Organizations: Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan · Department of Aeronautics and Astronautics, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
AI agents built on a few shared models increasingly act for many people. A shared forecast about others can align their choices and change how scarce capacity is allocated. We tested this feedback in a two-road congestion game. Adding one sentence warning that others might follow a routing tip made populations of 50 GPT agents crowd one road while avoiding the nearly empty alternative. Average travel time rose from 64 to 95 min, although any crowded-road agent could have saved 69 min by switching alone. The warning discouraged the very move it predicted. The pattern persisted for 100 rounds. Two other model families shifted the same way without locking onto one road. Twelve all-human groups (240 participants) stayed near balance under numerical reports or the tip and warning. In 24 mixed groups with a further 240 participants, imbalance grew with the share of agents in the registered analysis, while people increasingly took the road the agents avoided. Collective costs stayed below the allagent reference, but with 15 agents and 5 humans, agent seats averaged 80 min, compared with 44 min for human seats. Shared forecasts can thus sustain collective inefficiency among similar agents. A better group average can also hide an unequal burden. Evaluations of AI agents that share resources should test populations, treat messages as interventions and report who bears the costs.
Figures & tables
Figure 1: A shared warning produces persistent concentration in the primary model population. ( A ) The game: two identical roads, N commuters choosing simultaneously every round, travel time increasing linearly with a road’s share of commuters (inset). ( B ) The four daily broadcasts (verbatim). ( C to F ) For each condition of the prespecified core (50 GPT agents, 60 rounds, ten seeds), the upper strip shows the share of agents on physical Route A in one representative run (seed 3): lockstep oscillation under no report, damped oscillation under numbers, near-balance under the tip, and persistent concentration on one road under the tip plus warning. The main panel shows the share choosing the road that was less crowded in the previous round, f^t , for all ten runs (thin lines; thick line, median; number, median of run-mean travel time). ( G ) The ten F3 runs continued to round 100 (shaded). ( H ) Route imbalance I against switching fraction M for all 40 runs (filled) and for the multinomial-logit learning baseline on the same seeds (hollow); the shaded region marks the descriptive frozen criterion. ( I ) Mean travel time per run (bars, medians; dashed, balanced use; dotted, expectation for independent coin flips). ( J ) Paired F2 → F3 change in mean travel time by seed.
Figure 2: The collective state follows the message currently in force. ( A to C ) f^t when the broadcast is changed at round 31 (dashed line): the tip plus warning replaced by numerical reports (F3 → F1; A, five seeds), numerical reports replaced by the tip plus warning (F1 → F3; B, five seeds), and the warning given to 38 of 50 agents while the rest keep receiving numbers (C, three seeds); numbers give mean travel time in rounds 16–30 and 36–50. In A, 96–100% choose the previously less-crowded road in the first post-switch round; 86–98% actually change roads, and congestion remains high before costs subsequently decline. ( D , E ) Imbalance and mean travel time against the fraction of agents receiving the warning while the rest receive numbers (points, runs; lines, medians; diamonds, pure populations); dashed curves, linear mixing of the two pure populations’ tip-following shares with no fitted parameter, which approximates the shape but under-predicts cost near the minimum. ( F ) Appending yesterday’s travel times to the tip or to the tip plus warning: ⟨fˉ⟩ and the median run-mean travel time per cell. ( G ) Run-mean travel time (dot, median across runs; bar, range) for message, history and model variants; windows are rounds 6–40 for the 20-seat history variants and 6–60 for the remaining runs. ⟨fˉ⟩ is shown where round-level data are available. ( H ) Share of agents’ stated reasons that invoke other drivers switching to or crowding a road (solid) or the agent’s own slow recent commute (light), seed 3, 2,750 decisions per condition (coding rules in Materials and Methods).
Figure 3: Average response and temporal variation contribute to cost, while individual response patterns differ. ( A ) Mean travel time on tie-free analysis rounds against fˉ for the core, matched and cross-provider/numeric all-agent runs (color, message; marker, model family), for the twelve all-human rooms (stars) and for the 24 mixed rooms of Fig. 5 (hollow diamonds; room-level share over all seats). The dashed curve is the zero-variance reference from Eq. 1 . Both axes use the same rounds, so each point lies above it by exactly 160VarR(f^t) . ( B ) ⟨fˉ⟩ under the tip and under the tip plus warning for each model family (five to ten runs per point): the warning lowered average tip-following in all three families, from different baselines. ( C ) Decomposition of excess travel time into the average-response component, 160(fˉ−21)2 , and temporal variation, 160Var(f^t) ; components are calculated within each run or room and then averaged with equal weight. For Claude and Gemini, their opposing changes reduce the net cost increase. ( D ) Distribution of individuals’ tendency to follow the tip (share of tie-free rounds 6–40), as a proportion of individuals, for 120 humans (20 × six rooms) and 100 GPT agents (20 × five runs) per condition in 20-seat groups; annotations give the SD, the SD expected for identical choosers at the same mean, and the split-half correlation of individual tendencies. ( E ) Mean individual probability of switching after a slow ( >60 min) or fast ( <60 min) day, for transitions from rounds 6–39 to 7–40. Individuals with no qualifying previous outcome are omitted from that conditional mean. ( F ) Verbatim reasons given by GPT agents under F3.
Figure 4: Humans in the same game. ( A to D ) f^t in six human rooms per condition (Prolific, 20 participants, 40 rounds) and in ten GPT runs of the same size; thin lines, rooms or runs; thick lines, round-wise medians; inset travel times, means across rooms or runs. Gaps mark rounds in which the previous counts were equal. ( E , F ) Imbalance and mean travel time per room or run (points; bars, means); dotted, expectation for independent coin flips; dashed, balanced use. ( G ) Participants’ self-reported usual response to the report in the all-human rooms and in the mixed rooms of Fig. 5.
Figure 5: Human choices change within mixed rooms, with unequal costs by seat type (24 rooms). ( A ) Route imbalance in rooms of 20 with K GPT agents, all under F3 (purple, one point per completed room; bars, means), against the prediction if humans kept their all-human lean (dashed; linear mixing), the lower bound if all agents sit on one road (solid; accounting bound), and the bound given the agents’ actual choices (crosses; mean per K ); non-concurrent all-human and all-agent reference groups are shown at K=0 and K=20 . ( B ) Tip-following share of the human seats and of the agent seats in the same rooms (tie-free rounds 6–40). ( C ) Mean travel time of the human seats, of the agent seats and of the room; dashed, the 60 min of equal sharing. ( D ) Share of human seats (purple, by K ) and of agent seats (orange) choosing the tipped road, round by round, averaged over rooms. ( E ) Human tip-following per room in the specified early (rounds 6–20) and late (26–40) windows; black segments join composition means. Panels summarize all eight rooms per composition; registered block-level inference and dependence sensitivities are reported in the text.
Figure S1: Physical route shares in the prespecified core. Share of agents on physical Route A in every run of the four conditions (50 GPT agents, 60 rounds, ten seeds per condition). Road labels are mapped to physical roads with a seed-dependent parity; frozen runs can therefore concentrate on either physical road.
Figure S2: Cross-provider extension, all paired seeds. Route imbalance, switching fraction, mean travel time and tip-following share for Claude Haiku 4.5 ( A to D ) and Gemini 3.5 Flash ( E to H ) under the tip and under the tip plus warning, five matched seeds each.
Figure S3: Drift control and numeric variants by seed. September 2026 runs compared with August 2026 runs at the same environment seed. Filled points repeat the original F3 condition; hollow points add numerical reports to F3 or F2. The diagonal marks equal outcomes, not identical model samples.
Figure S4: Exposure grid and exposure switch. ( A , B ) Every run of the 20- and 50-agent exposure grids. ( C ) Physical Route A share in the three runs in which the warning was given to 38 of 50 agents from round 31.
Figure S5: Human rooms, physical route share. Share of participants on physical Route A in the six F1 rooms ( A ) and six F3 rooms ( B ).
Figure S6: Individual tip-following tendencies of 50-agent GPT populations. Each agent’s share of tie-free rounds 6–60 on the road that was less crowded in the previous round, seed 3, under numbers ( A ), the tip ( B ) and the tip plus warning ( C ).
Figure S7: Every room of the mixed-group experiment. Columns, K=5 , 10 and 15 GPT agents among 20 seats; first eight rows, blocks 1–8; bottom row, the two original aborted attempts. R and F mark valid rooms from the 16 and 17 September collections, respectively. Purple, share of human seats on the tip road; orange, share of GPT seats on it (both undefined on tie rounds); dashed, room imbalance scaled to 1 when everyone is on one road. Titles give I and the mean travel time of the room and of each seat type over rounds 6–40. Aborted rooms show the rounds played before the server fault.
Figure S8: Design and execution record of the completed mixed-group experiment. Initial and current status of the 24 registered slots by block and K , showing the six valid additional rooms and retaining the two original aborted attempts in the history. All eight blocks are complete (Text S8).
Figure S9: Post-task estimates of the automated share. Actual percentages of 25%, 50% and 75% correspond to K=5 , 10 and 15 of 20 players. ( A ) Formal numeric answers from 116, 76 and 38 respondents; horizontal bars are respondent means. ( B ) The eight room means per composition; bars weight rooms equally. Horizontal jitter only separates points. Dashed lines show accurate estimates. Ten missing answers, including one unsubmitted numeric draft, are omitted; all 240 humans remain in the behavioral analysis. These are descriptive distributions, not independent treatment replicates.
Figure S10: Reasoning and current-model extension. ( A to D ) Route imbalance, switching fraction, mean travel time and tip-following share (rounds 6–60) for each request setting under the tip (F2, green) and under the tip plus warning (F3, orange), five paired seeds each. Gray lines join runs of the same seed; black bars mark means over the five runs. The first setting is the core reference at the same seeds. The numbers at the top of A count runs meeting the frozen criterion, whose thresholds for I and M are dashed (it also requires ten consecutive rounds with the same majority road). Reasoning-enabled requests omitted temperature; its internal numerical value was not independently verified. ( E ) Share of agents on physical Route A in every run.
Population and message
N
rounds
runs
I
M
time (min)
E[ft]
frozen
GPT, F0 no report
50
6–60
10
0.476
0.993
96.4
0.96
0/10
GPT, F1 numbers
50
6–60
10
0.230
0.660
71.5
0.69
0/10
GPT, F2 tip
50
6–60
10
0.134
0.713
64.4
0.54
0/10
GPT, F3 tip + warning
50
6–60
10
0.465
0.070
94.8
0.04
10/10
MNL baseline, F0
50
6–60
10
0.063
0.496
61.0
–
0/10
MNL baseline, F1
50
6–60
10
0.437
0.881
90.7
–
0/10
Table S1: Condition-level summary. Medians across runs or rooms of run-mean outcomes; E[ft] is the mean across runs of the run-mean tip-following share (tie-free rounds); “frozen” counts runs meeting the descriptive classifier. MNL, multinomial-logit learning baseline.
Condition
seed
I
M
time (min)
E[ft]
Var(ft)
F0
3
0.478
0.993
96.7
0.978
0.0006
F0
4
0.433
0.993
90.1
0.933
0.0005
F0
5
0.474
0.995
96.0
0.974
0.0003
F0
6
0.492
0.995
98.9
0.992
0.0009
F0
7
0.487
0.990
98.3
0.987
0.0018
F0
8
0.414
0.988
87.6
0.914
0.0011
Table S2: All 40 runs of the prespecified core (50 GPT agents, rounds 6–60; the core was fixed by an execution-time code freeze, not publicly registered).
Model
message
seed
I
M
time (min)
E[ft]
state
GPT-5.4-mini
tip + numbers
3
0.334
0.756
80.1
0.833
oscillation
GPT-5.4-mini
tip + numbers
4
0.287
0.715
76.1
0.787
oscillation
GPT-5.4-mini
tip + numbers
5
0.337
0.761
80.7
0.837
oscillation
GPT-5.4-mini
tip + numbers
6
0.329
0.776
79.5
0.829
oscillation
GPT-5.4-mini
tip + numbers
7
0.329
0.768
79.6
0.829
oscillation
GPT-5.4-mini
tip + warning + numbers
3
0.402
0.192
86.4
0.098
frozen
Table S3: All 33 runs of the September 2026 extension (50 agents, rounds 6–60). State labels follow the descriptive classifier in Text S4; “partial” denotes runs meeting none of its frozen, oscillation or near-equilibrium criteria.
Variant
runs
I
M
time (min)
frozen
F3, full history (rounds 6–40, 20 seats)
5
0.479
0.041
96.9
5/5
F1 + past tips in history (20 seats)
5
0.247
0.492
72.6
0/5
F3 + past tips in history (20 seats)
5
0.497
0.005
99.6
5/5
F3, stronger wording (50 agents)
3
0.499
0.003
99.8
3/3
Claude/Gemini, F0 (2 seeds each)
4
0.249
0.835
73.3
0/4
Claude/Gemini, F1 (2 seeds each)
4
0.361
0.917
83.1
0/4
Table S4: Robustness variants (means across runs; from the audited run table). Rounds 6–40 for 20-seat variants and 6–60 otherwise.
Room
block
message
I
M
time (min)
E[ft]
tie rounds
pure-b1-2
1
F1
0.089
0.420
61.9
0.527
4
pure-b1-3
1
F1
0.086
0.467
61.8
0.508
5
pure-b2-roomwise-r1-2
2
F1
0.094
0.353
62.3
0.505
4
pure-b2-roomwise-r1-4
2
F1
0.093
0.457
62.0
0.503
5
pure-b3-roomwise-r3-1
3
F1
0.081
0.397
61.7
0.524
4
pure-b3-roomwise-r3-2
3
F1
0.103
0.484
62.2
0.517
2
Table S5: Human rooms (rounds 6–40; carried choices retained). E[ft] is the share of participants on the tip road over tie-free rounds; the last column counts the analyzed rounds in which the previous counts were equal.
Item / response
F1, all human
F3, all human
F3, with agents
Report influence: not at all / slightly / moderately / strongly
5 / 16 / 50 / 47
3 / 20 / 42 / 54
9 / 41 / 90 / 98
Usual response: faster-looking road / other road expecting others to switch / ignored / it depended
35 / 62 / 4 / 17
38 / 47 / 10 / 24
146 / 39 / 12 / 41
Rules understood: yes / mostly / no
104 / 12 / 2
108 / 11 / 0
202 / 33 / 3
Table S6: Questionnaire counts. All-human rooms: 120 participants per message (two F1 and one F3 participant did not answer). Mixed rooms: the 240 participants of the 24 completed rooms (two did not answer).
N
warned
runs
I
M
time
Emix[ft]
∣Emix[ft]−21∣
Tlin
Iind
Tind
20
0
3
0.229
0.697
71.1
0.695
0.195
66.1
0.198
67.8
20
5
3
0.140
0.667
65.0
0.531
0.031
60.2
0.091
62.1
20
10
3
0.200
0.292
68.6
0.367
0.133
62.8
0.145
64.7
20
15
3
0.345
0.148
79.9
0.202
0.298
74.2
0.298
75.5
20
20
3
0.468
0.064
95.4
0.038
0.462
94.1
0.462
94.4
50
6
5
0.176
0.688
67.0
0.616
0.116
62.2
0.119
62.9
Table S7: Exposure grids, the linear-mixing rule and the independent-choice benchmark. Medians across runs of I , M and mean travel time; Emix[ft] mixes the pure-population leans of the core with no fitted parameter; ∣Emix[ft]−21∣ and Tlin are the linear-mixing predictions and Iind , Tind the independent-choice benchmark at the same mean (Text S5).
Block
K
I
M
Mh
Ma
E[Tt]
E[Th,t]
E[Ta,t]
E[fh,t]
E[fa,t]
frozen
1
5
0.063
0.45
0.48
0.37
61.1
60.7
62.3
0.61
0.000
no
2
5
0.063
0.50
0.50
0.51
61.2
61.3
60.9
0.66
0.000
no
3
5
0.091
0.48
0.48
0.46
61.9
62.3
60.7
0.66
0.000
no
4
5
0.059
0.45
0.46
0.40
60.9
60.9
61.0
0.67
0.000
no
5
5
0.070
0.47
0.48
0.43
61.3
61.2
61.7
0.64
0.000
no
6
5
0.079
0.49
0.49
0.49
61.3
61.3
61.5
0.64
0.000
no
Table S8: Mixed rooms (rounds 6–40; carried choices retained). Subscripts h and a denote human and GPT seats; E[ft] is the share of that seat type on the tip road over defined-tip rounds. “Frozen” applies the descriptive classifier to the room. Tie-round ranges are given in Text S4. All 24 slots are complete; the two invalid original attempts are retained separately in the execution record (Figs. S7 and S8).
Arm
seed
T30
f31
I31
M31
T31
T32
T33
T34
T35
E36:50[Tt]
F3 → F1
3
91.0
0.96
0.46
0.94
93.9
60.3
70.8
80.7
60.6
72.3
F3 → F1
4
80.7
1.00
0.50
0.86
100.0
63.1
61.6
69.2
64.1
71.3
F3 → F1
5
93.9
0.96
0.46
0.92
93.9
60.1
70.8
83.1
60.6
73.6
F3 → F1
6
88.2
0.98
0.48
0.90
96.9
70.8
60.3
76.4
61.0
73.1
F3 → F1
7
96.9
0.96
0.46
0.98
93.9
64.1
67.7
83.1
63.1
67.2
F1 → F3
3
91.0
0.00
0.50
0.06
100.0
100.0
93.9
93.9
96.9
95.4
Table S9: Switch experiments round by round. T30 , mean travel time in the last round under the original message; f31 , I31 , M31 and T31 , the first round under the new message; T32 to T35 , the following rounds; E[Tt]36–50 , the prespecified post-intervention window.
Block
bb(I)
bb(M)
LOO mean I slope
LOO mean M slope
1
+0.0993
-0.2086
+0.0945
-0.2080
2
+0.1150
-0.2007
+0.0922
-0.2091
3
+0.0764
-0.2150
+0.0978
-0.2070
4
+0.0950
-0.2007
+0.0951
-0.2091
5
+0.0857
-0.2079
+0.0964
-0.2081
6
+0.0900
-0.2129
+0.0958
-0.2073
Table S10: Registered block slopes and leave-one-block-out estimates. Slopes are per five additional agents. Leave-one-block-out columns are mean slopes across the other seven blocks, without additional tests. The full-sample means are 0.0951 for I and −0.2080 for M (Text S8).
Nuisance variable
γ
Mean I slope
Mean M slope
Carryover
-0.050
+0.0982
-0.2049
Carryover
-0.020
+0.0963
-0.2068
Carryover
-0.010
+0.0957
-0.2074
Carryover
-0.005
+0.0954
-0.2077
Carryover
+0.000
+0.0951
-0.2080
Carryover
+0.005
+0.0948
-0.2083
Table S11: Registered nuisance sensitivity grids. Each row reports the equally weighted mean block slope after subtracting the stated hypothetical nuisance effect from room outcomes. Carryover is binary and wait is measured in minutes. These are descriptive sensitivity calculations, not estimated causal corrections (Text S8).
K
Actual (%)
Responses
Mean (%)
SD
Median [IQR]
Bias (pp)
MAE (pp)
5
25
116/120
63.1
24.9
65.0 [50.0, 80.0]
+38.1
39.4
10
50
76/80
67.2
19.0
70.0 [50.0, 80.0]
+17.2
20.4
15
75
38/40
68.9
21.2
70.0 [60.0, 83.0]
-6.1
17.1
Table S12: Recovered formal estimates of the automated share. Each composition comprises eight rooms. Responses gives numeric respondents / all human participants. Means and SDs weight respondents equally; IQR gives the 25th and 75th percentiles. Bias is estimated minus actual percentage; MAE is mean absolute error, both in percentage points (pp). Missingness comprises eight unanswered items among submitted questionnaires and two unsubmitted questionnaires. No missing or draft-only value is imputed.
Message
frozen
I
M
time (min)
E[ft]
response
variation
GPT-5.4-mini, no reasoning, temperature 0.7 (core runs at the same seeds)
tip
0/5
0.146
0.714
65.2
0.555
0.7
4.6
tip + warning
5/5
0.460
0.079
94.0
0.040
33.9
0.2
warning − tip
+0.314 (5)
− 0.635 (5)
+28.8 (5)
− 0.515 (5)
+33.2
− 4.4
GPT-5.4-mini, no reasoning, temperature 1.0
tip
0/5
0.131
0.687
63.9
0.495
0.1
3.7
Table S13: Reasoning and current-model extension, summary (50 agents, rounds 6–60, seeds 3–7; means over five runs). The first block is the core reference at the same seeds. “Response” and “variation” are the two terms of Eq. 1, 160(E[ft]−21)2 and 160Var(ft) in minutes, calculated within each run. Rows “warning − tip” give mean paired differences. In parentheses is the number of pairs, of five, whose difference has the sign of the core warning effect (higher I and travel time, lower M and E[ft] ).
Message
seed
I
M
time (min)
E[ft]
ties
state
GPT-5.4-mini, no reasoning, temperature 1.0
tip
3
0.139
0.691
64.3
0.519
3
near equilibrium
tip
4
0.126
0.686
63.6
0.467
2
near equilibrium
tip
5
0.133
0.681
64.0
0.519
1
near equilibrium
tip
6
0.127
0.692
64.0
0.494
5
near equilibrium
tip
7
0.131
0.688
63.9
0.477
2
near equilibrium
Table S14: All 50 runs of the reasoning and current-model extension (50 agents, rounds 6–60). “Ties” counts analysis rounds whose previous counts were equal; these are excluded from E[ft] . State labels follow the descriptive classifier in Text S4.