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.

中文翻译：

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网络中的不和谐与和谐

考虑一个在网络上玩的协调游戏，代理人更喜欢采取更接近其邻居的行动以及接近行动空间中自己理想点的行动。我们探讨了协调博弈的福利结果如何取决于网络结构和整个网络中理想点的分布。为此，我们设想一个善意的或对抗性的计划者，要付出一定的代价来改变理想点，以便在受到约束的情况下最大化或最小化功利主义福利。通过将干预分解为网络邻接矩阵的主要组成部分，可以获得最佳干预的完整表征。福利对于与最后一个主要组成部分成比例的干预最为敏感，后者主要关注局部分歧。福利最大化的规划师可以最佳地减少当地的分歧，使邻居的理想点更接近，而恶意的对手则最佳地驱使邻居的理想点分开，从而减少福利。这种使福利最大化/最小化的干预措施与改变某些传统的不和谐措施（例如均衡行动的横截面变化）所采取的措施截然不同。实际上，一个反对者在最大程度上提高对福利的影响方面会产生分歧，这将最大程度地降低其对均衡行为的整体变化的影响，从而突出说明了改善福利与增强均衡行为的整体凝聚力之间的紧张关系。这种使福利最大化/最小化的干预措施与改变某些传统的不和谐措施（例如均衡行动的横截面变化）所采取的措施截然不同。实际上，一个反对者在最大程度上提高对福利的影响方面会产生分歧，这将最大程度地降低其对均衡行为的整体变化的影响，从而突出说明了改善福利与增强均衡行为的整体凝聚力之间的紧张关系。这种使福利最大化/最小化的干预措施与改变某些传统的不和谐措施（例如均衡行动的横截面变化）所采取的措施截然不同。实际上，一个反对者在最大程度上提高对福利的影响方面会产生分歧，这将最大程度地降低其对均衡行为的整体变化的影响，从而突出说明了改善福利与增强均衡行为的整体凝聚力之间的紧张关系。