Computer-aided mechanism design: designing revenue-optimal mechanisms via neural networks

Using AI approaches to automatically design mechanisms has been a central research mission at the interface of AI and economics [Conitzer and Sandholm, 2002]. Previous approaches that a empt to design revenue optimal auctions for the multi-dimensional settings fall short in at least one of the three aspects: 1) representation --- search in a space that probably does not even contain the optimal mechanism; 2) exactness --- finding a mechanism that is either not truthful or far from optimal; 3) domain dependence --- need a different design for different environment settings. To resolve the three difficulties, in this paper, we put forward a uni ed neural network based framework that automatically learns to design revenue optimal mechanisms. Our framework consists of a mechanism network that takes an input distribution for training and outputs a mechanism, as well as a buyer network that takes a mechanism as input and output an action. Such a separation in design mitigates the difficulty to impose incentive compatibility constraints on the mechanism, by making it a rational choice of the buyer. As a result, our framework easily overcomes the previously mentioned difficulty in incorporating IC constraints and always returns exactly incentive compatible mechanisms. We then applied our framework to a number of multi-item revenue optimal design settings, for a few of which the theoretically optimal mechanisms are unknown. We then go on to theoretically prove that the mechanisms found by our framework are indeed optimal.