christian_2026_resolving
One preregistered online experiment (N=2520) on Feynman's restaurant problem, an optimal-stopping task, with one sequence of nights per participant (horizon 7, 14, or 28). On each night a participant chose to explore a new restaurant or exploit the best one seen so far, with hidden restaurant quality values drawn from one of four distributions (uniform, exponential, power law, triangular) varied between subjects. Responses are discrete choices logged per night (with best-known value and reward), and the paper tests whether humans use stopping thresholds that decline linearly with nights remaining, fitting linear-threshold and hierarchical Bayesian models plus reinforcement-learning baselines.
Responses
41,160
1,624 held out
CORE effects
3 / 3
CORE test NLL (avg)
0.367
rank 1 of 7 models
Best model
CORE
test NLL (avg) 0.367
Likelihood of human responses
| model | PNLL | test NLL (avg) | test responses | train NLL (avg) | train responses |
|---|---|---|---|---|---|
| CORE best | 596.6 | 0.3673 | 1,624 | 0.3661 | 39,536 |
| CORE (no prediction errors) | 597.9 | 0.3681 | 1,624 | 0.3678 | 39,536 |
| CORE (no phonemes) | 599.8 | 0.3694 | 1,624 | 0.3564 | 39,536 |
| CORE (no forgetting) | 611.2 | 0.3764 | 1,624 | 0.3763 | 39,536 |
| CORE (no hierarchy) | 871.5 | 0.5366 | 1,624 | 0.5573 | 39,536 |
| Transformer | 646.3 | 0.3980 | 1,624 | 0.4076 | 39,536 |
| Centaur | 701.2 | 0.4318 | 1,624 | – | – |
Experiments
| exp | task class | participants | responses | conditions | simulated | effects |
|---|---|---|---|---|---|---|
| exp0 | RestaurantProblem | 2,520 | 41,160 | 4 | yes | exploit_increases_as_nights_remaining_decreases, exploit_timing_across_horizons, runtime_balance |
Behavioral effects
| effect | experiment | paper | CORE | CORE (no prediction errors) | CORE (no phonemes) | CORE (no forgetting) | CORE (no hierarchy) |
|---|---|---|---|---|---|---|---|
exploit_increases_as_nights_remaining_decreases | exp0 | -0.073 | ✓ yes -0.072 | ✓ yes -0.074 | ✓ yes -0.064 | ✓ yes -0.071 | ✓ yes -0.040 |
logistic regression of exploit choice (response==1, freely-chosen valid trials only) on nights_remaining; expected negative coefficient (people explore early, exploit late). | |||||||
exploit_timing_across_horizons | exp0 | -0.073 | ✓ yes -0.340 | ✓ yes -0.395 | ✓ yes -0.362 | ✓ yes -0.379 | ✓ yes -0.191 |
the same negative effect reproduces within each total_nights horizon (7, 14, 28); each subgroup's coefficient must be negative and significant. | |||||||
runtime_balance | exp0 | +0.000 | ✓ yes +0.050 | ✓ yes +0.036 | ✓ yes +0.050 | ✓ yes +0.025 | ✓ yes +0.007 |
total_nights is balanced across participants (equal counts of 7/14/28-night sequences); a chi-square test of equal participant counts should not reject balance. | |||||||
Transcript
You are about to spend 7 nights in a new city. Restaurants in the city vary in quality: you cannot know a restaurant's quality until you visit it, and once you visit it its quality never changes. Quality scores are distributed randomly with a mean of 50. Before your trip you saw 84 sample scores from this city to get a sense of how scores are distributed. Your goal is to maximize the total score of the restaurants you visit across all your nights, and you will earn a bonus proportional to your total score. On each of the 7 nights you choose a restaurant. On every night respond with a single letter: press A to visit a NEW restaurant you have not been to before, press C to return to the BEST restaurant you have found so far, or press B to return to some other restaurant you have already visited. Night 1 of 7, 7 night(s) remaining. You have not visited any restaurant yet. You press A. You visit a new restaurant; its score is 21. Night 2 of 7, 6 night(s) remaining. Your best score so far is 21. You press C. You return to your best restaurant; its score is 21. Night 3 of 7, 5 night(s) remaining. Your best score so far is 21. You press A. You visit a new restaurant; its score is 42. Night 4 of 7, 4 night(s) remaining. Your best score so far is 42. You press A. You visit a new restaurant; its score is 55. Night 5 of 7, 3 night(s) remaining. Your best score so far is 55. You press A. You visit a new restaurant; its score is 60. Night 6 of 7, 2 night(s) remaining. Your best score so far is 60. You press A. You visit a new restaurant; its score is 49. Night 7 of 7, 1 night(s) remaining. Your best score so far is 60. You press C. You return to your best restaurant; its score is 60.
You are about to spend 7 nights in a new city. Restaurants in the city vary in quality: you cannot know a restaurant's quality until you visit it, and once you visit it its quality never changes. Quality scores are distributed randomly with a mean of 50. Before your trip you saw 84 sample scores from this city to get a sense of how scores are distributed. Your goal is to maximize the total score of the restaurants you visit across all your nights, and you will earn a bonus proportional to your total score. On each of the 7 nights you choose a restaurant. On every night respond with a single letter: press C to visit a NEW restaurant you have not been to before, press B to return to the BEST restaurant you have found so far, or press A to return to some other restaurant you have already visited. Night 1 of 7, 7 night(s) remaining. You have not visited any restaurant yet. You press C. You visit a new restaurant; its score is 16. Night 2 of 7, 6 night(s) remaining. Your best score so far is 16. You press C. You visit a new restaurant; its score is 9. Night 3 of 7, 5 night(s) remaining. Your best score so far is 16. You press C. You visit a new restaurant; its score is 25. Night 4 of 7, 4 night(s) remaining. Your best score so far is 25. You press C. You visit a new restaurant; its score is 15. Night 5 of 7, 3 night(s) remaining. Your best score so far is 25. You press C. You visit a new restaurant; its score is 49. Night 6 of 7, 2 night(s) remaining. Your best score so far is 49. You press C. You visit a new restaurant; its score is 49. Night 7 of 7, 1 night(s) remaining. Your best score so far is 49. You press C. You visit a new restaurant; its score is 32.
You are about to spend 28 nights in a new city. Restaurants in the city vary in quality: you cannot know a restaurant's quality until you visit it, and once you visit it its quality never changes. Quality scores are distributed randomly with a mean of 50. Before your trip you saw 84 sample scores from this city to get a sense of how scores are distributed. Your goal is to maximize the total score of the restaurants you visit across all your nights, and you will earn a bonus proportional to your total score. On each of the 28 nights you choose a restaurant. On every night respond with a single letter: press B to visit a NEW restaurant you have not been to before, press A to return to the BEST restaurant you have found so far, or press C to return to some other restaurant you have already visited. Night 1 of 28, 28 night(s) remaining. You have not visited any restaurant yet. You press B. You visit a new restaurant; its score is 76. Night 2 of 28, 27 night(s) remaining. Your best score so far is 76. You press B. You visit a new restaurant; its score is 70. Night 3 of 28, 26 night(s) remaining. Your best score so far is 76. You press B. You visit a new restaurant; its score is 7. Night 4 of 28, 25 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 5 of 28, 24 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 6 of 28, 23 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 7 of 28, 22 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 8 of 28, 21 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 9 of 28, 20 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 10 of 28, 19 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 11 of 28, 18 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 12 of 28, 17 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 13 of 28, 16 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 14 of 28, 15 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 15 of 28, 14 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 16 of 28, 13 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 17 of 28, 12 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 18 of 28, 11 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 19 of 28, 10 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 20 of 28, 9 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 21 of 28, 8 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 22 of 28, 7 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 23 of 28, 6 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 24 of 28, 5 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 25 of 28, 4 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 26 of 28, 3 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 27 of 28, 2 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76. Night 28 of 28, 1 night(s) remaining. Your best score so far is 76. You press A. You return to your best restaurant; its score is 76.
You are about to spend 28 nights in a new city. Restaurants in the city vary in quality: you cannot know a restaurant's quality until you visit it, and once you visit it its quality never changes. Quality scores are distributed randomly with a mean of 50. Before your trip you saw 84 sample scores from this city to get a sense of how scores are distributed. Your goal is to maximize the total score of the restaurants you visit across all your nights, and you will earn a bonus proportional to your total score. On each of the 28 nights you choose a restaurant. On every night respond with a single letter: press A to visit a NEW restaurant you have not been to before, press B to return to the BEST restaurant you have found so far, or press C to return to some other restaurant you have already visited. Night 1 of 28, 28 night(s) remaining. You have not visited any restaurant yet. You press A. You visit a new restaurant; its score is 39. Night 2 of 28, 27 night(s) remaining. Your best score so far is 39. You press A. You visit a new restaurant; its score is 31. Night 3 of 28, 26 night(s) remaining. Your best score so far is 39. You press A. You visit a new restaurant; its score is 33. Night 4 of 28, 25 night(s) remaining. Your best score so far is 39. You press A. You visit a new restaurant; its score is 31. Night 5 of 28, 24 night(s) remaining. Your best score so far is 39. You press A. You visit a new restaurant; its score is 25. Night 6 of 28, 23 night(s) remaining. Your best score so far is 39. You press C. You return to a previously visited restaurant; its score is 31. Night 7 of 28, 22 night(s) remaining. Your best score so far is 39. You press A. You visit a new restaurant; its score is 25. Night 8 of 28, 21 night(s) remaining. Your best score so far is 39. You press A. You visit a new restaurant; its score is 28. Night 9 of 28, 20 night(s) remaining. Your best score so far is 39. You press A. You visit a new restaurant; its score is 32. Night 10 of 28, 19 night(s) remaining. Your best score so far is 39. You press B. You return to your best restaurant; its score is 39. Night 11 of 28, 18 night(s) remaining. Your best score so far is 39. You press A. You visit a new restaurant; its score is 33. Night 12 of 28, 17 night(s) remaining. Your best score so far is 39. You press A. You visit a new restaurant; its score is 30. Night 13 of 28, 16 night(s) remaining. Your best score so far is 39. You press A. You visit a new restaurant; its score is 55. Night 14 of 28, 15 night(s) remaining. Your best score so far is 55. You press B. You return to your best restaurant; its score is 55. Night 15 of 28, 14 night(s) remaining. Your best score so far is 55. You press A. You visit a new restaurant; its score is 36. Night 16 of 28, 13 night(s) remaining. Your best score so far is 55. You press C. You return to a previously visited restaurant; its score is 36. Night 17 of 28, 12 night(s) remaining. Your best score so far is 55. You press A. You visit a new restaurant; its score is 37. Night 18 of 28, 11 night(s) remaining. Your best score so far is 55. You press C. You return to a previously visited restaurant; its score is 37. Night 19 of 28, 10 night(s) remaining. Your best score so far is 55. You press A. You visit a new restaurant; its score is 114. Night 20 of 28, 9 night(s) remaining. Your best score so far is 114. You press B. You return to your best restaurant; its score is 114. Night 21 of 28, 8 night(s) remaining. Your best score so far is 114. You press A. You visit a new restaurant; its score is 30. Night 22 of 28, 7 night(s) remaining. Your best score so far is 114. You press B. You return to your best restaurant; its score is 114. Night 23 of 28, 6 night(s) remaining. Your best score so far is 114. You press A. You visit a new restaurant; its score is 46. Night 24 of 28, 5 night(s) remaining. Your best score so far is 114. You press C. You return to a previously visited restaurant; its score is 46. Night 25 of 28, 4 night(s) remaining. Your best score so far is 114. You press A. You visit a new restaurant; its score is 33. Night 26 of 28, 3 night(s) remaining. Your best score so far is 114. You press B. You return to your best restaurant; its score is 114. Night 27 of 28, 2 night(s) remaining. Your best score so far is 114. You press A. You visit a new restaurant; its score is 158. Night 28 of 28, 1 night(s) remaining. Your best score so far is 158. You press B. You return to your best restaurant; its score is 158.