  Cooperation or defection and participation or withdrawal are well-known
options of behavior in game-like activities in free societies, yet the
co-evolutionary dynamics of these behavioral traits in the individual level are
not well understood. Here we investigate the continuous voluntary public good
game, in which individuals have two types of continuous-valued options: a
probability of joining the public good game and a level of cooperative
investment in the game. Our numerical results reveal hitherto unreported
phenomena: (i) The evolutionary dynamics are initially characterized by
oscillations in individual cooperation and participation levels, in contrast to
the population-level oscillations that have previously been reported. (ii)
Eventually, the population's average cooperation and participation levels
converge to and stabilize at a center. (iii) Then, a most peculiar phenomenon
unfolds: The strategies present in the population diversify and give rise to a
"cloud" of tinkering individuals who each tries out a different strategy, and
this process continues unchecked as long as the population's cooperation and
participation levels remain balanced. Over time, however, imbalances build up
as a consequence of random drift and there is a sudden and abrupt collapse of
the strategy-diversity cloud. The process then repeats again in a cyclic
manner. To understand the three aforementioned phenomena, we investigate the
system analytically using adaptive-dynamics techniques. Our analysis casts
light on the mechanisms which underpin the unexpected and surprising
evolutionary dynamics.
