  Our wellbeing depends as much on our personal success, as it does on the
success of our society. The realization of this fact makes cooperation a very
much needed trait. Experiments have shown that rewards can elevate our
readiness to cooperate, but since giving a reward inevitably entails paying a
cost for it, the emergence and stability of such behavior remain elusive. Here
we show that allowing for the act of rewarding to self-organize in dependence
on the success of cooperation creates several evolutionary advantages that
instill new ways through which collaborative efforts are promoted. Ranging from
indirect territorial battle to the spontaneous emergence and destruction of
coexistence, phase diagrams and the underlying spatial patterns reveal
fascinatingly reach social dynamics that explains why this costly behavior has
evolved and persevered. Comparisons with adaptive punishment, however, uncover
an Achilles heel of adaptive rewarding that is due to over-aggression, which in
turn hinders optimal utilization of network reciprocity. This may explain why,
despite of its success, rewarding is not as firmly weaved into our societal
organization as punishment.
