COOP$^2$: Defining, Observing, and Repairing Cooperation in LLM Multi-Agent Systems

Hanqing Yang; Narjes Nourzad; Shiyu Chen; Marie Siew; Jingdi Chen; Carlee Joe-Wong

cs.AIFeb 27, 2026

COOP $^2$ : Defining, Observing, and Repairing Cooperation in LLM Multi-Agent Systems

Authors: Hanqing Yang, Narjes Nourzad, Shiyu Chen, Marie Siew, Jingdi Chen, Carlee Joe-Wong

Organizations: CMU · USC · SUTD · UArizona

Abstract

Many complex tasks require extended effort, diverse capabilities, or coordinated actions beyond what a single agent can provide. However, simply adding more agents does not guarantee better performance, as effective cooperation depends on how agents interact with each other and with task structure to satisfy evolving constraints over time. This challenge is amplified for LLM-based multi-agent systems (LLM-MAS): plans, messages, and revisions occur in natural language, whereas task progress depends on grounded environment actions. Current evaluations mostly treat cooperation as an implicit ingredient of final task success, leaving both cooperation and the effect of multi-agent interaction on task dynamics difficult to study. We introduce COOP $^2$ , an evaluation framework that grounds high-level agent cooperation dynamics in LLM-MAS within task progress in the environment. COOP $^2$ then defines cooperative tasks with verifiable cooperative requirements, allowing us to analyze how cooperation unfolds over time with respect to task progress, as well as where and why cooperation breaks down. Building on this framework, we develop COOP $^2$ -Repair, which predicts constraint failures from group plans and opens targeted repair channels for guided revisions. Across two environments and three communication structures, COOP $^2$ -Repair improves task success and constraint satisfaction while exposing the additional decision overhead and communication load required for repair. The project web page can be found at: https://happyeureka.github.io/coop2.

Figures & tables

Figure 1: Overview of COOP 2 . COOP 2 models LLM-MAS through a cognitive–primitive interface (top) that couples a symbolic cognitive layer , where agents plan, communicate, interrupt, and replan through the Multi-Agent Environment Interaction Loop (MAEIL, bottom-left), with a primitive layer , where joint actions drive environment states and task-state transitions (sec. 3 ). Cooperative tasks , instantiated in MA-CRAFTER and CUBE, are guarded by participation and task-progress constraints; joint executions that satisfy all active constraints succeed while violations identify which cooperative requirements failed. These constraint signals support process-level diagnosis and feed COOP 2 -Repair (sec. 5 ), which opens targeted repair channels to revise plans before primitive execution.

Figure 2: Decoupling cognitive and environment clocks in multi-agent execution. At each cognitive step, an agent maintains an internal state consisting of its current interaction stage and its committed symbolic plan. Plans may be newly generated (green), resumed (yellow), or terminated (red, indicating success or failure).

Figure 3: Two cooperative environment instantiations. CUBE : agents push weighted blocks where heavier blocks require more participants in spatial alignment. MA-Crafter : agents collect resources whose difficulty scales with prerequisites, tools, and required participants.

Constraint	MA-Crafter	CUBE
$C_{\mathrm{n}}^{i}(g,t)$	$\mathrm{cap}_{i}(t)\succeq\mathrm{cap}(g,t)$	$\mathrm{cap}_{i}(t)$
$C_{\Delta\ell}^{i}(g,t)$	$\lVert\mathcal{x}_{i,t}-y_{g}\rVert\leq d$	$\min_{y\in\mathcal{Y}_{g}}\lVert\mathcal{x}_{i,t}-y\rVert\leq 1$
$C_{\Delta t}^{i}(g,t)$	$a_{i,t}=\texttt{collect}(g)$	$a_{i,t}=\texttt{push}(b(g))$

Table 1: Cooperation constraint specifications for task

g

at time

t

in MA-Crafter and CUBE.

Structure	Score $\uparrow$	Steps	Score/ Step $\uparrow$	Plans/ Agent	Msg.	Intr.	Total Dec.	Spat. Viol. $\downarrow$	Temp. Viol. $\downarrow$	Dep. Viol. $\downarrow$
3-agent GPT-5.4-mini
Individual	$\mathbf{146.8\pm 141.6}$	$117.4\pm 13.0$	$\mathbf{1.26\pm 1.29}$	$42.8\pm 1.2$	$0.0\pm 0.0$	$0.0\pm 0.0$	$196.1\pm 8.1$	$0.10\pm 0.07$	$0.01\pm 0.02$	$\mathbf{0.23\pm 0.23}$
Centralized	$39.4\pm 24.3$	$88.4\pm 12.1$	$0.45\pm 0.30$	$33.7\pm 0.9$	$88.4\pm 6.9$	$34.6\pm 5.6$	$251.9\pm 5.3$	$0.12\pm 0.08$	$0.01\pm 0.01$	$0.57\pm 0.17$
Chain	$29.4\pm 5.7$	$61.8\pm 11.9$	$0.49\pm 0.10$	$33.3\pm 1.5$	$57.4\pm 3.0$	$48.0\pm 4.9$	$200.0\pm 3.7$	$\mathbf{0.05\pm 0.05}$	$\mathbf{0.00\pm 0.00}$	$0.44\pm 0.26$
3-agent Llama-Scout
Individual	$\mathbf{30.4\pm 8.0}$	$62.6\pm 7.1$	$0.48\pm 0.11$	$33.3\pm 2.2$	$0.0\pm 0.0$	$0.0\pm 0.0$	$242.9\pm 9.6$	$\mathbf{0.04\pm 0.04}$	$0.01\pm 0.02$	$0.24\pm 0.19$

Table 2: MA-Crafter recorded outcomes for different agent-model settings and communication structures. Values are mean

\pm

standard deviation over five runs. Arrows indicate better direction when a clear direction exists; bold marks the best value within each agent-model setting.

Figure 4: COOP 2 process traces for MA-Crafter with 3-agent teams, averaged over five runs. Columns compare backbones, and rows compare communication structures. The blue heatmap in each cell shows the number of agents whose active plans target each resource or tool at each environment step. The black curve shows cumulative team score with shaded 95% confidence intervals across runs, and the red dashed line marks the mean episode termination step under the cognitive-time budget $\hat{\mathcal{T}}$ . The top of each cell reports observed spatial, temporal, and dependency satisfaction for attempted collection actions, indicating when and where cooperation succeeds or breaks down during execution.

Figure 5: COOP 2 -Repair process trace for a centralized 3-agent GPT-5.4-mini run. Gold markers indicate steps where COOP 2 predicts an upcoming constraint failure and opens a targeted repair round. The top rows show observed satisfaction across the spatial, temporal, and dependency constraints.

Appendix figures & tables23 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: MA-Crafter can host 100 agents, and more!

Figure 8: CUBE is a grid world where teams push weighted blocks into a goal zone while respecting embodied constraints. A single scaling parameter n jointly sets team size, block weights, and grid size, creating a transparent curriculum from small to large-scale cooperation. Each panel illustrates a snapshot of a cooperative block pushing scenario at increasing scales (n from 2 to 256).

Panel of Figure 9 — Figure 9: Timeline visualizations for the three communication structures considered in this work.

Action	Arguments	Effect
noop	( num_steps )	Do nothing for a specified number of steps (default: 1).
move	( direction , num_steps )	Move in a direction (left, right, up, down) for a specified number of steps (default: 1).
collect	( Resource )	Collect a resource in front of the agent. All participating agents receive the resource if participation requirements are met.
craft	( object_type )	Craft an item (e.g., wood_pickaxe, stone_sword). All participating agents receive the crafted item if participation requirements are met.
sleep	( )	Sleep to recover energy.
place	( object_type )	Place an object in the environment (e.g., stone, table, furnace, plant).

Appendix

Table 3: Symbolic actions in MCrafter used in our experiments. Action space covers all high-level behaviors available to agents.

Resource	Required agents	Required tool
tree / wood	1	–
stone	1	wood_pickaxe
coal	2	wood_pickaxe
iron	3	stone_pickaxe
diamond	3	iron_pickaxe
cow	1	–

Appendix

Table 4: MA-Crafter cooperative collection configuration. The spatial distance threshold is

1

Manhattan step for all resources.

Scored resource	Base value
wood	1
stone	10
coal	25
iron	25
diamond	80

Appendix

Table 5: MA-Crafter team-score values.

Preset	Block specification
Setting	9 blocks in total: 3 blocks each of weights 1, 2, and 3

Appendix

Table 6: CUBE cooperative block-pushing configuration. A block’s weight is both its side length and the number of agents required to push it.

Panel of Figure 14 — Figure 14: Illustration of chains: a chain succeeds or fails depending on whether available agents meet the block’s weight requirement and the maximum force exerted on the block face.

Action	Arguments	Effect
move	( direction , steps )	Move in the specified direction for a fixed number of steps (compiled into primitive moves).
wait	( steps )	Remain idle for a fixed number of steps (compiled into STAY ).
push	( block_id , steps )	Push against the specified block by repeatedly issuing primitive actions directed into the block face; succeeds only if enough agents align and apply sufficient force.

Appendix

Table 7: Symbolic actions in CUBE used in our experiments. Each action specifies a high-level effect that is decomposed into primitive actions.

Figure 15: COOP 2 process traces for MA-Crafter with 6-agent teams, averaged over five runs. The traces show active task focus, observed constraint satisfaction at collection attempts, and cumulative team score across backbones and communication structures.

Figure 16: COOP 2 process traces for MA-Crafter with 3-agent teams, single run. The traces show how agents’ active task focus, constraint satisfaction, and cumulative score evolve over time, providing an additional view of cooperation dynamics in a spatial coordination environment.

Structure	Score $\uparrow$	Steps	Score/Step	Plans/Agent	Msg.	Intr.	Total Dec.	Spat. Viol.	Temp. Viol.	Dep. Viol.
3-agent GPT-5.4-mini
Individual	3.0	116.0	0.03	30.7	0.0	0.0	137.0	0.20	0.26	0.00
Centralized	3.0	80.0	0.04	23.3	54.0	29.0	183.9	0.27	0.30	0.00
Chain	1.0	54.0	0.02	23.7	48.0	46.0	197.8	0.17	0.23	0.00
3-agent GPT-5.4
Individual	1.0	78.0	0.01	16.3	0.0	0.0	130.1	0.29	0.48	0.00

Appendix

Table 8: CUBE cooperation results.

Figure 17: COOP 2 process traces for CUBE with 3-agent teams, single run. The traces show how agents’ active task focus, constraint satisfaction, and cumulative score evolve over time, providing an additional view of cooperation dynamics in a spatial coordination environment.

Figure 18: COOP 2 process traces for CUBE with 6-agent teams, single run. The traces show how agents’ active task focus, constraint satisfaction, and cumulative score evolve over time, providing an additional view of cooperation dynamics in a spatial coordination environment.

Figure 19: Communication messages of LLM-MAS operating under centralized communication structures. The left panel shows a 2-agent setting in Easy mode, the middle panel shows 3 agents in Easy mode, and the right panel shows 3 agents in Hard mode. In the Easy setting, the leader assigns distinct tasks to workers. In Hard settings, although agents recognize the presence of constraints, they struggle to determine how to satisfy them. The leader is aware that coordination is required, but lacks grounding in how to execute effective teamwork within the environment.

Figure 20: COOP 2 bridges the cognitive layer, where agents perform reasoning, planning, and communication, and the primitive layer, where plans are grounded into primitive actions. The figure depicts a centralized communication structure under COOP 2 : the leader broadcasts messages to workers, interrupting workers’ ongoing execution and triggering replanning or resumption.

Figure 21: Individual communication structure.

Figure 22: Chain communication structure.

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