  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.
