Collaborative Decision-Making and the k-Strong Price of Anarchy in Common Interest Games

Abstract: The control of large-scale, multi-agent systems often entails distributing decision-making across the system components. However, with advances in communication and computation technologies, we can consider new collaborative decision-making paradigms that exist somewhere between centralized and distributed control. In this work, we seek to understand the benefits and costs of increased collaborative communication in multi-agent systems. We specifically study this in the context of common interest games in which groups of up to k agents can coordinate their actions in maximizing the common objective function. The equilibria that emerge in these systems are the k-strong Nash equilibria of the common interest game; studying the properties of these states can provide relevant insights into the efficacy of inter-agent collaboration. Our contributions come threefold: 1) provide bounds on how well k-strong Nash equilibria approximate the optimal system welfare, formalized by the k-strong price of anarchy, 2) study the run-time and transient performance of collaborative agent-based dynamics, and 3) consider the task of redesigning objectives for groups of agents which improve system performance. We study these three facets generally as well as in the context of resource allocation problems, in which we provide tractable linear programs that give tight bounds on the k-strong price of anarchy.