Introduction

This study uses agent-based modeling to explore the effects of learning mechanisms and population scaling on inequality and cooperation within a framework combining the Ultimatum Game (UG) with the Public Goods Game (PGG). Initially, agents participate in UG sessions, where their accumulated payoffs determine their initial endowments for subsequent PGG sessions. Agent behavior—reflecting traits like fairness, selfishness, and cooperativeness—is based on experimental data from a lab-in-the-field study integrating both games. This research aims to understand how different learning dynamics and structural conditions affect strategy evolution and outcome distribution.

Methods

We conducted several agent-based simulations to replicate a real-world experimental design. In the first four simulations, 182 agents played 30 rounds of the UG followed by 30 rounds of the PGG, starting with fixed strategies and a marginal per capita return (MPCR) of 0.3. We later introduced a higher MPCR, medium-level learning, and imitative learning. A final simulation expanded the imitative learning model to 500 agents over 100 rounds. The results showed that increasing the MPCR and implementing learning mechanisms enhanced cooperation and reduced inequality in the PGG. Imitative learning notably yielded the most significant improvements.

Results

The larger final simulation, with extended interactions, resulted in the highest PGG payoffs and the lowest inequality levels. While payoffs from the UG remained stable, inequality decreased as learning fostered fairer strategies. Inferential tests highlighted significant differences in decision-making across simulations, underscoring the role of behavioral adaptation.

Conclusions

By integrating the UG with the PGG, this study clarifies how initial bargaining influences subsequent cooperation. Overall, learning mechanisms, especially imitation, and prolonged interactions promote successful strategies, encouraging fairness and enhancing cooperative outcomes.