Talk by Peng Jia (McGill)

Time and place: Thursday, May 13, 5:20-5:50, 202 Chernoff Hall
Title: Analysis of Two Classes of Decentralized Decision Systems: Quantized Single and Double-Sided Auctions in Competitive Markets (½ hour)
Abstract: In this talk two quantized dynamical auction systems are introduced to solve resource allocation problem in competitive markets. Toy models for these proposed decentralized processes are similar to those for market models in such areas as electricity systems [1,7,8,10,11] and communication networks [5,9,3,6,4]. First, we present quantized dynamical auctions for supply markets (that is to say, markets where only sellers are assumed to have market power) which allocate a divisible resource among arbitrary populations of suppliers. This case is symmetric to that where quantized dynamical auctions are considered for demand markets. Rapid convergence and approximate social optima are achieved in both cases [2]. Second, we describe the extension of these quantized mechanisms to the double auction case where competition among both sellers and buyers is considered. Double auctions are formulated in this work as two single-sided quantized auctions which depend upon joint market quantities and price constraints. Finally, the extended mechanism is shown to have similar rapid convergence and market efficiency (i.e., maximum of social welfare) properties to single-sided dynamical auctions.

[1] Dekrajangpetch, S., Shebl, G. B., June 2000. Structures and formulations for electric power auctions. Electric Power Systems Research 54 (3), 159-167.
[2] Jia, P., Caines, P. E., 2009. Analysis of a class of decentralized dynamical systems: Rapid convergence and efficiency of dynamical quantized auctions, under revision for IMA Journal of Mathematical Control and Information, submitted September, 2009.
[3] Jia, P., Caines, P. E., December 2009. Auctions on networks: Efficiency, consensus, passivity, rate of convergence. In: Proc. 48th IEEE Conf. Decision and Control. Shanghai, China, pp. 8606~8611.
[4] Jia, P., Qu, C. W., Caines, P. E., 2009. On the rapid convergence of a class of decentralized decision processes: Quantized progressive second price auctions. IMA Journal of Mathematical Control and Information 26 (3), 325-355.
[5] Lazar, A. A., Semret, N., 1999. Design and analysis of the progressive second price auction for network bandwidth sharing. Telecommunication Systems, Special Issue on Network Economics, to appear.
[6] Maille, P., Tuffin, B., March 7-11 2004. Multibid auctions for bandwidth allocation in communication networks. In: INFOCOM 2004. Twenty-third Annual Joint Conference of the IEEE Computer and Communications Societies. Vol. 1. Hong Kong, pp. 54~65.
[7] Nicolaisen, J., Petrov, V., Tesfatsion, L., October 2001. Market power and efficiency in a computational electricity market with discriminatory double-auction pricing. IEEE Transactions on Evolutionary Computation 5 (5), 504~523.
[8] Post, D., Coppinger, S., Sheble, G., August 1995. Application of auctions as a pricing mechanism for the interchange of electric power. IEEE Transactions on Power Systems 10 (3), 1580~1584.
[9] Semret, N., Liao, R. R.-F., Campbell, A. T., Lazar, A. A., December 2000. Pricing, provisioning and peering: Dynamic markets for differentiated internet service and implications for network interconnections. IEEE Journal on Selected Areas in Communications 18 (12), 2499~2513.
[10] Swider, D. J., Weber, C., September 2007. Bidding under price uncertainty in multi-unit pay-as-bid procurement auctions for power systems reserve. European Journal of Operational Research 181 (3), 1297~1308.
[11] Wolfram, C. D., 1998. Strategic bidding in a multiunit auction: An empiri- cal analysis of bids to supply electricity in England and Wales. The RAND Journal of Economics 29 (4), 703~725.

Andrew D. Lewis (andrew at