Equilibria and convergence of auctions on networks

Authors:
Peng Jia;Peter E. Caines
Affiliations:
Centre for Intelligent Machines and Department of Electrical and Computer Engineering, McGill University, Montreal, Canada;Centre for Intelligent Machines and Department of Electrical and Computer Engineering, McGill University, Montreal, Canada
Venue:
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
Year:
2009

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Abstract

First, a quantized progressive second price auction mechanism called UQ-PSP is developed to allocate a divisible resource among arbitrary populations of agents. It is shown that (i) the states (i.e. bid prices and quantities) of the corresponding iterative dynamical auction system converge to a unique quantized (Nash) equilibrium with a common limit price for all agents, and (ii) the dynamics are independent of the initial data. Second, a network based auction is developed where each agent employs a UQ-PSP scheme by observing only their neighbors' bids. The equilibria and convergence properties of this class of distributed auctions are established and are shown to depend on the network topology, and numerical examples are given.