  In this paper, we study the effect of preferential assistance on cooperation
in the donation game. Cooperators provide benefits to their neighbors at some
costs. Defectors pay no cost and do not distribute any benefits. The total
contribution of a cooperator is fixed and he/she distributes his/her
contribution unevenly to his/her neighbors. Each individual is assigned a
weight that is the power of its degree, where the exponent $\alpha$ is an
adjustable parameter. The amount that cooperator $i$ contributes to a neighbor
$j$ is proportional to $j$'s weight. Interestingly, we find that there exists
an optimal value of $\alpha$ (which is positive), leading to the highest
cooperation level. This phenomenon indicates that, to enhance cooperation,
individuals could give high-degree neighbors more help, but only to a certain
extent.
