Excluding selfish people results in more overall cooperation

Mathematically, cooperation can be modeled through evolutionary game theory using models like the public goods game. In this game, participants can choose to invest their resources in a central pot that pays all players equally, whether they invested or not. This game can model real-world scenarios like vaccination policy or climate inaction.

However, because each player benefits from group investments whether they pitch in or not, individuals benefit in the short term if they opt out. This is known as the first-order free-riding problem. Players can try to exclude free riders to encourage participation, but this costs additional resources and creates a second-order free-riding problem. Those who do not invest should be excluded, but no individual wants to be the excluder, or the one to commit resources to discourage free riders.

Wang and Perc detail a version of the public goods game featuring global exclusion, which circumvents both the first- and second-order free-riding problems. In contrast to local exclusion, which operates only within small groups, global exclusion operates between groups where at least one excluder is always present, providing a much stronger incentive to participate in exclusion. Their model leads to stable states of cooperation, even when cooperation is initially rare.

The authors hope their results can be applied to practical problems in other fields.

“Our results have shown that cooperation can emerge and be maintained in the population by the spontaneous formation of cyclic dominance between defectors, cooperators, and global excluders, even in parameter regions that may fit realistic scenarios,” said author Xiaofeng Wang. “We also wonder whether our theoretical predictions can be confirmed by empirical data from experiments.”

Source: “Replicator dynamics of public goods games with global exclusion,” by Xiaofeng Wang and Matjaz Perc, Chaos (2022). The article can be accessed at https://doi.org/10.1063/5.0099697 .