  We propose a strategy for achieving maximum cooperation in evolutionary games
on complex networks. Each individual is assigned a weight that is proportional
to the power of its degree, where the exponent alpha is an adjustable parameter
that controls the level of diversity among individuals in the network. During
the evolution, every individual chooses one of its neighbors as a reference
with a probability proportional to the weight of the neighbor, and updates its
strategy depending on their payoff difference. It is found that there exists an
optimal value of alpha, for which the level of cooperation reaches maximum.
This phenomenon indicates that, although high-degree individuals play a
prominent role in maintaining the cooperation, too strong influences from the
hubs may counterintuitively inhibit the diffusion of cooperation. We provide a
physical theory, aided by numerical computations, to explain the emergence of
the optimal cooperation. Other pertinent quantities such as the payoff, the
cooperator density as a function of the degree, and the payoff distribution,
are also investigated. Our results suggest that, in order to achieve strong
cooperation on a complex network, individuals should learn more frequently from
neighbors with higher degrees, but only to certain extent.
