A study of auction mechanisms for multilateral procurement based on subgradient and bundle methods

The use of iterative auctions is very common in procurement processes, where the market‐maker often does not have access to complete and truthful information about the bidders’ private valuations of the resources on sale. The literature on the design of iterative mechanisms for combinatorial auctions has addressed only the most basic cases and has been dominated by primal‐dual approaches. In this paper, we consider a general production/consumption exchange of interdependent goods, for which we investigate iterative auction mechanisms based on mathematical programming dual decomposition methods. We focus on Lagrangian relaxation and the solution of the Lagrangian dual through subgradient algorithms and the bundle method. A case study of a simulated wood chip market is used to evaluate numerically the efficiency of the mechanisms.