Stable and balanced outcomes of network bargaining games have been investigated recently, but the existence of such outcomes requires that the linear program relaxation of a certain maximum matching problem have integral optimal solution. We propose an alternative model for network bargaining games in which each edge acts as a player, who proposes how to split the weight of the edge among the two incident nodes. Based on the proposals made by all edges, a selection process will return a set of accepted proposals, subject to node capacities. An edge receives a commission if its proposal is accepted. The social welfare can be measured by the weight of the matching returned. The node users exhibit two characteristics of human nature: greed and idealism. We define these notions formally and show that the distributed protocol by Kanoria et al. can be modified to be run by the edge players such that the configuration of proposals will converge to a pure Nash Equilibrium, without the integrality gap assumption. Moreover, after the nodes have made their greedy and idealistic choices, the remaining ambiguous choices can be resolved in a way such that there exists a Nash Equilibrium that will not hurt the social welfare too much.

中文翻译：

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面对不稳定，贪婪和理想主义，优化网络讨价还价游戏的社会福利

网络讨价还价博弈的稳定均衡结果最近得到了研究，但是这种结果的存在要求某个最大匹配问题的线性程序松弛具有整体最优解。我们为网络讨价还价游戏提出了一种替代模型，其中每个边缘都充当玩家，提出了如何在两个入射节点之间分配边缘权重的方法。根据各方面提出的建议，选择过程将返回一组接受的建议，取决于节点的能力。如果边缘的提议被接受，则边缘获得佣金。社会福利可以通过匹配的权重来衡量。节点用户表现出人性的两个特征：贪婪和理想主义。我们正式定义了这些概念，并表明了Kanoria等人的分布式协议。可以修改为由边缘参与者运行，以便提案的配置将收敛到纯Nash均衡，而无需完整性缺口假设。此外，在节点做出贪婪和理想的选择之后，可以以某种方式解决剩余的歧义选择，使得存在纳什均衡不会对社会福利造成太大损害。