Stochastic and Strategy-Proof Auctions for Statistical Inferences

Abstract

We study a stochastic auction in a multi-items and unit-demand setting where bidders have one-dimensional type spaces. In a usual Pareto-efficient auction such as the VCG auction, items are allocated deterministically to bidders depending on their bids. However, even if an auctioneer implements a deterministic auction repeatedly, data that the auctioneer and bidders can get from the auction would be limited because the bidder with the highest bid gets the best item, the bidder with second highest bid gets the second best item, and so on surely. Then, for example, the auctioneer cannot infer what happens if the best item was allocated to the other bidder. We consider a stochastic auction which allocates items stochastically to bidders according to their bids in order to get rich data. We introduce a stochastic auction rule that is strategy-proof and individual rational. Moreover, we show that our stochastic auction can be used to get rich data, and yields relatively high revenue compared to the VCG auction in a computer experiment.