Redistribution in Public Project Problems via Neural Networks

Abstract

Many important problems in multiagent systems involve resource allocations. Self-interested agents may lie about their valuations if doing so increases their own utilities. Therefore, it is necessary to design mechanisms (collective decision-making rules) with desired properties and objectives. The VCG redistribution mechanisms are efficient (the agents who value the resources the most will be allocated), strategy-proof (the agents have no incentives to lie about their valuations), and weakly budget-balanced (no deficits). We focus on the VCG redistribution mechanisms for the classic public project problem, where a group of agents needs to decide whether or not to build a non-excludable public project. We design mechanisms via neural networks with two welfare-maximizing objectives: optimal in the worst case and optimal in expectation. Previous studies showed two worst-case optimal mechanisms for 3 agents, but worst-case optimal mechanisms have not been identified for more than 3 agents. For maximizing expected welfare, there are no existing results. We use neural networks to design VCG redistribution mechanisms. Neural networks have been used to design the redistribution mechanisms for multi-unit auctions with unit demand. We show that for the public project problem, the previously proposed neural networks, which led to optimal/near-optimal mechanisms for multi-unit auctions with unit demand, perform abysmally for the public project problem. We significantly improve the existing networks on multiple fronts: We conduct a GAN network to generate worst-case type profiles and feed prior distribution into loss function to provide quality gradients for the optimal-in-expectation objective. We adopt dimension reduction to handle a larger number of agents and we adopt supervised learning into the best manual mechanism as initialization, then leave it into unsupervised learning. For the worst case, we get better results than the existing manual mechanisms, and for the optimal-in-expectation objective, our mechanisms’ performances are close to the theoretical optimal performance.