Mechanism Design for Data Science

Abstract: Good economic mechanisms depend on the preferences of participants in the mechanism. For example, the revenue-optimal auction for selling an item is parameterized by a reserve price, and the appropriate reserve price depends on how much the bidders are willing to pay. A mechanism designer can potentially learn about the participants' preferences by observing historical data from the mechanism; the designer could then update the mechanism in response to learned preferences to improve its performance. The challenge of such an approach is that the data corresponds to the actions of the participants and not their preferences. Preferences can potentially be inferred from actions but the degree of inference possible depends on the mechanism. In the optimal auction example, it is impossible to learn anything about preferences of bidders who are not willing to pay the reserve price. These bidders will not cast bids in the auction and, from historical bid data, the auctioneer could never learn that lowering the reserve price would give a higher revenue (even if it would). To address this impossibility, the auctioneer could sacrifice revenue optimality in the initial auction to obtain better inference properties so that the auction's parameters can be adapted to changing preferences in the future. This paper develops the theory for optimal mechanism design subject to good inferability.