Strategic Resource Pricing and Allocation in a 5G Network Slicing Stackelberg Game

We consider a marketplace in the context of 5G network slicing, where service providers (SP), i.e., slice tenants, are in competition for the access to the network resource owned by an infrastructure provider who relies on network slicing. We model the interactions between the end-users (followers) and the SPs (leaders) as a Stackelberg game. We prove that the competition between the SPs results in a multi-resource Tullock rent-seeking game. To determine resource pricing and allocation, we devise two innovative market mechanisms. First, we assume that the SPs are pre-assigned with fixed shares (budgets) of infrastructure, and rely on a trading post mechanism to allocate the resource. Under this mechanism, the SPs can redistribute their budgets in bids and customise their allocations to maximise their profits. We prove that their decision problems give rise to a noncooperative game, which admits a unique Nash equilibrium when dealing with a single resource. Second, when SPs have no bound on their budget, we formulate the problem as a pricing game with coupling constraints and derive the market prices as the duals of the coupling constraints. In addition, we prove that the pricing game admits a unique variational equilibrium. We propose two online learning algorithms to compute solutions to the market mechanisms. A third fully distributed algorithm based on a proximal method is proposed to compute the variational equilibrium solution to the pricing game. Finally, we run numerical simulations to analyse the economic properties of the market mechanisms and the convergence rates of the algorithms