  In a static environment, optional participation and a local agglomeration of
cooperators are found to be beneficial for the occurrence and maintenance of
cooperation. In the optional public goods game, the rock-scissors-paper cycles
of different strategies yield oscillatory cooperation but not stable
cooperation. In this paper, by incorporating population density and individual
mobility into the spatial optional public goods game, we study the
coevolutionary dynamics of strategy updating and benefit-seeking migration.
With low population density and slow movement, an optimal level of cooperation
is easy to be reached. An increase in population density and speed-up of
free-floating of competitive agents will suppress cooperation. A log-log
relation between the levels of cooperation and the free-floating probability is
found. Theoretical analysis indicates that the decrease of cooperator frequency
in the present model should result from the increased interactions between
different agents, which may originate from the increased cluster size or the
speed-up of random-movement.
