Learning Utilities and Equilibria in Non-Truthful Auctions

Mechanism design devises systems in which multiple agents take strategic actions based on their private preferences (designated as types). For example, an auctioneer devises rules that determine an auction's winner and payments, based on bidders' actions (the bids); the bidders then, knowing the rule and their types -- in this case their own values for the item at sale -- strategize over their bids. The following task is central to many aspects of mechanism design: given agents' strategies, evaluate each agent's performance, or utility. To start with, agents are most often interested in predicting the performance of their strategies given what the other agents do; nowadays, auctioneers and third-party service providers often give guidance to bidding, and are interested in such evaluations as well. An auctioneer often would like to find out if a profile of strategies best respond to each other and are hence at equilibrium; revenue, welfare and surplus analysis at equilibrium is all based on utility estimation. Recent development in online ad auctions (such as the oCPX auctions) sees growing popularity of delegated bidding, where bidders entrust the auctioneer/platform with the task of bidding. Auctioneers in this scenario must estimate the bidders' utilities given their bidding strategies.