  The optimal offloading of tasks in heterogeneous edge-computing scenarios is
of great practical interest, both in the selfish and fully cooperative setting.
In practice, such systems are typically very large, rendering exact solutions
in terms of cooperative optima or Nash equilibria intractable. For this
purpose, we adopt a general mean-field formulation in order to solve the
competitive and cooperative offloading problems in the limit of infinitely
large systems. We give theoretical guarantees for the approximation properties
of the limiting solution and solve the resulting mean-field problems
numerically. Furthermore, we verify our solutions numerically and find that our
approximations are accurate for systems with dozens of edge devices. As a
result, we obtain a tractable approach to the design of offloading strategies
in large edge-computing scenarios with many users.
