Efficient and dynamic double auctions for resource allocation

We formulate a class of divisible resource allocation problems among a collection of suppliers and demanders as double-sided auction games. The auction mechanism adopted in this paper inherits some properties of the VCG style auction mechanism, like the incentive compatibility and the efficiency of Nash Equilibrium (NE). In this paper, we propose a novel dynamic process to implement the efficient NE for the underlying auction game. Basically, the double-sided auction game is formulated as a pair of single-sided auction games which are coupled via a joint potential quantity such that the best responses of the players in each single-sided auction and the potential quantity are updated under certain regulations. We introduce a pair of parameters which reveals some rough information related to the valuation or cost functions of players; then, assisted with the given parameters, at each iteration step, a pair of buyer and seller update their best responses under the constrained sets of their bid profiles respectively. We show the advantage of the increase of the potential quantity and individual allocation, and hence the auction game system converges to the efficient NE.