A Unified Framework for Strong Price of Anarchy in Clustering Games

We devise a unified framework for quantifying the inefficiency of equilibria in clustering games on networks. This class of games has two properties exhibited by many real-life social and economic settings: (a) an agent’s utility is affected only by the behavior of her direct neighbors rather than that of the entire society, and (b) an agent’s utility does not depend on the actual strategies chosen by agents, but rather by whether or not other agents selected the same strategy. Our framework is sufficiently general to account for unilateral versus coordinated deviations by coalitions of different sizes, different types of relationships between agents, and different structures of strategy spaces. Many settings that have been recently studied are special cases of clustering games on networks. Using our framework: (1) We recover previous results for special cases and provide extended and improved results in a unified way. (2) We identify new settings that fall into the class of clustering games on networks and establish price of anarchy and strong price of anarchy bounds for them.