Redistribution in Public Project Problems via Neural Networks
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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......
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