  The emergence of new communication technologies allows us to expand our
understanding of distributed control and consider collaborative decision-making
paradigms. With collaborative algorithms, certain local decision-making
entities (or agents) are enabled to communicate and collaborate on their
actions with one another to attain better system behavior. By limiting the
amount of communication, these algorithms exist somewhere between centralized
and fully distributed approaches. To understand the possible benefits of this
inter-agent collaboration, we model a multi-agent system as a common-interest
game in which groups of agents can collaborate on their actions to jointly
increase the system welfare. We specifically consider $k$-strong Nash
equilibria as the emergent behavior of these systems and address how well these
states approximate the system optimal, formalized by the $k$-strong price of
anarchy ratio. Our main contributions are in generating tight bounds on the
$k$-strong price of anarchy in finite resource allocation games as the solution
to a tractable linear program. By varying $k$ --the maximum size of a
collaborative coalition--we observe exactly how much performance is gained from
inter-agent collaboration. To investigate further opportunities for
improvement, we generate upper bounds on the maximum attainable $k$-strong
price of anarchy when the agents' utility function can be designed.
