On the rapid convergence of a class of decentralized decision processes: quantized progressive second-price auctions

A progressive second price (PSP) auction mechanism was proposed in (Semret, Liao, Campbell & Lazar 2000) for network bandwidth allocation. In this paper a quantized version of this mechanism (Q-PSP) is analyzed where the agents have similar demand functions and submit bids synchronously. It is shown that the non-linear dynamics induced by this mechanism are such that the prices bid by the various agents and the quantities allocated to these agents converge in at most five iterations or oscillate indefinitely; this behaviour is not only independent of the number of agents involved but is also independent of the number of quantization levels. keywords: complex networks, non-linear dynamics, multi-agent systems, markets, auctions, games