In order to coordinate players in a game must first identify a target pattern of behaviour. In this paper we investigate the difficulty of identifying prominent outcomes in two kinds of binary action coordination problems in social networks: pure coordination games and anti-coordination games. For both environments, we determine the computational complexity of finding a strategy profile that (i) maximises welfare, (ii) maximises welfare subject to being an equilibrium, and (iii) maximises potential. We show that the complexity of these objectives can vary with the type of coordination problem. Objectives (i) and (iii) are tractable problems in pure coordination games, but for anti-coordination games are NP-hard. Objective (ii), finding the best Nash equilibrium, is NP-hard for both. Our results support the idea that environments in which actions are strategic complements (e.g., technology adoption) facilitate successful coordination more readily than those in which actions are strategic substitutes (e.g., public good provision).

翻译：为了在博弈中实现协调，玩家必须首先确定一个目标行为模式。本文研究了在社交网络中的两类二元行动协调问题（纯协调博弈与反协调博弈）中识别显著结果的难度。针对这两种环境，我们确定了以下策略组合的计算复杂度：(i) 最大化福利；(ii) 在满足均衡约束条件下最大化福利；(iii) 最大化势函数。结果表明，这些目标的复杂度会随协调问题的类型而变化。在纯协调博弈中，目标(i)和(iii)是可解问题，但在反协调博弈中属于NP难问题。目标(ii)——寻找最优纳什均衡——在两类博弈中均为NP难问题。我们的研究结果支持了以下观点：行动具有战略互补性（如技术采纳）的环境比行动具有战略替代性（如公共物品供给）的环境更能促进成功协调。