We study the problem of auction design for advertising platforms that face strategic advertisers who are bidding across platforms. Each advertiser's goal is to maximize their total value or conversions while satisfying some constraint(s) across all the platforms they participates in. In this paper, we focus on advertisers with return-over-investment (henceforth, ROI) constraints, i.e. each advertiser is trying to maximize value while making sure that their ROI across all platforms is no less than some target value. An advertiser interacts with the platforms through autobidders -- for each platform, the advertiser strategically chooses a target ROI to report to the platform's autobidder, which in turn uses a uniform bid multiplier to bid on the advertiser's behalf on the queries owned by the given platform.

The rise of interactive platforms like conversational AI assistants introduces a new dimension to ad auctions: time. As a conversation evolves, a platform can learn more about a user's interests, creating a fundamental trade-off: delay ad delivery to acquire precise information about ad quality, or deliver the ad immediately to capitalize on a thick market before potential bidders are revealed to be poor matches. We study this trade-off in a model where a revenue-maximizing platform can commit to an auction format (first- or second-price) but not to its timing, endogenously choosing when to run the auction after observing its beliefs about advertisers' ad quality.

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.

We study a setting where agents use no-regret learning algorithms to participate in repeated auctions. Recently, Kolumbus and Nisan [2022a] showed, rather surprisingly, that when bidders participate in second-price auctions using no-regret bidding algorithms, no matter how large the number of interactions $T$ is, the runner-up bidder may not converge to bidding truthfully. Our first result shows that this holds forall deterministictruthful auctions. We also show that the ratio of the learning rates of different bidders can qualitatively affect the convergence of the bidders. Next, we consider the problem of revenue maximization in this environment. In the setting with fully rational bidders, the seminal result of Myerson [1981] showed that revenue can be maximized by using a second-price auction with reserves. We show that, in stark contrast, in our setting with learning bidders, randomized auctions can have strictly better revenue guarantees than second-price auctions with reserves, when $T$ is large enough. To do this, we provide a black-box transformation from any truthful auction $A$ to an auction $A'$ such that: i) all mean-based no-regret learners that participate in $A'$ converge to bidding truthfully, ii) the distance between the allocation rule and the payment rule between $A, A'$ is negligible. Finally, we study revenue maximization in the non-asymptotic regime. We define a notion of auctioneer regret that compares the revenue generated to the revenue of a second price auction with truthful bids. When the auctioneer has to use the same auction throughout the interaction, we show an (almost) tight regret bound of $\tilde{\Theta}(T^{3/4})$. Then, we consider the case where the auctioneer can use different auctions throughout the interaction, but in a way that is oblivious to the bids. For this setting, we show an (almost) tight bound of $\tilde{\Theta}(\sqrt{T})$.

Over the past few years, more and more Internet advertisers have started using automated bidding for optimizing their advertising campaigns. Such advertisers have an optimization goal (e.g. to maximize conversions), and some constraints (e.g. a budget or an upper bound on average cost per conversion), and the automated bidding system optimizes their auction bids on their behalf. Often, these advertisers participate on multiple advertising channels and try to optimize across these channels. A central question that remains unexplored is how automated bidding affects optimal auction design in the multi-channel setting.

Auto-bidding has recently become a popular feature in ad auctions. This feature enables advertisers to simply provide high-level constraints and goals to an automated agent, which optimizes their auction bids on their behalf. These auto-bidding intermediaries interact in a decentralized manner in the underlying auctions, leading to new interesting practical and theoretical questions on auction design, for example, in understanding the bidding equilibrium properties between auto-bidder intermediaries for different auctions. In this paper, we examine the effect of different auctions on the incentives of advertisers to report their constraints to the auto-bidder intermediaries. More precisely, we study whether canonical auctions such as first price auction (FPA) and second price auction (SPA) are auto-bidding incentive compatible (AIC): whether an advertiser can gain by misreporting their constraints to the autobidder.

Auto-bidding is now widely adopted as an interface between advertisers and internet advertising as it allows advertisers to specify high-level goals, such as maximizing value subject to a value-per-spend constraint. Prior research has mainly focused on auctions that are truthful (such as a second-price auction) because these auctions admit simple (uniform) bidding strategies and are thus simpler to analyze. The main contribution of this paper is to characterize the efficiency across the spectrum of all auctions, including non-truthful auctions for which optimal bidding may be complex.

Advertisers in online ad auctions are increasingly using auto-bidding mechanisms to bid into auctions instead of directly bidding their value manually. One of the prominent auto-bidding formats is that of target cost-per-acquisition (tCPA) which maximizes the volume of conversions subject to a return-of-investment constraint. From an auction theoretic perspective however, this trend seems to go against foundational results that postulate that for profit-maximizing (aka quasi-linear) bidders, it is optimal to use a classic bidding system like marginal CPA (mCPA) bidding rather than using strategies like tCPA.

We study the mechanism design problem of selling $k$ items to unit-demand buyers with private valuations for the items. A buyer either participates directly in the auction or is represented by an intermediary, who represents a subset of buyers. Our goal is to design robust mechanisms that are independent of the demand structure (i.e. how the buyers are partitioned across intermediaries), and perform well under a wide variety of possible contracts between intermediaries and buyers. We first study the case of $k$ identical items where each buyer draws its private valuation for an item i.i.d. from a known $λ$-regular distribution. We construct a robust mechanism that, independent of the demand structure and under certain conditions on the contracts between intermediaries and buyers, obtains a constant factor of the revenue that the mechanism designer could obtain had she known the buyers' valuations. In other words, our mechanism's expected revenue achieves a constant factor of the optimal welfare, regardless of the demand structure. Our mechanism is a simple posted-price mechanism that sets a take-it-or-leave-it per-item price that depends on $k$ and the total number of buyers, but does not depend on the demand structure or the downstream contracts. Next we generalize our result to the case when the items are not identical. We assume that the item valuations are separable. For this case, we design a mechanism that obtains at least a constant fraction of the optimal welfare, by using a menu of posted prices. This mechanism is also independent of the demand structure, but makes a relatively stronger assumption on the contracts between intermediaries and buyers, namely that each intermediary prefers outcomes with a higher sum of utilities of the subset of buyers represented by it.