Optimal-in-expectation redistribution mechanisms

• Authors: Mingyu Guo;Vincent Conitzer
• Venue: Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
• Year: 2008

Many important problems in multiagent systems involve the allocation of multiple resources to multiple agents. If agents are self-interested, they will lie about their valuations for the resources if they perceive this to be in their interest. The well-known VCG mechanism allocates the items efficiently, is incentive compatible (agents have no incentive to lie), and never runs a deficit. Nevertheless, the agents may have to make large payments to a party outside the system of agents, leading to decreased utility for the agents. Recent work has investigated the possibility of redistributing some of the payments back to the agents, without violating the other desirable properties of the VCG mechanism. We study multi-unit auctions with unit demand, for which previously a mechanism has been found that maximizes the worst-case redistribution percentage. In contrast, we assume that a prior distribution over the agents' valuations is available, and try to maximize the expected total redistribution. We analytically solve for a mechanism that is optimal among linear redistribution mechanisms. The optimal linear mechanism is asymptotically optimal. We also propose discretization redistribution mechanisms. We show how to automatically solve for the optimal discretization redistribution mechanism for a given discretization step size, and show that the resulting mechanisms converge to optimality as the step size goes to zero. We also present experimental results showing that for auctions with many bidders, the optimal linear redistribution mechanism redistributes almost everything, whereas for auctions with few bidders, we can solve for the optimal discretization redistribution mechanism with a very small step size.