  The growing demand for edge computing resources, particularly due to
increasing popularity of Internet of Things (IoT), and distributed machine/deep
learning applications poses a significant challenge. On the one hand, certain
edge service providers (ESPs) may not have sufficient resources to satisfy
their applications according to the associated service-level agreements. On the
other hand, some ESPs may have additional unused resources. In this paper, we
propose a resource-sharing framework that allows different ESPs to optimally
utilize their resources and improve the satisfaction level of applications
subject to constraints such as communication cost for sharing resources across
ESPs. Our framework considers that different ESPs have their own objectives for
utilizing their resources, thus resulting in a multi-objective optimization
problem. We present an $N$-person \emph{Nash Bargaining Solution} (NBS) for
resource allocation and sharing among ESPs with \emph{Pareto} optimality
guarantee. Furthermore, we propose a \emph{distributed}, primal-dual algorithm
to obtain the NBS by proving that the strong-duality property holds for the
resultant resource sharing optimization problem.
  Using synthetic and real-world data traces, we show numerically that the
proposed NBS based framework not only enhances the ability to satisfy
applications' resource demands, but also improves utilities of different ESPs.
