Analysis of decentralized decision processes in competitive markets: Quantized single and double-sided auctions

In this paper two decentralized decision processes for competitive markets are analyzed under quantized pricing; these proposed decentralized processes have toy models which are similar to those for market models in such areas as electricity systems, and communication networks. First, quantized dynamical auctions for supply markets (i.e., only sellers are assumed to have market power) are presented to allocate a divisible resource target among arbitrary populations of suppliers. Both rapid convergence and approximate social optima are achieved. Second, the quantized mechanism is extended to a double auction case where competition of both sellers and buyers is considered. Under the non-discriminatory pricing assumption (i.e., charging the same price for different agents), the aforementioned mechanism is shown to have rapid convergence and efficiency performance (i.e., maximum of social welfare) as in the single-sided dynamical auction case.