Wireless and Computing Resource Allocation for Selfish Computation Offloading in Edge Computing

We consider the problem of allocating wireless and computing resources to a set of autonomous wireless devices in an edge computing system. Devices in the system can decide whether or not to use edge computing resources for offloading computing tasks so as to minimize their completion time, while the edge cloud operator can allocate wireless and computing resources to the devices. We model the interaction between devices and the operator as a Stackelberg game, prove the existence of Stackelberg equilibria, and propose an efficient decentralized algorithm for computing equilibria. We provide a bound on the price of anarchy of the game, which also serves as an approximation ratio bound for the proposed algorithm. Our simulation results show that the joint allocation of wireless and computing resources by the operator can halve the completion times compared to a system with static resource allocation. At the same time, the convergence time of the proposed algorithm is approximately linear in the number of devices, and thus it could be effectively implemented for edge computing resource management.