Expectation-driven migration promotes cooperation by group interactions.

"Voting with feet" describes the prominent social phenomenon that people tend to move away from deteriorating neighborhoods and search for and join prosperous groups. To quantify the role this kind of expectation-driven migration plays in the evolution of cooperation, here we study a simple yet effective model of cooperation based on spatial public goods games. The population structure is characterized by a square lattice with some nodes being left empty. Individuals have expectations toward their current habitats. Dissatisfied players, whose expectation is not met after interacting with all directly connected neighbors, tend to abstain from the groups of low quality by moving away and explore the physical niches of avail. How fast interaction happens relatively to selection is regulated by the time-scale ratio of game interaction to natural selection. Under strong selection, simulation results show that cooperation is greatly improved for either low, moderate, or high expectations compared to whenever the expectation-driven migration is absent. Further explorations reveal that neither too high nor too low but rather a combination of moderate expectations and rapid interaction establishes cooperation for a moderate public goods enhancement factor. There exists an optimal interval of expectation level most favoring the evolution of cooperation as the required time-scale ratio is minimized.