Equilibria and convergence of auctions on networks

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.