Assessing bargaining and cooperation through longitudinal clustering analysis: Evidence from a lab-in-the-field experiment

This study investigates human economic behaviour through longitudinal clustering methods applied to lab-in-the-field experimental data. The experimental design combines the ultimatum game and the public goods game, which are widely used to examine behaviours in both the private and public sectors. To reproduce a more realistic scenario involving bargaining, resource inequality, and cooperation, the final payoffs from 30 rounds of the ultimatum game were used as initial endowments in the subsequent public goods game. The Gini coefficient illustrates how the ultimatum game generates imbalances, thereby providing an experimental foundation for studying resource inequality. Participants endowed with greater resources contributed proportionately larger amounts. Over time, contributions declined across all groups, reaching similar levels despite persistent resource inequalities at the start of the public goods game. The behavioural trajectories were analysed using k-means longitudinal clustering (KML) and growth mixture modelling (GMM). In the ultimatum game, proposers were classified into two categories: Those who consistently tended to make fair offers and those offering smaller amounts. The responders exhibited considerable heterogeneity, with unexpectedly high acceptance rates for relatively unfair offers. Two distinct contribution trajectories were identified in the public goods game. One group contributed a more significant proportion of their endowment than the mean, while the other contributed less. A joint trajectory analysis revealed consistent behavioural pathways observed in the two games. Proposers who made more equitable offers in the ultimatum game were likelier to contribute a greater proportion of their endowment in the subsequent public goods game. Ultimatum game data showed significant behavioural heterogeneity, while public goods game contributions averaged around 40 per cent with notable uniformity. Cooperative behaviour persisted regardless of initial endowment size or ultimatum game decisions, with notable differences across academic backgrounds.