Double-Sided Auction Games for Efficient Resource Allocation

Abstract

With an effort to allocate divisible resources among suppliers and consumers, a double-sided auction model is designed to decide strategies for individual players in this chapter. Under the auction mechanism with the VCG-type payment, the incentive compatibility holds, and the efficient bid profile is a Nash equilibrium (NE). Different from the single-sided auction in the previous chapter, there exists an infinite number of NEs in the underlying double-sided auction game, which brings difficulties for players to implement the efficient solution. To overcome this challenge, we formulate the double-sided auction game as a pair of single-sided auction games which are coupled via a joint potential quantity of the resource. A decentralized iteration procedure is then designed to achieve efficient solution, where a single player, a buyer or a seller, implements his best strategy with respect to a given potential quantity and a constraint on his bid strategy. Accordingly, the potential quantity is updated with respect to iteration steps as well. It is verified that the system converges to the efficient NE within finite iteration steps in the order of \(\mathscr {O}(\ln (1/\varepsilon ))\) with \(\varepsilon \) representing the termination criterion of the algorithm.