网络中的不和谐与和谐
Discord and Harmony in Networks
摘要：
考虑一个在网络上进行的协调博弈，其中代理更喜欢采取更接近其邻居和行动空间中自己的理想点的行动。我们探讨了协调博弈的福利结果如何依赖于网络结构和整个网络中理想点的分布。为此，我们设想一个仁慈的或敌对的计划者，他以一定的代价进行干预，改变理想点，以最大化或最小化受约束的功利福利。最优干预的一个完整的表征是通过将干预分解成网络邻接矩阵的主成分来获得的。福利是最敏感的干预措施成比例的最后一个主要组成部分，重点是当地的分歧。一个福利最大化的规划者最佳地工作，以减少当地的分歧，使邻居的理想点更接近，而恶意的对手最佳地驱动邻居的理想点，以减少福利。这种福利最大化/最小化的干预措施与改变一些传统的不和谐措施（如均衡行动的横截面变化）的干预措施有很大的不同。事实上，一个对手为了最大化自己对福利的影响而散布分歧，将最大限度地减少自己对均衡行动中全球差异的影响，这突出了改善福利与增强均衡行为的全球凝聚力之间的紧张关系。
英文摘要：
Consider a coordination game played on a network, where agents prefer taking actions closer to those of their neighbors and to their own ideal points in action space. We explore how the welfare outcomes of a coordination game depend on network structure and the distribution of ideal points throughout the network. To this end, we imagine a benevolent or adversarial planner who intervenes, at a cost, to change ideal points in order to maximize or minimize utilitarian welfare subject to a constraint. A complete characterization of optimal interventions is obtained by decomposing interventions into principal components of the network's adjacency matrix. Welfare is most sensitive to interventions proportional to the last principal component, which focus on local disagreement. A welfare-maximizing planner optimally works to reduce local disagreement, bringing the ideal points of neighbors closer together, whereas a malevolent adversary optimally drives neighbors' ideal points apart to decrease welfare. Such welfare-maximizing/minimizing interventions are very different from ones that would be done to change some traditional measures of discord, such as the cross-sectional variation of equilibrium actions. In fact, an adversary sowing disagreement to maximize her impact on welfare will minimize her impact on global variation in equilibrium actions, underscoring a tension between improving welfare and increasing global cohesion of equilibrium behavior.
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