Human behavior and beliefs in social contexts are shaped by a complex interplay of material incentives, social influences, and cognitive processes. For centuries, debates have raged over the relative importance of these factors. Economic theories often emphasize material cost-benefit analysis, formalized in various game-theoretic models. However, the deeply social nature of humans is undeniable, with models of social learning, imitation, and opinion spread capturing this aspect. Furthermore, the influence of social norms (both descriptive and injunctive) and authority figures plays a significant role. Psychological processes like cognitive dissonance and social projection further complicate the picture. This research aims to disentangle these interwoven factors using a novel integrative mathematical model and a controlled behavioral experiment. Unlike previous studies focusing on individual factors, this work simultaneously examines the influence of expected material payoffs, cognitive dissonance, three types of social influence (peer disapproval, authority influence, and peer conformity), and belief dynamics in a Common Pool Resources (CPR) game. The 35-day experiment allowed for the measurement of actions, personal norms, beliefs about others, and their evolution over time, providing a rich dataset for model validation and parameterization. The experiment also included a treatment condition with messaging from an authority, allowing for the investigation of its impact on behavior and beliefs.

The paper draws upon a wide range of literature spanning economics, sociology, psychology, and game theory. Classical and evolutionary game theory models are acknowledged, along with mean-field and quantum game theory approaches, which generally focus on material incentives. The social aspect is represented by numerous mathematical models of social learning, imitation, and opinion dynamics. The influence of social norms is supported by research highlighting the impact of descriptive (what others do) and injunctive (what others think one should do) norms on behavior. The authors also consider the effects of authority figures, referencing classic works on propaganda and its influence. Cognitive factors, such as cognitive dissonance (the discomfort of conflicting beliefs and actions) and social projection (assuming others are similar to oneself), are included based on established psychological research. However, existing work is noted to often focus on one or two factors at a time. This paper addresses this gap by synthesizing the existing literature into an integrative model that considers the co-evolution of decision-making and beliefs in the presence of both individual and social factors and influence of authority.

The study uses a novel integrative mathematical model (Gavrilets 2021) coupled with a 35-day online behavioral experiment. The model incorporates the following variables: * **x:** Individual action (resource extraction level in CPR game) * **y:** Personal norm (perceived appropriate action) * **x̄:** Empirical expectation (belief about average peer action) * **ȳ:** Normative expectation (belief about average peer attitude) * **G:** Authority's promoted action The model postulates a subjective utility function for individuals, balancing material payoffs, cognitive dissonance (mismatch between action and personal norm), conformity with peers, and disapproval from authority. The best response action (x) is modeled as a weighted sum of these factors, with weights (B0, B1, B2, B3, B4) representing the relative importance of each factor. Belief dynamics (y, x̄, ȳ) are modeled using linear recurrence equations capturing the influence of cognitive dissonance, social projection, logic constraints, peer learning, and authority messaging. All parameters are individual-specific. A Common Pool Resources (CPR) game was implemented in the online experiment. Participants (N=300) were randomly assigned to groups of six and received an endowment of points to invest in either resource extraction from the CPR or a safe outside activity. They were asked to state their personal norms (y), normative expectations (ȳ), and empirical expectations (x̄) before making decisions on resource extraction (x). Incentives were provided for accurate predictions of peer behavior and norms. One treatment group received a message promoting the socially optimal resource extraction level, while the control group received no message. The experiment lasted 35 days, with group composition randomized each day. Data analysis involved a mean group estimation method to address individual heterogeneity and potential multicollinearity, combining model averaging with the Akaike Information Criterion (AICc) and non-parametric bootstrapping for confidence intervals.

The experiment yielded several key findings: 1. **Personal norms (y) and conformity (with x̄) were the strongest predictors of individual actions (x).** Material payoffs (B0) and normative expectations (ȳ) had smaller effects. The weight of personal norms was significantly reduced by authority messaging, while the weight of conformity increased. 2. **Both cognitive and social factors significantly impacted belief dynamics.** Cognitive dissonance, social projection, and logic constraints had comparable effects to social influences (learning from peers and authority). Authority messaging significantly affected personal norms and normative expectations, but its effect was weaker on empirical expectations (directly observable peer behavior). 3. **Individual heterogeneity was substantial.** Cluster analysis revealed behavioral types. Individuals with high resource extraction were characterized by a stronger reliance on conformity and weaker influence of personal norms compared to individuals with low resource extraction levels. The latter group were largely affected by their personal norms. Prosocial individuals showed higher weights for personal norms and lower sensitivity to normative and empirical expectations compared to individualistic types. Rule-followers also exhibited higher weights for personal norms and reduced sensitivity to expectations. Messaging amplified these differences. 4. **Authority messaging did not directly impact average extraction levels but increased the variability of actions.** Prosocial individuals reduced efforts while individualistic types increased them, leading to a cancellation effect on the average, but higher standard deviations. 5. **The model demonstrated reasonable predictive accuracy.** Comparing observed, predicted (using the model with estimated parameters and observed data), and simulated trajectories (iterating the model from initial conditions), showed a fairly close match, with some discrepancies for the x and x̄ variables, particularly in the messaging condition.

The findings address the research question by quantifying the relative importance of material, social, and cognitive factors influencing behavior and beliefs in a social dilemma. The results show that personal norms and conformity are primary drivers of individual actions, but their relative weights are significantly influenced by authority messaging. This highlights the importance of considering both cognitive (internal) and social (external) influences when predicting and influencing behavior. The substantial individual heterogeneity suggests the limitations of aggregate-level analysis, underscoring the need for more personalized approaches in policy interventions. The study's strength lies in its integrated approach, combining a mathematical model with a long-term experiment that captures the dynamic interplay between actions and beliefs. The findings are relevant to various fields, including behavioral economics, social psychology, and political science, providing a framework for understanding social dynamics and designing effective behavioral interventions.

This study offers a valuable contribution by integrating material, social, and cognitive factors to explain human behavior and beliefs in social interactions. The findings highlight the critical roles of personal norms and conformity, and how authority messaging can reshape these influences. Individual heterogeneity significantly impacts collective outcomes, suggesting the need for tailored interventions. Future research could expand this framework to diverse populations and social contexts, explore more complex models of learning and decision-making, and investigate the effectiveness of diverse messaging strategies.

The study primarily focuses on WEIRD (Western, Educated, Industrialized, Rich, and Democratic) participants in a specific CPR game. The generalizability of these findings to other cultures and social contexts requires further investigation. The model's simplicity, particularly regarding payoff functions and action spaces, could be refined to better capture the complexities of real-world decision-making. The elicitation of norms and beliefs, although incentivized, might influence behavior; however, this effect is likely to be minimal given the existing evidence. Finally, some subjects did not fit the model well, potentially affecting the accuracy of the parameter estimates for some variables (such as the material payoff weight).