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Convergence of Lump-Sum Markets with Price-Anticipating Agents

Large engineering systems exist, such as air traffic control and Internet routing, for which resources must be allocated amongst a few competitive agents with significant market power. Lump-sum market mechanisms are attractive for these resource allocation problems because the ability of individual agents to manipulate market prices has been shown to be limited. This work addresses the issue of convergence to the Nash equilibrium of lump-sum markets with price-anticipating agents. By defining a continuous time agent update dynamic and employing Lyapunov stability theory, convergence is guaranteed for arbitrary initial allocations and agent specific update rates. Simulation results demonstrate the convergence properties of both the continuous dynamics and the best response discrete update dynamic.