Collective cooperation and social mobility are ubiquitous in human societies. Due to information sharing and the complexity of everyday life, multidimensional mobility is also common, for example when moving into different districts of a city for better education or when settling permanently abroad due to better job prospects. Nevertheless, it is not clear how such complex mobility might affect cooperation in situations that constitute social dilemmas, where individual and public interests are at odds.

Here, as an initial step to understand the impact of multidimensional mobility, we investigate one of its significant dimensions, namely the range of mobility. We propose an updating algorithm where individuals either move adaptively in the area bounded by a mobility radius or stay put for social learning.

We use this on the prisoner’s dilemma and the snowdrift game, and we find that an increase in either probability or radius of mobility may weaken network reciprocity, simply by decreasing the odds of meeting old interaction partners.

However, if mobility is free, there is a window of parameters where synergies with network reciprocity are possible, and where indeed cooperation can be robust and significantly elevated. Local mobility in particular may favorably affect cooperation. In fact, even if mobility is costly, the failure of local mobility can often be associated with the risk caused by the shortage of available empty sites.

We also find that the synergistic effects of mobility superposed upon network reciprocity are best expressed for small flow rates. Overall, we hope that our research will promote the better understanding of the complex interplay between networks reciprocity and mobility and their coaction.

W. Li, Z. Chen, K. Jin, J. Wang, L. Yuan, C. Gu, L. Jiang, M. Perc, Options for mobility and network reciprocity to jointly yield robust cooperation in social dilemmas, Applied Mathematics and Computation 435 (2022) 127456