Warned alike, AI agents avoid the less-crowded road while people take it

Introduction

• A shared message can link otherwise separate decisions when many agents interpret it alike, affecting access to limited capacity.The authors frame this as a resource-allocation problem relevant to roads, computing services and electricity demand.Source: Introduction · p. 1
• The study asks whether a shared forecast of others’ reactions can sustain costly avoidance despite repeated feedback and opportunities to deviate.A further question is whether people sharing the resource with aligned agents bear a different burden.Source: Introduction · p. 2
• The authors manipulate broadcasts in a congestion game and compare model populations, all-human groups and mixed groups.The reported results include persistent crowding by the primary model population, near balance in all-human groups, and unequal costs across seat types in mixed groups.Source: Introduction · p. 2

One warning produces persistent concentration

• 95 min under the tip plus warning versus 64 min under the bare tip: the 50-agent primary population concentrated on one road, with I = 0.47 and M = 0.07.All ten warning runs met the descriptive frozen criterion; at a 47:3 split, a crowded-road agent could save 69 min by switching alone, and the state persisted through round 100.Source: One warning produces persistent… · p. 4

Changing the broadcast changes the collective dynamics

• Changing the broadcast from warning to numerical reports immediately raised switching in all five seeds, and travel time later declined from 92 min before intervention to 67–74 min.Changing from numbers to warning induced avoidance; these interventions changed both the warning and information format.Source: Changing the broadcast changes the… · p. 4

Dose–response, and the benefit of warning a minority

• In 20-agent populations, warning exposure produced a non-monotonic response: median travel time was 71, 65, 69, 80 and 95 min at 0, 5, 10, 15 and 20 warned agents.A linear mixture approximated the response shape but under-predicted imbalance near the minimum.Source: Dose–response, and the benefit of… · pp. 4, 6

Numerical feedback and message variants define the effect’s limits

• Explicit travel-time feedback reduced warning-condition travel time from 95 to 86 min, but strong avoidance remained and two of five runs still met the frozen criterion.Other message variants and model families did not uniformly reproduce the complete frozen state, marking boundaries to the effect.Source: Numerical feedback and message… · p. 6

Reasoning changes the collective outcome but does not consistently remove avoidance

• The warning reduced average tip-following in all three tested model families, while Claude and Gemini’s opposing cost-component changes reduced their net cost increases.Reasoning settings also altered whether populations froze, but responses shifted toward avoidance where avoidance was not already complete.Source: Average response and temporal… · p. 8, Reasoning changes the collective… · p. 8

Human groups remain near balance under both tested broadcasts

• All-human groups stayed near balance under both broadcasts, with I = 0.09 and mean travel times of 62.0 min under numbers and 61.8 min under the warning.The small number of rooms and intervals do not establish equivalence between conditions.Source: Human groups remain near balance under… · p. 8

Individual response patterns differ between human and model populations

• Human tip-following tendencies were more dispersed and reproducible across session halves than GPT tendencies, while GPT switching under warning was 0.03 after a slow day and 1.00 after a fast day.Human switching probabilities changed little by prior travel-time category; these summaries describe experienced-payoff responses without directly measuring beliefs.Source: Individual response patterns differ… · p. 9

Human choices shift in mixed groups, with unequal costs by seat type

• Mixed-room imbalance increased by 0.0951 per five additional agents, while agents largely avoided the tip and human tip-following rose with agent share.In K = 15 rooms, human tip-following averaged 0.91, and within-session increases were observed in most K = 10 and K = 15 rooms.Source: Human choices shift in mixed groups,… · p. 11

Discussion

• The warning sustained costly avoidance in the primary model, but the frozen state was not universal across model families or reasoning settings.The primary model with reasoning enabled and two other model families shifted toward avoidance without freezing; a newer model froze under the tip alone.Source: Discussion · p. 12
• The authors interpret persistent avoidance as alignment between similar decision rules and a shared warning that discourages the migration it predicts.The primary model stayed near balance under the tip alone, indicating that homogeneity did not concentrate choices under every message.Source: Discussion · p. 12
• For Claude and Gemini, the warning increased average tip-following bias but reduced its variation across rounds, limiting the net cost increase.Warning only a minority also reduced costs relative to uniform numerical reports or uniform warnings.Source: Discussion · p. 12
• In mixed groups, imbalance rose and mobility fell with agent share, while human choices increasingly favored the road agents avoided.At K = 15, human and agent seats averaged 44 and 80 min, respectively; dispersed human tendencies may help explain balance, but the design does not isolate their contribution.Source: Discussion · p. 12
• The experiments manipulate a shared anticipatory message without direct communication, extending work on algorithmic monoculture and routing behavior.Choices remain coupled through congestion, unlike conventions developed through explicit agent interactions.Source: Discussion · p. 12
• Evaluation of resource-sharing agents should test populations and message exposure, and report costs by participant type as well as group averages.Seat costs in this game do not establish client losses; testing that deployment hypothesis requires comparisons under alternative messages and exposure patterns.Source: Discussion · pp. 12–13
• The findings are bounded by a two-road symmetric game with immediate feedback, and mixed-group composition effects need stronger causal testing.The authors note recruitment-order and amendment issues, shared recruitment windows, and recommend independent replication across days with random allocation of ready participants.Source: Discussion · pp. 12–13

Congestion game

• Two identical roads impose travel times of 20 + 80n/N minutes, and the round mean weights each road’s time by its commuter share.Analysis windows vary by study; the persistence extension is summarized separately over rounds 61–100.Source: Congestion game · p. 13

Language-model agents

• Each agent receives a separate stateless model call with its own recent road and travel history, a time-sensitivity trait, and the broadcast.Agents are asked to consider expected travel times and others’ responses, then return a route and one-sentence reason; provider sampling seeds were not supplied.Source: Language-model agents · pp. 13–14

Multinomial-logit learning baseline

• The multinomial-logit baseline updates experienced-road estimates and, under numerical reports, both road estimates; it cannot interpret the warning sentence.Choice probabilities use a sensitivity-weighted estimate, while tips and tips plus warnings each reduce the indicated road’s effective estimate by four minutes.Source: Multinomial-logit learning baseline · p. 14

Computational experiments

• The prespecified computational core compared four broadcast conditions across ten paired seeds, with 50 agents and 60 rounds per run.The two prespecified claims compared language-model and multinomial-logit responses to numerical reports and tested the warning against the bare tip.Source: Computational experiments · p. 14
• The computational extensions varied histories, warning strength, labels, wording, model family, numerical reports, and reasoning settings, with later extensions described as exploratory.The cross-provider and numeric extension was descriptive, and sampling variation could not be separated from change over time.Source: Computational experiments · p. 15

Human benchmark

• The all-human benchmark assigned 240 participants to twelve 20-person rooms receiving numerical reports or the tip and warning, and analyzed 40 rounds.Participants were recruited through Prolific in a nonprobability, opt-in online sample; one room was excluded only from a registered per-protocol sensitivity analysis.Source: Human benchmark · p. 15

Mixed-group experiment

• The mixed study placed 5, 10, or 15 GPT agents in each of 24 rooms with 20 seats, and tested the mean within-block imbalance slope as its primary statistic.Composition was associated with arrival order because larger human quotas were filled first, limiting causal interpretation; outcomes used rounds 6–40.Source: Mixed-group experiment · pp. 15–16

Registration and study periods

• Human-study plans were registered, while computational core hypotheses were fixed in an execution-time code freeze; treatment comparisons used rooms or runs as units.Other comparisons were descriptive, and individual-level analyses were not treatment-effect tests.Source: Registration and study periods · p. 16, Statistics · p. 16

• Takahiro Ezaki, Naoto Imura, and Katsuhiro Nishinari are named in the supporting-information material.Source: Supporting Information for Warned… · p. 20
• The supporting-information file includes sections S1–S10, Figures S1–S10, and Tables S1–S14.Source: Supporting Information for Warned… · p. 20

S1. Verbatim agent prompt and request parameters

• The prompt presents two physically identical roads whose travel times depend on commuter counts, and asks agents to decide independently before seeing actual traffic.It supplies an individual sensitivity trait, recent personal travel history, and the broadcast, and asks agents to consider others’ reactions to the same information.Source: S1. Verbatim agent prompt and request… · p. 20
• Agents return a route and a one-sentence reason in a JSON object, with no additional text.Source: S1. Verbatim agent prompt and request… · p. 20
• Primary-model request logs record a configuration that did not request extended reasoning, but they do not independently verify provider-side implementation.The recorded settings covered the core decisions and individual-level traces.Source: S1. Verbatim agent prompt and request… · p. 21
• Run seeds fix starting assignments, traits, road-label mapping, and baseline random draws, but not the sequence of model samples.The drift-control reruns combine sampling variability with any change over time.Source: S1. Verbatim agent prompt and request… · p. 21

S2. Verbatim broadcasts

• F0 provides no traffic broadcast, F1 reports yesterday’s travel times, and F2 identifies the currently less-crowded road.Source: S2. Verbatim broadcasts · p. 21
• F3 adds that many drivers may see the same advisory and switch, potentially making the named road congested.Source: S2. Verbatim broadcasts · p. 21
• F4 strengthens the warning by saying the route may become more congested and that blindly following the advisory could backfire.Source: S2. Verbatim broadcasts · p. 21
• When previous-round counts tied, F1 reported equal times, while F2 and F3 still named a road using a fixed tie-break.The human studies used the F1 and F3 texts verbatim with the same label convention.Source: S2. Verbatim broadcasts · p. 22

S3. Multinomial-logit learning baseline

• Under F1, the multinomial-logit baseline oscillates (I = 0.44, M = 0.88), and its F0-to-F1 change is contrasted with the language-model population’s change on the same seeds.Because the baseline does not represent the warning sentence, its F2 and F3 conditions are identical by construction; the contrast describes one prespecified adaptive policy, not why the language model responds to F3.Source: S3. Multinomial-logit learning baseline · p. 22

S4. Outcomes, ties, classifier, prespecified tests and reason coding

• Tip-following excludes rounds preceded by equal road counts, while imbalance, switching and travel time retain those rounds.The analysis window begins at round 6, and mobility includes the transition from round 5 to 6.Source: S4. Outcomes, ties, classifier,… · p. 22
• The frozen classifier requires I ≥ 0.25, M ≤ 0.20 and ten consecutive rounds with the same majority road; trajectory labels are descriptive, not equilibrium tests.The two prespecified core claims concern the F0-to-F1 interaction and the F3-minus-F2 contrast, tested on ten paired seeds with Holm adjustment.Source: S4. Outcomes, ties, classifier,… · p. 22
• Human tip-following tendencies were more dispersed and more stable across halves than GPT tendencies under both F1 and F3, but the pooled correlations retain shared room histories.For example, human split-half correlations were 0.73 under F1 and 0.81 under F3, versus 0.14 and 0.23 for GPT; reason codes classify stated text, not internal reasoning.Source: S4. Outcomes, ties, classifier,… · p. 23

Cost identity and tie rounds

• On tie-free rounds, the cost identity expresses mean travel time through the population variance of tip-following, and the relation holds for any population or room composition.Primary travel-time summaries elsewhere include all rounds, so they can differ from the tie-free mean.Source: S5. The cost identity, tie rounds, the… · p. 23

Mixing rule

• The linear mixing rule predicts a minimum near 30% warning exposure, but under-predicts imbalance near that minimum: 0.14 was observed for 5 of 20 warned and 0.13 for 12 of 50.The constant-mean approximations reproduce the broad U-shape but do not isolate temporal adaptation or dependence as the cause of the discrepancies.Source: S5. The cost identity, tie rounds, the… · p. 23
• The dashed reference near K = 0 first reaches balance because the all-human mean tip-following tendency is just above one-half; fractional agents were not tested.Source: S5. The cost identity, tie rounds, the… · p. 24

Bounds in mixed rooms

• At K = 15, agents occupied one road in a mean 80% of rounds, and the bound given their actual choices yielded mean imbalance 0.238 versus observed 0.241–0.293.At K = 5 and K = 10, that bound's mean was zero.Source: S5. The cost identity, tie rounds, the… · p. 24
• With K = 10 and K = 15, the predicted imbalance from observed human tip tendencies was 0.084 and 0.272, versus all-round observed means of 0.085 and 0.259.The comparisons also reflect occasional agent tip choices and, at K = 10, different treatment of tie rounds; they do not test independence among humans.Source: S5. The cost identity, tie rounds, the… · p. 24

S6. Switch experiments round by round

• Under F3→F1, 96–100% of agents chose the previously less-crowded road in round 31, but travel time remained 94–100 min; rounds 36–50 averaged 67–74 min.Under F1→F3, no agent chose the tipped road in round 31, and rounds 36–50 averaged 91–96 min; F3→F1 tests replacement of the entire message, not deletion of the warning alone.Source: S6. Switch experiments round by round · p. 24

S7. Human study

• The two human studies analyzed 240 participants each, and the twelve benchmark rooms assigned two F1 and two F3 rooms per block using within-block randomization.Participants were told their bonus depended on their own mean travel time, not their rank or group performance, and unlike agent instructions were not asked to anticipate others’ reactions.Source: S7. Human study · pp. 24–26
• The last B1 retry was authorized after the three completed B1 rooms had already been inspected descriptively; the report states that failed-attempt entrant counts are incomplete.Source: S7. Human study · p. 25
• For all-human rooms, the F3-minus-F1 descriptive estimates were I = −0.005 and M = +0.026, with no confirmatory alpha; non-rejection does not establish equivalence.The mean travel-time estimate was −0.22 min, with a 95% interval of −0.53 to +0.07.Source: S7. Human study · p. 26

S8. Mixed-group experiment: completion, analysis and limitations

• The final sample comprised 24 complete 40-round rooms with 240 humans and 240 agent seats, after technical failures and unformed rooms were replaced or completed.The completion amendments followed the authors’ review of earlier behavioral results; recruitment order and waiting could also associate composition with arrival time, limiting causal interpretation.Source: S8. Mixed-group experiment:… · p. 26
• The primary contrast compared imbalance in each block’s 15-agent and 5-agent rooms, divided by two to express the difference per five additional agents.Eight block slopes were averaged; K = 10 rooms show the intermediate response but do not enter this endpoint contrast.Source: S8. Mixed-group experiment:… · pp. 26–27
• The registered sign-flip test assumes independent, symmetric block errors, while recruitment windows could link blocks and the procedure did not guarantee independence.Pairing blocks by four original recruitment windows limited the test to 16 sign combinations, with a minimum p = 0.0625; grouping all shared-window connections left four combinations and a minimum p = 0.25.Source: S8. Mixed-group experiment:… · p. 27
• All eight imbalance slopes were positive, averaging +0.0951 per five additional agents (p = 1/256); all eight switching slopes were negative (mean −0.2080, p = 1/256).Reversing signs by original recruitment pairs gave p = 0.0625 for both outcomes; grouping all shared-window connections gave p = 0.25, so the primary evidence remains conditional on independence.Source: S8. Mixed-group experiment:… · p. 27
• Humans’ estimated AI shares averaged 63.1%, 67.2% and 68.9% for actual shares of 25%, 50% and 75%, respectively.Estimates came from one optional post-task question; the study did not test beliefs or use them for primary adjustment or exclusion.Source: S8. Mixed-group experiment:… · p. 28
• Every K = 15 room had higher imbalance than every K ≤10 room, and later-room ranges overlapped initial ranges, but date checks do not remove collection-date or recruitment confounding.The later K = 15 rooms had I = 0.241–0.260 versus 0.244–0.293 initially; replacement K = 5 rooms had I = 0.061 and 0.069 versus 0.059–0.091 initially.Source: S8. Mixed-group experiment:… · p. 28
• Across compositions, mean adjacent contrasts were +0.0161 and +0.1741 for I, and −0.2991 and −0.1170 for M, from K = 5 to 10 and K = 10 to 15, respectively.Mean curvature was +0.1580 for I and +0.1821 for M.Source: S8. Mixed-group experiment:… · p. 28
• Carryover and waiting-time sensitivity grids preserved positive mean I slopes and negative mean M slopes; the no-timeout slopes were +0.0974 for I and −0.2121 for M.The authors describe the grids as sensitivity to hypothetical bias, not identified causal adjustments.Source: S8. Mixed-group experiment:… · pp. 27–28

S9. Reasoning and current-model extension

• The extension tested five request settings under F2 and F3 at seeds 3–7, using 50 agents and 60 rounds; its plan fixed the design and descriptive analyses before formal runs.The plan named medians, but the report gives means; no significance criterion was added, and reasoning-enabled requests omitted temperature.Source: S9. Reasoning and current-model… · pp. 28–29
• Without reasoning at temperature 1.0, GPT-5.4-mini reproduced the core pattern at every seed, with all five F3 runs frozen and all five F2 runs near equilibrium.F3 travel time was 2.5 min lower and switching 0.036 higher than in same-seed core runs; these differences combine the temperature change with any change since the core runs.Source: S9. Reasoning and current-model… · p. 29
• With low or medium reasoning, no GPT-5.4-mini run froze, but the warning raised imbalance and travel time and lowered switching in each of ten pairs.Compared with no reasoning at temperature 1.0, warning-condition travel time was 70.0 min at low effort and 74.7 min at medium effort, versus 91.5 min; avoidance was weakened, not eliminated.Source: S9. Reasoning and current-model… · p. 29
• GPT-6 Luna without reasoning moved toward warning-associated avoidance in all five pairs without freezing, while default medium reasoning froze in all ten runs under both the tip and warning.At default medium reasoning, the warning made no consistent difference across pairs.Source: S9. Reasoning and current-model… · p. 29
• Visible reasons under the warning referred to other drivers switching or crowding in 81–86% of GPT-5.4-mini decisions and 80–83% of Luna decisions.The corresponding core share was 89%; under the bare tip, Luna with reasoning had 88%, against 61% in the core.Source: S9. Reasoning and current-model… · p. 29
• The extension script recomputes the reported numbers and tables and first checks that the core run table and reason codes are reproduced.The experiment plan and client-side attempt log were stored with the runs.Source: S9. Reasoning and current-model… · p. 29

S10. Reproducibility of the analysis

• The authors report that the private Zenodo draft and GitHub repository were not publicly accessible at preprint time, with public release planned upon journal publication.The reserved DOI was not yet an active public record.Source: S10. Reproducibility of the analysis · p. 30
• Released observations, scripts, summary data, hashes, and registration materials support figure reconstruction and numerical checks without restricted exports or new provider requests.Original-source reconstruction requires restricted exports; age and gender are available only as aggregate counts.Source: S10. Reproducibility of the analysis · p. 30
• A validation record documents checks of room outcomes, automation estimates, manuscript quantities, figures, and reasoning-extension analyses.The record also specifies that paths elsewhere in the supporting text are relative to the manuscript/paper directory unless stated otherwise.Source: S10. Reproducibility of the analysis · p. 30

Supplementary Figures

• Figure S1 tracks physical Route A shares across four core conditions, 50-agent runs, and ten seeds per condition.Seed-dependent parity maps road labels to physical roads, so frozen runs can concentrate on either road.Source: Figure S1 · p. 31
• Figure S2 compares route imbalance, switching, travel time, and tip-following for Claude Haiku 4.5 and Gemini 3.5 Flash under two messages across five matched seeds.Source: Figure S2 · p. 32
• Figure S3 compares September runs with August runs at matched environment seeds, distinguishing repeated F3 runs from numeric-report variants.The diagonal marks equal outcomes, not identical model samples.Source: Figure S3 · p. 32
• Figure S4 shows every run in the 20- and 50-agent exposure grids and Route A shares in three runs where 38 of 50 agents received the warning from round 31.Source: Figure S4 · p. 33
• Figures S5–S8 cover human physical-route shares, GPT tip-following, mixed-room outcomes, and the completed mixed-experiment record.Figure S7 distinguishes human and GPT seat shares on the tip road and reports room imbalance and travel times; Figure S8 records the 24 registered slots, including two aborted attempts.Source: Figure S5 · p. 33, Figure S6 · p. 33, Figure S7 · p. 34
• Figures S9–S10 show post-task estimates of the automated share and reasoning/current-model results across request settings and paired seeds.Figure S9 reports respondent and room estimates by composition; Figure S10 summarizes four outcomes under the tip and tip-plus-warning conditions.Source: Figure S9 · p. 35, Figure S10 · p. 36

Supplementary Tables

• Table S1 summarizes condition-level median outcomes; Tables S2–S4 list core and extension runs and robustness variants.The S1 caption defines E[ft] and the frozen-run count; S4 reports means across runs and analysis windows.Source: Table S1 · p. 37, Table S2 · p. 38, Table S3 · p. 39
• Tables S5–S7 cover human-room outcomes, questionnaire counts, and exposure grids with linear-mixing and independent-choice benchmarks.Source: Table S5 · p. 41, Table S6 · p. 41, Table S7 · p. 42
• Table S8 summarizes 24 mixed rooms, distinguishing human and GPT seats; the two invalid original attempts remain separate in the execution record.Source: Table S8 · p. 43, Supplementary Tables · p. 43
• Table S9 records switch-experiment outcomes by round, while Tables S10–S11 report registered block slopes and descriptive nuisance-sensitivity calculations.The S11 calculations are not estimated causal corrections.Source: Table S9 · p. 44, Table S10 · p. 45, Table S11 · p. 45
• Table S12 summarizes recovered formal estimates by composition, and Table S13 reports reasoning/current-model extension outcomes across five paired seeds.S12 defines response counts, bias, and mean absolute error; S13 gives paired differences and counts of pairs matching the core warning-effect direction.Source: Table S12 · p. 45, Table S13 · p. 46
• Table S14 lists all 50 reasoning and current-model extension runs; tie rounds are excluded from E[ft] and state labels follow the descriptive classifier.Source: Table S14 · p. 47