heffner_2022_probabilistic
Across three economic games with MTurk participants — Ultimatum Game (exp0, N=715), Prisoner's Dilemma (exp1, N=306), and Public Goods Game (exp2, N=470) — participants rated their emotional state on a valence-arousal affect grid before making a decision each round (UG: accept/punish over 20 rounds; PD: $0–1 contribution over 22 rounds; PGG: $0–1 contribution over 62 rounds, two recorded responses per round). Participants additionally completed a feeling-word (emotion) classification task rating 20 words on the same valence-arousal grid (exp3, N=1491). Classifiers trained on the classification task were then applied to the game ratings to derive probabilistic emotion attributions, revealing that heterogeneous emotions — especially muted high-arousal negative ones like sadness and disappointment — drive punishment, defection, and free riding, rather than anger alone. Response types are discrete accept/punish choices (UG) and continuous contribution ratings (PD, PGG, emotion grid).
Likelihood of human responses
| model | PNLL | test NLL (avg) | test responses | train NLL (avg) | train responses |
|---|---|---|---|---|---|
| CORE best | 310.3 | 0.2185 | 1,420 | 0.2082 | 12,880 |
| CORE (no prediction errors) | 327.5 | 0.2307 | 1,420 | 0.2070 | 12,880 |
| CORE (no phonemes) | 322.6 | 0.2272 | 1,420 | 0.1894 | 12,880 |
| CORE (no forgetting) | 352.2 | 0.2480 | 1,420 | 0.2226 | 12,880 |
| CORE (no hierarchy) | 593.7 | 0.4181 | 1,420 | 0.4118 | 12,880 |
| Transformer | 499.6 | 0.3518 | 1,420 | 0.3416 | 12,880 |
| Centaur | 356.2 | 0.2508 | 1,420 | – | – |
Experiments
| exp | task class | participants | responses | conditions | simulated | effects |
|---|---|---|---|---|---|---|
| exp0 | UltimatumGame | 715 | 14,300 | 1 | no | – |
Behavioral effects
No behavioral effects were simulated for this study.
Transcript
You will play 20 one-shot rounds of the Ultimatum Game as the Responder. Each round you are paired with a new Proposer who receives $1 and splits it with you: the Proposer keeps part of it and offers you the rest. After you see the offer, On an affect grid you report how you feel by typing two integers: first your valence rating, an integer from -250 (extremely unpleasant) to +250 (extremely pleasant); then your arousal rating, an integer from -250 (very calm) to +250 (very aroused). Then you decide whether to accept the offer (type A) or reject it (type R), in which case neither of you receives anything. A proposer keeps $0.50 and offers you $0.50. You rate how you feel on the affect grid: valence 167, arousal 64. You press A (accept). A proposer keeps $0.80 and offers you $0.20. You rate how you feel on the affect grid: valence -32, arousal -57. You press A (accept). A proposer keeps $0.95 and offers you $0.05. You rate how you feel on the affect grid: valence -202, arousal -225. You press A (accept). A proposer keeps $0.60 and offers you $0.40. You rate how you feel on the affect grid: valence 43, arousal 68. You press A (accept). A proposer keeps $0.75 and offers you $0.25. You rate how you feel on the affect grid: valence 8, arousal 9. You press A (accept). A proposer keeps $0.90 and offers you $0.10. You rate how you feel on the affect grid: valence -44, arousal -117. You press A (accept). A proposer keeps $0.75 and offers you $0.25. You rate how you feel on the affect grid: valence -98, arousal -108. You press A (accept). A proposer keeps $0.60 and offers you $0.40. You rate how you feel on the affect grid: valence 19, arousal 21. You press A (accept). A proposer keeps $0.95 and offers you $0.05. You rate how you feel on the affect grid: valence -235, arousal -240. You press A (accept). A proposer keeps $0.70 and offers you $0.30. You rate how you feel on the affect grid: valence 19, arousal 44. You press A (accept). A proposer keeps $0.85 and offers you $0.15. You rate how you feel on the affect grid: valence -117, arousal -142. You press A (accept). A proposer keeps $0.65 and offers you $0.35. You rate how you feel on the affect grid: valence 10, arousal 18. You press A (accept). A proposer keeps $0.85 and offers you $0.15. You rate how you feel on the affect grid: valence -13, arousal -10. You press A (accept). A proposer keeps $0.55 and offers you $0.45. You rate how you feel on the affect grid: valence 114, arousal 134. You press A (accept). A proposer keeps $0.90 and offers you $0.10. You rate how you feel on the affect grid: valence -88, arousal -142. You press A (accept). A proposer keeps $0.70 and offers you $0.30. You rate how you feel on the affect grid: valence 21, arousal 31. You press A (accept). A proposer keeps $0.80 and offers you $0.20. You rate how you feel on the affect grid: valence -15, arousal -27. You press A (accept). A proposer keeps $0.50 and offers you $0.50. You rate how you feel on the affect grid: valence 232, arousal 237. You press A (accept). A proposer keeps $0.65 and offers you $0.35. You rate how you feel on the affect grid: valence 7, arousal 13. You press A (accept). A proposer keeps $0.55 and offers you $0.45. You rate how you feel on the affect grid: valence 241, arousal 227. You press A (accept).