标题： 通过给予高度邻居更多帮助来增强合作 显示英文标题

标题： Enhancement of cooperation by giving high-degree neighbors more help

摘要： 在本文中，我们研究了优先援助在捐赠博弈中对合作的影响。 合作者以一定成本为其邻居提供利益。 叛徒不支付成本，也不分配任何利益。 合作者的总贡献是固定的，他/她将贡献不均等地分配给其邻居。 每个个体被分配一个权重，该权重是其度数的幂，其中指数$\alpha$是一个可调参数。 合作者$i$对邻居$j$的贡献量与$j$的权重成比例。 有趣的是，我们发现存在一个$\alpha$的最优值（为正），导致合作水平最高。 这一现象表明，为了增强合作，个体可以给予高程度邻居更多帮助，但仅限于一定程度。 显示英文摘要

摘要： 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.