Double-Auction Mechanisms for Resource Trading Markets

We consider a double-auction mechanism, which was recently proposed in the context of rate allocation in mobile data-offloading markets; our mechanism is also applicable to the problem of bandwidth allocation in network slicing markets. Network operators (users) derive benefit from offloading their traffic to third party WiFi or femtocell networks (link-suppliers). Link-suppliers experience costs for the additional capacity that they provide. Users and link-suppliers (collectively referred to as agents) have their pay-offs and cost functions as private knowledge. A network-manager decomposes the problem into a network problem (with surrogate pay-offs and surrogate cost functions) and agent problems (one per agent). The surrogate pay-offs and cost functions are modulated by the agents' bids. Agents' payoffs and costs are then determined by the allocations and prices set by the network-manager. Under this design, so long as the agents do not anticipate the effect of their actions on the prices set by the network-manager (i.e., price-taking agents), a competitive equilibrium exists as a solution to the network and agent problems, and this equilibrium optimizes the sum utility of all agents. However, this design fails when the agents (including the link-supplier) are all strategic (price-anticipating). Specifically, the presence of a strategic link-supplier drives the system to an undesirable equilibrium with zero participation resulting in an efficiency loss of 100%. This is in stark contrast to an earlier setting where the users alone are strategic but the link-supplier is not - the efficiency loss is known to be at most 34%. The paper then proposes the following Stackelberg game modification with asymmetric information structures for link-supplier and users in order to alleviate the efficiency-loss problem: the network-manager first announces the allocation and payment functions; he then invites the link-supplier to announce its bid, following which the users are invited to respond with their bids. The resulting Stackelberg games' efficiency losses can be characterized in terms of the link-supplier's cost function when the users' pay-off functions are linear. Specifically, when the link-supplier's cost function is quadratic, the worst case efficiency loss is 25%. Further, the loss in efficiency improves for polynomial cost functions of higher degree. For non-linear utility functions (e.g., α-fair and log utilities), we demonstrate the efficacy of the proposed mechanism via. a detailed numerical study.