From social contracts to climate agreements, individuals engage in groups that must collectively reach decisions with varying levels of equality and fairness. These dilemmas also pervade Distributed Artificial Intelligence, in domains such as automated negotiation, conflict resolution or resource allocation. As evidenced by the well-known Ultimatum Game -- where a Proposer has to divide a resource with a Responder -- payoff-maximizing outcomes are frequently at odds with fairness. Eliciting equality in populations of self-regarding agents requires judicious interventions. Here we use knowledge about agents' social networks to implement fairness mechanisms, in the context of Multiplayer Ultimatum Games. We focus on network-based role assignment and show that preferentially attributing the role of Proposer to low-connected nodes increases the fairness levels in a population. We evaluate the effectiveness of low-degree Proposer assignment considering networks with different average connectivity, group sizes, and group voting rules when accepting proposals (e.g. majority or unanimity). We further show that low-degree Proposer assignment is efficient, not only optimizing fairness, but also the average payoff level in the population. Finally, we show that stricter voting rules (i.e., imposing an accepting consensus as requirement for collectives to accept a proposal) attenuates the unfairness that results from situations where high-degree nodes (hubs) are the natural candidates to play as Proposers. Our results suggest new routes to use role assignment and voting mechanisms to prevent unfair behaviors from spreading on complex networks.

中文翻译：

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通过基于学位的角色分配，复杂网络中集体公平的演变

从社会契约到气候协议，个人参与必须以不同程度的平等和公正共同做出决定的群体。这些难题在自动协商，冲突解决或资源分配等领域也普遍存在于分布式人工智能中。正如著名的最后通Game博弈所证明的那样（提议者必须用响应者来划分资源），使收益最大化的结果常常与公平性相矛盾。争取自律代理人的平等需要明智的干预。在这里，我们在多人最后通Games游戏的背景下，使用有关代理人社交网络的知识来实现​​公平机制。我们专注于基于网络的角色分配，并表明将Proposer的角色优先分配给低连接节点可以提高总体的公平性。我们在接受提案（例如多数或一致意见）时，考虑具有不同平均连通性，小组规模和小组投票规则的网络，评估低度提案者分配的有效性。我们进一步表明，低学位的提议者分配是有效的，不仅可以优化公平性，而且可以优化总体中的平均收益水平。最后，我们表明，更严格的投票规则（即，将接受共识作为要求集体接受提案的条件），可以减轻由于高度节点（集线器）自然充当提案人而导致的不公平现象。