Auction-based resource allocation game under a hierarchical structure

This paper studies a class of auction-based resource allocation games under a hierarchical structure, such that each supplier is assigned a certain amount of resource from a single provider and allocates it to its buyers with auction mechanisms. To implement the efficient allocations for the underlying hierarchical system, we first design an auction mechanism, for each local system composed of a supplier and its buyers, which inherits the advantages of the progressive second price mechanism. By employing a dynamic algorithm, each local system converges to its own efficient Nash equilibrium, at which the efficient resource allocation is achieved and the bidding prices of all the buyers in this local system are identical with each other. After the local systems reach their own equilibria respectively, the resources assigned to suppliers are readjusted via a dynamic hierarchical algorithm with respect to the bidding prices associated with the implemented equilibria of local systems. By applying the proposed hierarchical process, the formulated hierarchical system can converge to the efficient allocation under certain mild conditions. The developed results in this work are demonstrated with simulations.