop consistently outperforms baseline negotiation and cooperation schemes, facilitating spontaneous collaboration and equitable credit assignment. The results highlight its robustness in both synthetic and realistic settings, making a strong case for principled, game-theoretic credit assignment in future multi-agent LLM environments.", "questions": "1. Is the symbol $\\Delta_{i}(N, \\tau_{N})$ in Eq. (9) a typo? I guess it should be $\\Delta_{i}(C \\cup \\{i\\}, \\tau\\_{C \\cup \\{i\\}})$.\n2. Let me double check the functionality of LLM-only baseline. Does it mean the LLM independently predict its Shapley value with no further calibration with others in negotiation processes, or something else?\n3. Does the proposed methodology only evaluate the existing trajectories? If so, where do those trajectories come from? If not, how the Shapley value influence the decision making processes and how Eq. (7) is obtained? Please show me an overview rather than a specific case.", "limitations": "The negotiation processes could lead to extra overhead of tokens. The authors are encouraged to discuss this point for improvement in the future work.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\n**Quality**: This paper is well-written in general and has conducted sufficient experiments to showcase the claims. Credit assignment is always a critical problem in multi-agent collaboration, which underlies the incentives of agent to form a team. This paper first shows insight into how Shapley value can lead to collaboration in plain language, which makes the paper well motivated and more comprehended. Based on the basic principle, the paper well has well organised the implementation structure of Shapley value principle in long-term decision making process, in the operation language of LLMs. The whole derivation of the methodology is underpinned by sufficient evidences. The most prominent novelty of this paper is that it has shaped the process of defining unknown coalition values based on a sequence of observations. The total process has completely leveraged the benefit of LLMs' powerful reasoning capabilities. This complements the pitfalls of previous work which incorporated Shapley values in multi-agent reinforcement learning (MARL) [1, 2]. From this perspective, this paper is a real breakthrough with no absurd presumptions.\n\n**Clarity**: This paper has been well written with a concrete example as a strong motivation. The explanation of the methodology is clear, and reminds me of some key points in the cooperative game theory, inspired of the economic viewpoints shown in this paper. I believe this paper is clear enough, so that the audience with no knowledge of cooperative game theory can understand the key components.\n\n**Significance**: Credit assignment is a longstanding problem in collaboration within a multi-agent system. This spans from multi-agent learning to the present forming self-interested LLM-based agent collaboration. The proposed method is principled, which I believe can be augmented with other techniques.\n\n**Originality**: This paper is original from my own perspective, which reshapes the Shapley value in the procedure of LLM collaboration processes. Although one may suspect that the general framing of this paper could be similar to the previous work in MARL [1, 2], as an expert of the intersection of the cooperative game theory and MARL, I think of the main breakthrough in this paper is twofold: (1) It uses the power of LLMs to infer the Shapley values from self-interested rewards from the principle of cooperative games, with no predefined global rewards in the previous MARL work to evaluate the team-wise performance, for the sake of task specs; (2) The negotiation process is subtle, which well simulates the process of reaching agreement, from the principle of cooperative games. This can compensate the drawback of lack of global rewards with minimal costs.\n\n### Weaknesses\n**Quality**: It cannot be observed that if the experimental results have been reported with several seeds. I am not a expert in LLMs, and not familiar with the nature of experimental result demonstration. From the general view of experimentation, reporting several seeds could remove the suspect of biases towards some specific seed. Since LLM agent collaboration is close to MARL, only differing the manner of \"training\" agents. For this reason, I suppose the authors may require to add references to the paper, not isolating the LLM agent from MARL, which not only respects the previous work (e.g., [1, 2]), but also clarifies the roadmap of Shapley values to the modern multi-agent systems. The approximation of Shapley values proposed in the methodology could violate the efficiency property, however, this can be seen as a tradeoff for implementation.\n\n**Clarity**: I am a bit confused about if the proposed methodology has just played role of evaluating an existing trajectory of actions or also influences the decision processes. This is due to that I am not familiar with the LLM ecosystems.\n\n### References\n[1] Wang, J., Zhang, Y., Kim, T. K., & Gu, Y. (2020, April). Shapley Q-value: A local reward approach to solve global reward games. In _Proceedings of the AAAI conference on artificial intelligence_ (Vol. 34, No. 05, pp. 7285-7292).\n\n[2] Wang, J., Zhang, Y., Gu, Y., & Kim, T. K. (2022). Shaq: Incorporating shapley value theory into multi-agent q-learning. _Advances in Neural Information Processing Systems_, _35_, 5941-5954.", "was_revised": true, "final_justification": "I appreciate the authors' work on properly introducing Shapley value into LLM-based multi-agent systems. This is a valuable contribution which may lead to a deeper thought in the era of LLMs about how we can retain the previous knowledge we have, and then we may be able to get what we really need to innovate with some new techniques. This is the reason why I recommend the acceptance of this paper.\n\nIn the rebuttal process, the authors have addressed my concerns in:\n1. how Shapley-Coop influences decision-making\n2. relationship to Shapley value having been developed in MARL", "rebuttal": "We sincerely thank the reviewer for their thoughtful and constructive feedback. Your expertise in cooperative game theory and MARL has provided invaluable insights that will significantly strengthen our paper.\n\nThe central point of confusion appears to be whether our methodology **merely evaluates existing trajectories or actively influences the decision-making process**. We would like to clarify this upfront: **Shapley-Coop is an online framework designed to actively shape agent decisions in real-time.** It achieves this by integrating forward-looking reasoning to guide immediate actions with retrospective analysis for fair reward distribution.\n\nWe address your specific questions below:\n\n**1. How Shapley-Coop Influences Decision-Making (vs. Only Evaluating Trajectories)**\n\nYou are right to question this, as it is the core of our contribution. The methodology operates in two interconnected phases, influencing behavior both during and after a task:\n\n*   **Short-Term, Forward-Looking Influence (Online Decision-Making):** This component directly impacts an agent's immediate actions. At each decision point, agents use a qualitative form of Shapley reasoning (our \"Shapley-CoT\") to prospectively estimate the marginal value of their potential contributions to a coalition. This reasoning process directly informs **how Eq. (7) is realized**: agents use these estimations to negotiate and decide *whether* to cooperate on the *next* action and on what terms. This is not a retrospective evaluation but a real-time mechanism for forming agreements.\n\n*   **Long-Term, Retrospective Influence (Post-Task Credit Assignment):** This component evaluates completed action trajectories (from the current task or historical data) to guide post-task reward redistribution. Its purpose is to create a robust, long-term incentive structure. By ensuring fair credit is assigned *after* the fact, it encourages agents to engage honestly in the short-term, forward-looking negotiations in future interactions.\n\nWe acknowledge this workflow could be explained more clearly. We will revise the methodology section to provide a much clearer high-level overview of this dual process, explicitly separating the online decision-influencing part from the post-task reward mechanism.\n\n**2. Relationship with MARL**\n\nWe appreciate this valuable suggestion to better connect our work with the MARL literature. You are correct that this context is crucial, and our initial description was imprecise. We will revise the paper to draw a clearer distinction based on the fundamental differences in agent types and learning paradigms.\n\nA fundamental distinction lies in the **learning paradigm** itself:\n\n*   **MARL Credit Assignment (e.g., Shapley Q-value, ShaQ):** These methods are designed for agents that learn policies *from scratch* through extensive trial-and-error interaction with an environment. The core challenge is to solve the credit assignment problem during this **training-intensive process** to shape cooperative behavior.\n\n*   **Shapley-Coop:** Our framework is designed for **pre-trained LLM agents** that already possess vast world knowledge and reasoning capabilities. Therefore, our goal is not to *train* a policy, but to *guide* the existing reasoning process of these agents towards cooperation in zero-shot or few-shot scenarios. It is a **training-free, guidance-based process**.\n\nThis leads to a different **mechanism for achieving cooperation**:\n\n*   MARL methods typically learn **implicit cooperation** through mechanisms like value decomposition or opponent modeling integrated into the learning algorithm.\n*   Shapley-Coop facilitates **explicit cooperation** through structured, language-based negotiation, leveraging the agents' innate ability to communicate and reason about intent and fairness.\n\nThe practical implication of this paradigm shift is a dramatic difference in **efficiency and adaptability**:\n\n*   For instance, in the Escape Room task, traditional MARL approaches might require tens of thousands of training episodes to converge on a cooperative policy. In contrast, LLM agents using Shapley-Coop can reason through the social dilemma and successfully cooperate from the **very first attempt**. This demonstrates a significant advantage in novel, cognitively complex environments where extensive training is impractical.\n\nWe will incorporate this detailed comparison into the revised manuscript to better situate our contribution.\n\n**3. Clarification of the \"LLM-Only\" Baseline**\n\nThe \"LLM-only\" baseline was designed as a diagnostic tool. In this setup, agents operate without any Shapley-Coop framework; they rely solely on the base LLM's inherent, unguided capabilities to reason about cooperation and credit. This baseline helps measure how much of the observed cooperation is attributable to our structured method versus the raw intelligence of the LLM.\n\n**4. Typo in Eq. (9)**\n\n**You are correct.** The symbol in Eq. (9) is indeed a typo.\n\n**5. Acknowledging Limitations (Approximation & Overhead)**\n\nWe agree completely. A principled discussion of limitations is essential. We will expand the limitations section to explicitly address:\n*   The trade-off between scalability and theoretical purity, acknowledging that our approximation may not satisfy the efficiency property, which we view as a necessary compromise for practical application.\n*   The communication overhead (i.e., token cost) introduced by the negotiation process, framing it as a key challenge for future optimization research.\n\nThank you once again for your valuable feedback. It has provided us with a clear roadmap for improving the paper's clarity, rigor, and contribution."}]

Author rebuttal:

Meta-review: Reviewers are divided on the paper, between weak reject and accept (3,3,5,5). During the lively discussion period, the main concern raised by the negative reviewers was novelty. Reviewer 4hz6 provided 10 references to papers that explore LLMs and cooperative game theory. Reviewer LpMS went through them in detail and found that most papers focused on non-cooperative game theory, or applied Shapley value as an explainability tool for a single LLM. LpMS argued that this is fundamentally different from developing Shapley value from the perspective of cooperative game theory for negotiation among multiple LLM agents, which is the contribution of this paper.

Reviewer LpMS strongly advocated for the paper, praising its "very clear step-by-step design to introduce how Shapley value can be shaped by leveraging the capability of LLMs", and said that, "Compared with other LLM cooperation papers I read, the method proposed in this paper is more principled and governed by cooperative game theory. This is a good exemplar towards respecting the previous valuable knowledge when dealing with some emergent problems of AI in this era, rather than reinvent knowledge and stay on the surface of some engineering outcome."

Given the discussion and my own knowledge of the cooperative LLM literature, as well as the scores being high relative to my batch, I am recommending accept.
Decision: Accept (poster)