Autobidding With Interdependent Values

In this paper, we initiate the study of autobidding where the signals for each bidder can be noisy and correlated. Our first set of results showcases the failure of traditional auctions such as the second-price auction (SPA) and the first-price auction (FPA). In particular, uniform bidding is not an optimal bidding strategy for SPA and both SPA and FPA can have arbitrarily poor efficiency. To circumvent this, we propose the Contextual Second Price Auction (CSPA), a novel mechanism which mitigates the aforementioned adverse effects by leveraging multiple signals to adjust the allocation of SPA. We show that uniform bidding is an optimal bidding strategy in CSPA and we prove a tight bound on the price for anarchy for CSPA of 2, thus recovering the well-established results in the independent setting. Finally, we show that CSPA always achieves at least half the welfare of SPA; moreover this is also tight.