Theory of Scene: Breaking the Symmetry Trap in Multi-Agent LLM Coordination

• The coordination problem arises because a public role alone does not divide work, while ToM predictions by homogeneous agents recover their own reasoning rather than a shared division.The paper asks how agents can derive the same division from a shared scene that supports divergence, convergence, or turn-taking.Source: §1 · p. 2
• ToS derives a shared division of labor from public roles and task context, so agents diverge on Competitive targets and converge on Cooperative ones without communicating.Role gating determines whether ownership is already divided; task coupling determines whether agents converge, divide, or take target stages in turn.Source: §1 · p. 2
• ToS performs best across DivvyBench, GovSim, and Overcooked, while the strongest baseline varies across benchmarks.Adding ToS’s readings to ToM improves it but leaves it below ToS.Source: §1 · p. 2
• The symmetry trap is the double failure in which homogeneous agents collide on Competitive targets but separate on Cooperative targets.DivvyBench isolates the trap across Tabletop, Airspace, and Household, with episodes containing one target type or a mix.Source: §1 · p. 2

Multi-Agent Coordination: Competitive vs. Cooperative

• DivvyBench combines competitive and cooperative target demands within an episode for homogeneous agents acting simultaneously without communication and distinguished only by a public role.Prior benchmarks typically separate the settings or provide communication, while mixed-motive MARL suites train agents on both within an episode.Source: §2 · p. 3

Non-Communicating Coordination: ToM and Its Alternatives

• ToS uses public roles and task context rather than teammate prediction, a pre-scene division of labor, task training, or execution-time randomness.Prior non-communicating approaches include prediction and best response, conventions fixed before reading the scene, and MARL symmetry-breaking techniques.Source: §2 · p. 3

The DivvyBench Environment

• DivvyBench counts an episode as successful only if every target is taken within budget, with collisions and stuck steps consuming budget.Competitive targets require exactly one agent to select them; Cooperative targets require every agent to select the same target in the same step.Source: §3 · p. 3

The Public Role and Temperature Cannot Break Competitive Symmetry

• With identical prompts or fixed public roles, neither method completes a Competitive episode at temperature 0; higher temperature separates agents unreliably and lowers Cooperative success.Agents repeatedly select the same salient target without randomness, while independent sampling still collides with positive probability at each step.Source: §3 · p. 4, Figure 2 · p. 4

ToM Fails under Cooperative Symmetry

• ToM improves Competitive progress but fails the Cooperative requirement when homogeneous agents independently choose different targets amid ambiguity.ToM predicts teammates with over 90% accuracy in Cooperative settings but only about 30% in Competitive settings.Source: §3 · p. 4

4 THEORY OF SCENE

• The setup has homogeneous agents use one shared policy and reasoning schema, distinguished only by public roles, to act concurrently without same-step observation.At each step, agents produce one action, then the environment executes their joint action and returns new observations.Source: §4 · p. 4

4.1 THEORY OF MIND VERSUS THEORY OF SCENE

• ToS derives division from the observed world state and role, and withholding teammates’ past actions does not significantly lower its performance.Unlike ToM, it does not correct beliefs about other agents; both schemas receive the same inputs for comparison.Source: §4.1 · p. 5

4.2 ROLE GATING AND TASK COUPLING

• Role gating distinguishes overlapping ownership, which requires deriving a division, from divided ownership, where each agent advances its assigned part.Task coupling classifies targets as joint, exclusive, or sequential, calling for convergence, disjoint shares, or stages taken in turn.Source: §4.2 · pp. 5–6

4.3 ANALYSIS OF THE COORDINATION PROBABILITY

• At N = 2 and K = 8, shared-distribution sampling leaves convergence unconstrained but caps four-step divergence success at 0.27.The single-step divergence bound is 7/8, even when the distribution is retuned as targets are taken.Source: §4.3 · p. 6
• With per-agent distributions, larger minimum pairwise distance raises the divergence bound, while larger maximum distance lowers the convergence bound.The two demands apply per target: distributions should separate for targets to divide and overlap for targets to share.Source: §4.3 · p. 6

5.1 EXPERIMENTAL SETUP

• The evaluation runs concurrent, non-communicating agents on DivvyBench, GovSim, and Overcooked, with one shared LLM backbone and prompts differing by public role.DivvyBench uses two agents choosing among targets; GovSim has five agents harvesting a shared pool; Overcooked has two agents sharing single-use stations.Source: §5.1 · p. 7

5.2 RESULTS

• ToS is the only method that succeeds on all three benchmarks and outperforms every baseline on almost every metric.The reported comparison covers DivvyBench, GovSim, and Overcooked.Source: Table 1 · p. 8
• ToS leads at both the first step and the step after the first failure, while its resource pool stabilizes and ends each GovSim scenario above every baseline.Figure 3 compares DivvyBench progress rates at the two steps and GovSim resources over the horizon.Source: §5.2 · pp. 7–8, Figure 3 · p. 8
• Removing task coupling degrades all DivvyBench settings and GovSim, while removing role gating lowers Overcooked and GovSim performance.DivvyBench alone is unaffected by removing role gating because task context plus public role suffices; Overcooked barely changes without task coupling because its recipe states the ordering.Source: §5.2 · p. 8, Table 2 · p. 9
• Reordering ToS’s readings or withholding other agents’ actions does not significantly lower performance.The latter is a stronger test because every ToM baseline depends on those actions.Source: §5.2 · pp. 8–9
• Giving Classic ToM both ToS readings still fails to match ToS on GovSim survival and DivvyBench Cooperative success.ToS conditions actions on both readings, whereas Classic ToM uses them through its prediction; the table compares Classic ToM variants with ToS’s readings.Source: §5.2 · p. 9, Table 3 · p. 9

6 CONCLUSION

• The symmetry trap is the double failure to divide contested targets and converge on shared targets.The paper concludes that reasoning from the shared scene serves non-communicating coordination better than predicting other agents.Source: §6 · p. 9

A.1 IMPACT OF THE PUBLIC ROLE

• At temperature 0, leader/follower labels reach 100% in all three DivvyBench settings and reduce Mixed stuck steps from 9.8% to 6.4%.An index carries the same 1 bit but reaches 92.7% in Competitive; identical descriptions leave Competitive at 0.7%.Source: §A.1 · p. 14, Table 4 · p. 14
• Cooperative success remains 100% with no stuck steps even under identical descriptions, since selecting one shared target requires agreement rather than distinct roles.Source: §A.1 · p. 14
• At the highest temperature, identical descriptions reach only 11.3% in Competitive, while temperature raises the index result from 92.7% to 99.3%.Temperature adds nothing to leader/follower labels, which already complete all three settings at temperature 0.Source: §A.1 · p. 14, Table 4 · p. 14

A.2 IMPACT OF OBSERVATION ASYMMETRY

• Only ToS succeeds in all three settings under reversed or shuffled observations, deriving a canonical target order and dividing it by role.Baselines improve in Competitive but collapse in Cooperative; in Mixed, every baseline collapses.Source: §A.2 · pp. 14–15, Table 5 · p. 15

A.3 IMPACT OF THE MODEL BACKBONE

• Across three additional backbones, ToS remains near-perfect and has the highest average, while baseline success and ranking vary sharply by backbone.ToS derives its coordination decision from the scene, which does not vary with the backbone.Source: §A.3 · p. 15, Table 6 · p. 16

A.4 IMPACT OF HETEROGENEOUS MODELS

• Against different backbones, Classic ToM is the strongest baseline but trails ToS by 16.2 points against Gemma-4-26B and 32.0 against Qwen3.5-9B.A weaker partner breaks symmetry but does not significantly raise baseline scores; ToS is unchanged in both pairings.Source: §A.4 · p. 16, Table 7 · p. 16

A.5 IMPACT OF HETEROGENEOUS REASONING SCHEMAS

• Every baseline scores above its homogeneous result beside an agent using a different reasoning schema, but none reaches ToS's success.ReAct's Cooperative score falls beside an unlike schema, while the other baselines do not show that decline.Source: §A.5 · p. 17, Table 8 · p. 17

A.6 IMPACT OF THE NUMBER OF AGENTS

• ToS stays near-perfect across all 12 DivvyBench panels as teams grow from 2 to 5 agents, while every baseline declines in Cooperative and Mixed.When each agent independently selects a shared target with probability p < 1, round success is about p^N.Source: §A.6 · p. 17, Figure 4 · p. 18
• With GovSim's pool fixed at capacity 100, ToS sustains the commons for more than half the horizon at 50 agents, while every baseline has all but collapsed.The sustainable share per agent falls as the population grows; at 100 agents survival requires half to harvest one unit and half to harvest nothing.Source: Figure 5 · p. 18, §A.6 · p. 18
• At 100 agents, ReAct, Focal, Classic ToM, and ProAgent each leave more than 20% of the population over-taking in the first round, while ToS's over-takers are negligible.ToS divides the sustainable harvest by the number of agents read from the scene.Source: Figure 6 · p. 19, §A.6 · p. 19

A.7 IMPACT OF THE INTERACTION HORIZON

• In a 120-round Fishery run, ToS sustains harvesting to the end with the pool still at capacity, while CFD and HypMinds lose theirs earlier.ToS also harvests the most over the rounds when all three methods remain alive.Source: §A.7 · p. 19, Figure 7 · p. 20
• In Pasture and Pollution, half of ToS runs have ended by rounds 12 and 28, respectively, after a single round of harvesting nearly the whole pool.Near-sustainable harvesting in ordinary rounds is insufficient protection against this irreversible-resource failure.Source: §A.7 · p. 20

A.8 FAILURE OF THEORY OF MIND

• Competitive ToM prediction accuracy stays near 30% after history arrives, while Cooperative accuracy remains above 70% with or without history.ProAgent and HypMinds are within a few points of Classic ToM on later Competitive steps.Source: Table 9 · p. 20, §A.8 · p. 20
• At 100 agents, HypMinds names 92 of 99 teammates and Classic ToM names 26, while ProAgent names 6 and holds prediction-loss decisions to 7%.Long or unparsable predictions remove 48% of HypMinds's and 37% of Classic ToM's decisions at that population size.Source: §A.8 · p. 21, Figure 8 · p. 21
• ToS conditions on the shared scene without per-agent prediction cost, so its reasoning does not lengthen as the team grows.Source: §A.8 · p. 21

A.9 ANALYSIS OF PER-AGENT DISTRIBUTIONS

• 0.780 is ToS’s distance between agent distributions in Competitive DivvyBench, versus 0.480 for the highest baseline, CFD.Across Cooperative and Competitive settings, ToS changes the distance by 0.780, compared with 0.440 for CFD; Cooperative distances are near 0 for every method.Source: §A.9 · p. 21, Table 10 · p. 22

A.10 CONFIDENCE INTERVALS AND SIGNIFICANCE TESTS

• 35 of 36 ToS-versus-baseline comparisons are significant; the exception is ReAct in DivvyBench Cooperative, where p = 0.054.ReAct scores 96.7% against ToS’s 100.0%; the interval excludes zero, but the permutation test is more conservative.Source: Table 11 · p. 22, §A.10 · p. 22

B PROOFS OF PROPOSITIONS

• Convergence requires δ_max = 0, while divergence requires that no agent pair select the same target.The proof identifies pairwise selection overlap as a necessary constraint on team-level convergence and divergence.Source: B PROOFS OF PROPOSITIONS · p. 23
• For divergence, the probability is bounded by 1 − (1 − δ_min)^2/K, and divergence with probability 1 requires δ_min = 1.At δ_min = 0, the bound reduces to 1 − 1/K, the two-agent case of Proposition 4.1.Source: B PROOFS OF PROPOSITIONS · p. 23

C.1 CONFIGURATION AND BENCHMARKS

• The evaluation covers introduced DivvyBench and existing GovSim and Overcooked, with communication removed from the latter two coordination settings.GovSim uses a shared regenerating pool; Overcooked requires two cooks to divide a single-use-station recipe pipeline. The implementation disables backbone thinking mode and repairs several common invalid-JSON forms.Source: §C.1 · p. 24, Table 12 · p. 24, Table 13 · p. 24

C.2 DIVVYBENCH

• DivvyBench uses eight targets and simultaneous, message-free actions; Competitive targets require exactly one selector, Cooperative targets require all agents, and Mixed combines both rules.The three task types run across Tabletop, Airspace, and Household scenarios; success measures completion within 10 steps, while Stuck measures steps taking nothing.Source: §C.2 · pp. 24–25

C.3 GOVSIM

• GovSim has agents privately harvest from one regenerating pool for up to 12 rounds, with both communication and the universalization hint removed.The pool collapses below five units; Survival measures rounds before collapse and Total Gain sums harvested units.Source: §C.3 · pp. 25–26

C.4 OVERCOOKED

• Overcooked uses two agents in an open kitchen with shared, single-use stations, and removes the request action that could send another agent an instruction.Because success is nearly universal, the evaluation reports throughput; its level-normalized ×ReAct measure puts difficulty levels on a common scale.Source: §C.4 · p. 26

D.1 DIVVYBENCH

• DivvyBench prompts provide the task description, rules, public role, current state, legal actions, history, and the method’s reasoning schema.The three settings share a prompt apart from the rules block.Source: §D.1 · p. 27, Figure 10 · p. 27, Figure 11 · p. 27

D.2 THEORY OF SCENE

• The implemented ToS schema separates planning the division of labor from selecting an action copied verbatim from the legal actions.The comparison methods use the same split schema.Source: §D.2 · p. 29, Figure 15 · p. 29

E THEORY OF SCENE REASONING EXAMPLES

• ToS examples show overlapping ownership on DivvyBench and GovSim but already-divided ownership on Overcooked, alongside Joint, Exclusive, and Sequential task couplings.The Tabletop Mixed example applies Joint coupling before Exclusive coupling; the Overcooked example advances stages of a recipe pipeline.Source: E THEORY OF SCENE REASONING EXAMPLES · p. 30, Figure 16 · p. 30, Figure 17 · p. 30