Computational behavioral models in public goods games with migration between groups

In this study we have simulated numerically two models of linear public goods games where players are equally distributed among a given number of groups. Agents play in their group by using two simple sets of rules, called ‘blind’ and ‘rational’ model, respectively, that are inspired by the observed behavior of human participants in laboratory experiments. In addition, unsatisfied agents have the option of leaving their group and migrating to a new random one through probabilistic choices. Stochasticity, and the introduction of two types of players in the blind model, help simulate the heterogeneous behavior that is often observed in experimental work. Our numerical simulations of the corresponding dynamical systems show that being able to leave a group when unsatisfied favors contribution and avoids free-riding to a good extent in a range of the enhancement factor where defection would prevail without migration. Our numerical simulation presents results that are qualitatively in line with known experimental data when human agents are given the same kind of information about themselves and the other players in the group. This is usually not the case with customary mathematical models based on replicator dynamics or stochastic approaches. As a consequence, models like the ones described here may be useful for understanding experimental results and also for designing new experiments by first running cheap computational simulations instead of doing costly preliminary laboratory work. The downside is that models and their simulation tend to be less general than standard mathematical approaches.