A probabilistic map of emotional experiences during competitive social interactions

The study investigates which specific emotions motivate competitive social decisions such as punishment, defection, and free riding. While prevailing theories posit that negatively valenced, high-arousal emotions—especially anger—drive punitive and uncooperative behaviors, precise quantification of emotion and traditional directed self-report measures may bias findings toward presumed emotions. The authors aim to develop an unbiased, data-driven method to infer emotions experienced during social interactions without constraining participants to specific labels, thereby clarifying the true emotional drivers of competitive versus cooperative choices across classic economic games.

Prior work has established a central role for emotion in decision-making and social cognition, linking negative arousal (often interpreted as anger) to punitive behaviors in contexts like the Ultimatum Game and moral violations. Physiological and neural studies have associated heightened arousal with punishment and defection, often inferred as anger. Other emotions—sadness, disgust, disappointment—have also been implicated in noncooperative behavior, though less prominently. The literature often uses directed probes (e.g., asking about anger) or infers discrete emotions from physiological/neural data, which may misidentify felt emotions. Theoretical frameworks emphasize valence and arousal dimensions of affect and propose mappings between discrete emotions and action tendencies (e.g., anger-approach, disgust-avoidance), but the field lacks consensus on which specific emotions primarily drive competitive social choices and how heterogeneous these experiences are across individuals.

Design: Three experiments embedded an affect measurement into economic games. Participants first completed an Emotion Classification Task, then played one of: Ultimatum Game (UG, Exp. 1), sequential Prisoner’s Dilemma (PD, Exp. 2), or four-person sequential Public Goods Game (PGG, Exp. 3). During games, participants rated their affect on a 500×500 valence (x) by arousal (y) grid before making decisions (punish/reject vs accept; contribute/defect). They were never asked to self-report discrete emotion labels in the games. Participants: Recruited on Amazon Mechanical Turk with informed consent (Brown University IRB protocol 1607001555). Initial N=1820; exclusions N=329 based on preregistered criteria (neutral must be placed within a 100×100 center square). Final samples: UG N=715 (320 females; mean age 34.4±10.1); PD N=306 (131 females; mean age 35.5±11.2); PGG N=470 (238 females; mean age 33.0±10.5). Total final N=1491 (689 females; mean age 34.2±10.5). Emotion Classification Task: Participants placed 20 feeling terms on the affect grid: neutral, surprised, aroused, peppy, enthusiastic, happy, satisfied, relaxed, calm, sleepy, still, quiet, sluggish, sad, disappointed, disgusted, annoyed, angry, afraid, nervous. These terms were selected to span the circumplex and emotions implicated in social decision-making. Coordinates from this task provide labeled examples for model training and reveal population-level emotion distributions. Economic games:

• Ultimatum Game (UG): 20 one-shot rounds as Responder (N=543) or third-party (N=172), roles collapsed. Offers ranged from fair ($0.50/$0.50) to highly unfair ($0.95/$0.05). After viewing each offer, participants rated affect on the grid, then accepted or rejected (rejection = costly punishment).
• Prisoner’s Dilemma (PD): 22 one-shot sequential rounds with new partners each round. Each player had $1 and chose a contribution in $0.10 increments; contributions were multiplied by 1.5 and split evenly. Participants rated affect after seeing partner’s contribution ($0–$1) and then chose their own contribution.
• Public Goods Game (PGG): 62 one-shot rounds in groups of four (other players anonymized). Each player had $1; contributions were doubled and split evenly. Participants saw the other three players’ collective contribution ($0–$3), rated affect, then chose their own contribution in $0.10 increments. Machine Learning:
• Supervised classifiers: Trained on the emotion-classification [x,y] data with labels (70/30 train-test split; tenfold cross-validation within training). Models: feed-forward neural network (NN), k-nearest neighbors (kNN), and support vector machine (SVM). Accuracy metric appropriate due to balanced classes (null accuracy 5%). • NN architecture: 2 inputs (valence, arousal), single hidden layer with 27 nodes (chosen via cross-validation), decay 0.035, 20 output nodes (emotion classes). • kNN: neighborhood size k=175 (via cross-validation). • SVM: one-vs-one multi-class with cost parameter C=0.01. Performance: NN 35.80% accuracy; kNN 35.97%; SVM 19.90% (null 5%). NN selected as final model due to smooth boundaries and comparable accuracy.
• Application: The trained NN assigned, for each unlabeled affect rating during games, a probability distribution over the 20 emotion labels (summing to 1). Probabilities were averaged within participant and then by choice condition to infer emotions associated with punish vs accept, defect vs cooperate, and free ride vs cooperate.
• Unsupervised clustering: k-means with k=9 to form a 3×3 grid of low/medium/high valence and arousal combinations, ignoring labels. Used to test whether high negative valence/high arousal clusters predict competitive choices.
• Individual-level analysis: For each participant, computed inverse Euclidean distance between their game affect ratings and their own coordinates for each of the 20 emotion terms, converting to probabilities via inverse distance weighting to account for idiosyncratic emotion representations. Analyses: Compared model-derived emotion likelihoods across choices using paired t-tests; examined distributions across unfairness levels in UG; chi-square tests for cluster frequencies across choices; also analyzed continuous contributions in PD/PGG (supplementary).

Model performance: NN and kNN achieved high multi-class accuracy (NN 35.80%, kNN 35.97%, null 5%); SVM performed poorly (19.90%). Population emotion structure: Emotions occupy distinct yet sometimes heterogeneous regions of the valence-arousal space (e.g., anger shows high-arousal negative cluster and a lower-arousal negative cluster; disappointment spans wider arousal variability). Ultimatum Game (punishment vs acceptance):

• Emotions associated with punishment (NN likelihoods): sadness 13.47%, disappointment 12.82%, disgust 12.54%; anger 10.28% (5th). • Paired t-tests vs anger: sadness t(558)=4.65, p<0.001, d=0.20; disappointment t(558)=4.06, p<0.001, d=0.17; disgust t(558)=5.52, p<0.001, d=0.23.
• Acceptance linked to: satisfied, happy, peppy.
• Unsupervised k-means: Cluster 3 (high negative valence, neutral arousal; modal emotion: disappointment) most frequent in punishment, nearly twice cluster 1 (high negative valence, high arousal; modal emotion: anger); χ²(1)=249.68, p<0.001. Acceptance linked most to cluster 5 (neutral valence/arousal; modal: neutral) over cluster 2 (positive valence, neutral arousal; modal: satisfied); χ²(1)=520.22, p<0.001.
• Unfairness modulation: As offers become more unfair, negative emotions (sadness, disgust, disappointment, anger) increase. Disappointment is most likely across most offer types; only at the most unfair offer (5% to responder) does anger become top for punishment, with no significant difference vs sadness (t(537)=0.03, p=0.98, d=0.001) or disgust (t(537)=0.59, p=0.55, d=0.03).
• Individual-level analysis (UG): most frequent emotions when punishing: disgust 9.41%, disappointment 8.15%, anger 7.97%. Disgust > anger (t(558)=3.50, p<0.001, d=0.15); disappointment vs anger ns (t(558)=0.42, p=0.68, d=0.02). Acceptance: neutral, happy, satisfied. Prisoner’s Dilemma (defection vs cooperation):
• Defection linked to: disappointment 8.83%, sadness 8.72%, disgust 7.38%; anger 5.11% (9th). • Paired t-tests vs anger: disappointment t(278)=8.26, p<0.001, d=0.50; sadness t(278)=6.84, p<0.001, d=0.41; disgust t(278)=8.37, p<0.001, d=0.50.
• Cooperation linked to: happiness 16.32%, satisfaction 14.60%, enthusiasm 13.88%.
• k-means: Cluster 5 (neutral valence/arousal) is over five times more common than cluster 1 (high negative valence/arousal) for defection; χ²(1)=662.88, p<0.001.
• Individual-level: anger ranks 11th for defection. Public Goods Game (free riding vs cooperation):
• Free riding linked to: sadness 10.36%, disappointment 9.63%, sluggishness 8.38%; anger 4.74% (8th). • Paired t-tests vs anger: sadness t(442)=12.9, p<0.001, d=0.61; disappointment t(442)=14.0, p<0.001, d=0.67; sluggishness t(442)=7.60, p<0.001, d=0.36.
• Cooperation linked to: happy 13.47%, enthusiastic 12.95%, satisfied 12.06%.
• k-means: Cluster 5 (neutral valence/arousal) over six times more likely than cluster 1 for free riding; χ²(1)=4948.80, p<0.001.
• Individual-level: anger ranks 9th when deciding to free ride. Overall: Across games and analyses (population NN, k-means, individual-level), punitive and uncooperative choices are most associated with negatively valenced, neutrally arousing emotions (e.g., disappointment, sadness), not anger. Cooperative choices align with positive valence emotions (happy, satisfied, enthusiastic).

The findings challenge the prevalent view that anger—a negatively valenced, high-arousal emotion—primarily motivates punishment, defection, and free riding. Instead, probabilistic classification of unlabeled affect shows that sadness and disappointment, characterized by negative valence and neutral arousal, are more strongly associated with competitive social choices across dyadic and group settings. This pattern holds even when examining individual-specific emotion representations and when using an unsupervised clustering that ignores labels, indicating robustness beyond label semantics. While extreme unfairness can elevate anger’s prominence, it does not consistently dominate over sadness or disgust. The results underscore the centrality of valence in predicting competitive social behavior, whereas self-reported arousal is less predictive than previously inferred from physiological studies. This discrepancy suggests distinct roles for subjective versus physiological arousal and cautions against inferring discrete emotions from arousal indices alone. The study highlights heterogeneity in emotion structure and experience, suggesting that a one-to-one mapping between discrete emotions and actions is overly simplistic and that multiple negatively valenced, lower arousal states can motivate noncooperation.

By combining a dimensional affect grid with supervised and unsupervised machine learning, the study provides a probabilistic map linking emotional experiences to social choices without imposing discrete labels during decision-making. Across the Ultimatum Game, Prisoner’s Dilemma, and Public Goods Game, competitive choices are more closely tied to disappointment and sadness than to anger, revising assumptions about the emotional drivers of punishment, defection, and free riding. The approach reveals population-level structure and individual heterogeneity of emotions in valence-arousal space. Future research should integrate additional affective dimensions (e.g., approach/avoidance, control, anticipated effort) to refine classification of similar emotions (anger vs disgust), and bridge subjective arousal reports with physiological measures to clarify their distinct contributions. Extending this framework to diverse contexts and populations may further elucidate how emotions guide complex social behavior.

• Measurement dimensionality: The two-dimensional valence-arousal grid may not capture key aspects such as approach/avoidance, control, or effort; adding dimensions could better differentiate similar emotions (e.g., anger vs disgust).
• Subjective vs physiological arousal: Self-reported arousal may not align with physiological indices; conclusions about arousal’s role may differ depending on measurement modality.
• Classification accuracy: Although far above chance for a 20-class problem, supervised model accuracy (~36%) indicates overlap and heterogeneity in emotion space; some misclassification is expected.
• Generalizability: Online MTurk sample and specific economic game contexts may limit generalization to other populations or real-world settings.
• Label set constraints: Although unlabeled during games, the training set relied on 20 predefined emotion terms, potentially limiting representation of other relevant emotions.
• Context specificity: Results are anchored in competitive economic games; other social contexts (e.g., cooperative dilemmas with communication, long-term relationships) may yield different emotion–choice couplings.