Speaker
Description
In many biological and social systems, cooperation depends on collective actions that generate benefits only when a minimal number of individuals coordinate to contribute. These interactions are often modeled using threshold public goods games, in which public goods are produced only if participation exceeds a critical threshold. Cooperative groups vary greatly in size across species, with some very large groups allowing sophisticated types of cooperation, such as division of labor. But how increasing group size influences the evolutionary stability of cooperation remains poorly understood. In this study, we investigate how increasing group size affects the evolutionary dynamics of cooperation, especially when cooperation depends on reaching a certain threshold. Previous work has shown that cooperation can collapse due to increasing costs \cite{pena2014gains}. Our model reveals that a similar collapse can arise even when costs and benefits remain fixed. Specifically, increasing group size alone can alter the stability of cooperative equilibria and can cause a saddle-node bifurcation that eliminates the stable cooperative states. As group size exceeds a critical value, the stable cooperation equilibrium can disappear abruptly, leading to an abrupt transition to full defection. These findings show that increases in group size may destabilize cooperation in threshold public goods systems, explaining how cooperative behavior breaks down when benefits require coordinated effort.
Bibliography
@article{pena2014gains,
title={Gains from switching and evolutionary stability in multi-player matrix games},
author={Pena, Jorge and Lehmann, Laurent and N{\"o}ldeke, Georg},
journal={Journal of Theoretical Biology},
volume={346},
pages={23--33},
year={2014},
publisher={Elsevier}
}
