arXiv subjects

Andres Perlroth

Publications and source records attributed to Andres Perlroth.

11 recordsLinked to original sources

arXiv2024

Randomized Truthful Auctions with Learning Agents

We study a setting where agents use no-regret learning algorithms to participate in repeated auctions. \citet{kolumbus2022auctions} 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 for \emph{general deterministic} truthful auctions. We also show that the ratio of the learning rates of the bidders can \emph{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, \citet{myerson1981optimal} 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, \emph{randomized} auctions can have strictly better revenue guarantees than second-price auctions with reserves, when $T$ is large enough. Finally, we study revenue maximization in the non-asymptotic regime. We define a notion of {\em auctioneer regret} comparing 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 $\smash{\widetilde \Theta(T^{3/4})}.$ If the auctioneer can change auctions during the interaction, but in a way that is oblivious to the bids, we show an (almost) tight bound of $\smash{\widetilde \Theta(\sqrt{T})}.$

cs.GT↗

arXiv2024

Auto-bidding and Auctions in Online Advertising: A Survey

In this survey, we summarize recent developments in research fueled by the growing adoption of automated bidding strategies in online advertising. We explore the challenges and opportunities that have arisen as markets embrace this autobidding and cover a range of topics in this area, including bidding algorithms, equilibrium analysis and efficiency of common auction formats, and optimal auction design.

cs.GT↗

arXiv2024

Platform Competition in the Autobidding World

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. Our main result is that for a platform trying to maximize revenue, competition with other platforms is a key factor to consider when designing their auction. While first-price auctions are optimal (for both revenue and welfare) in the absence of competition, this no longer holds true in multi-platform settings. We show that there exists a large class of advertiser valuations over queries such that, from the platform's perspective, running a second price auction dominates running a first price auction. Furthermore, our analysis reveals the key factors influencing platform choice of auction format: (i) intensity of competition among advertisers, (ii) sensitivity of bid landscapes to an auction change (driven by advertiser sensitivity to price changes), and (iii) relative inefficiency of second-price auctions compared to first-price auctions.

cs.GT↗

arXiv2024

Ads in Conversations

We study the optimal placement of advertisements for interactive platforms like conversational AI assistants. Importantly, conversations add a feature absent in canonical search markets -- time. The evolution of a conversation is informative about ad qualities, thus a platform could delay ad delivery to improve selection. However, delay endogenously shapes the supply of quality ads, possibly affecting revenue. We characterize the equilibria of first- and second-price auctions where the platform can commit to the auction format but not to its timing. We document sharp differences in the mechanisms' outcomes: first-price auctions are efficient but delay ad delivery, while second-price auctions avoid delay but allocate inefficiently. Revenue may be arbitrarily larger in a second-price auction than in a first-price auction. Optimal reserve prices alleviate these differences but flip the revenue ordering.

econ.TH↗

arXiv2023

Auctions without commitment in the auto-bidding world

Advertisers in online ad auctions are increasingly using auto-bidding mechanisms to bid into auctions instead of directly bidding their value manually. One prominent auto-bidding format is the 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 bidders, it is optimal to use a classic bidding system like marginal CPA (mCPA) bidding rather than using strategies like tCPA. In this paper we rationalize the adoption of such seemingly sub-optimal bidding within the canonical quasi-linear framework. The crux of the argument lies in the notion of commitment. We consider a multi-stage game where first the auctioneer declares the auction rules; then bidders select either the tCPA or mCPA bidding format and then, if the auctioneer lacks commitment, it can revisit the rules of the auction (e.g., may readjust reserve prices depending on the observed bids). Our main result is that so long as a bidder believes that the auctioneer lacks commitment to follow the rule of the declared auction then the bidder will make a higher profit by choosing the tCPA format over the mCPA format. We then explore the commitment consequences for the auctioneer. In a simplified version of the model where there is only one bidder, we show that the tCPA subgame admits a credible equilibrium while the mCPA format does not. That is, when the bidder chooses the tCPA format the auctioneer can credibly implement the auction rules announced at the beginning of the game. We also show that, under some mild conditions, the auctioneer's revenue is larger when the bidder uses the tCPA format rather than mCPA. We further quantify the value for the auctioneer to be able to commit to the declared auction rules.

econ.TH↗

arXiv2023

Multi-Channel Auction Design in the Autobidding World

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. In this paper, we study the problem of setting auction reserve prices in the multi-channel setting. In particular, we shed light on the revenue implications of whether each channel optimizes its reserve price locally, or whether the channels optimize them globally to maximize total revenue. Motivated by practice, we consider two models: one in which the channels have full freedom to set reserve prices, and another in which the channels have to respect floor prices set by the publisher. We show that in the first model, welfare and revenue loss from local optimization is bounded by a function of the advertisers' inputs, but is independent of the number of channels and bidders. In stark contrast, we show that the revenue from local optimization could be arbitrarily smaller than those from global optimization in the second model.

cs.GT↗

arXiv2023

Incentive Compatibility in the Auto-bidding World

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. 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. We consider value-maximizing advertisers in two important settings: when they have a budget constraint and when they have a target cost-per-acquisition constraint. The main result of our work is that for both settings, FPA and SPA are not AIC. This contrasts with FPA being AIC when auto-bidders are constrained to bid using a (sub-optimal) uniform bidding policy. We further extend our main result and show that any (possibly randomized) auction that is truthful (in the classic profit-maximizing sense), scalar invariant and symmetric is not AIC. Finally, to complement our findings, we provide sufficient market conditions for FPA and SPA to become AIC for two advertisers. These conditions require advertisers' valuations to be well-aligned. This suggests that when the competition is intense for all queries, advertisers have less incentive to misreport their constraints. From a methodological standpoint, we develop a novel continuous model of queries. This model provides tractability to study equilibrium with auto-bidders, which contrasts with the standard discrete query model, which is known to be hard. Through the analysis of this model, we uncover a surprising result: in auto-bidding with two advertisers, FPA and SPA are auction equivalent.

econ.TH↗

arXiv2022

A Characterization of the n-th Degree Bounded Stochastic Dominance

We provide a novel characterization of the $n$-th degree bounded stochastic dominance (BSD) order, linking it to the risk tolerance of decision-makers and providing a decision-theoretic foundation for these stochastic orders. Our results reveal that BSD reflects specific risk preferences through the choice of the interval $[a,b]$, by characterizing it in terms of utility functions with globally bounded Arrow--Pratt risk aversion or that satisfy an $n$-convexity condition. They also highlight limitations of BSD, including its dependence on the chosen support interval and the resulting peculiar risk aversion behavior of decision-makers included in the generator of BSD. To partially address this issue, we use our characterization to separate two roles that are combined in BSD: the largest payoff in the lotteries and the upper endpoint of the interval that determines the Arrow--Pratt lower bound. We then introduce a related lower-partial-moment order that provides a clean trade-off between expected value and downside-risk protection. Using our characterization, we present comparative statics results for decision-making under uncertainty with globally bounded risk aversion measures and savings decisions under globally bounded prudence measures, and derive inequalities for $n$-convex functions.

math.PR↗

arXiv2022

Efficiency of non-truthful auctions under auto-bidding

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 mostly focused on auctions which are truthful (such as SPA) since uniform bidding is optimal in such auctions, which makes it manageable to reason about equilibria. A tantalizing question is whether one can obtain more efficient outcomes by leaving the realm of truthful auctions. This is the first paper to study non-truthful auctions in the prior-free auto-bidding setting. Our first result is that non-truthfulness provides no benefit when one considers deterministic auctions. Any deterministic mechanism has a price of anarchy (PoA) of at least $2$, even for $2$ bidders; this matches what can be achieved by deterministic truthful mechanisms. In particular, we prove that the first price auction has PoA of exactly $2$. For our second result, we construct a randomized non-truthful auction that achieves a PoA of $1.8$ for $2$ bidders. This is the best-known PoA for this problem. The previously best-known PoA for this problem was $1.9$ and was achieved with a truthful mechanism. Moreover, we demonstrate the benefit of non-truthfulness in this setting by showing that the truthful version of this randomized auction also has a PoA of $1.9$. Finally, we show that no auction (even randomized, non-truthful) can improve upon a PoA bound of $2$ as the number of advertisers grow to infinity.

cs.GT↗

arXiv2021

Maximizing revenue in the presence of intermediaries

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.

cs.GT↗

arXiv2021

The Family of Alpha,[a,b] Stochastic Orders: Risk vs. Expected Value

In this paper we provide a novel family of stochastic orders that generalizes second order stochastic dominance, which we call the $α,[a,b]$-concave stochastic orders. These stochastic orders are generated by a novel set of "very" concave functions where $α$ parameterizes the degree of concavity. The $α,[a,b]$-concave stochastic orders allow us to derive novel comparative statics results for important applications in economics that cannot be derived using previous stochastic orders. In particular, our comparative statics results are useful when an increase in a lottery's riskiness changes the agent's optimal action in the opposite direction to an increase in the lottery's expected value. For this kind of situation, we provide a tool to determine which of these two forces dominates -- riskiness or expected value. We apply our results in consumption-savings problems, self-protection problems, and in a Bayesian game.

math.PR↗