We consider an extension to classic position auctions in which sponsored creatives are embedded within AI-generated content rather than shown in predefined slots. Leveraging advanced LLM technologies, it becomes viable to seamlessly integrate sponsored creatives with AI content and accurately estimate the context-aware benefits of differing insertion positions. However, this approach introduces novel challenges; substitution effects require rigorous treatment compared to standard position auction settings, where slots are independent of each other.

Electric power systems are undergoing a major transformation as they integrate intermittent renewable energy sources, and batteries to smooth out variations in renewable energy production. As privately-owned batteries grow from their role as marginal "price-takers" to significant players in the market, a natural question arises: How do batteries operate in electricity markets, and how does the strategic behavior of decentralized batteries distort decisions compared to centralized batteries? We propose an analytically tractable model that captures salient features of the highly complex electricity market. We derive in closed form the resulting battery behavior and generation cost in three operating regimes: (i) no battery, (ii) centralized battery, and (ii) decentralized profit-maximizing battery. We establish that a decentralized battery distorts its discharge decisions in three ways. First, there is quantity withholding, i.e., discharging less than centrally optimal. Second, there is a shift in participation from day-ahead to real-time, i.e., postponing some of its discharge from day-ahead to real-time. Third, there is reduction in real-time responsiveness, or discharging less in response to smoothing real-time demand than centrally optimal. We also quantify the impact of the battery market power on total system cost via the Price of Anarchy metric, and prove that it is always between 9/8 and 4/3. That is, incentive misalignment always exists, but it is bounded even in the worst case. We calibrate our model to real data from Los Angeles and Houston. Lastly, we show that competition is very effective at reducing distortions, but many market power mitigation mechanisms backfire, and lead to higher total cost. The work provides stakeholders with a framework to understand and detect market power from batteries. It also shows that the potential loss from battery market power is relatively small compared to the cost reduction achievable from having enough battery capacity in the system. Therefore, independent system operators in rapidly changing markets might want to prioritize market entry of batteries and only shift to market power mitigation once the market is more mature.

In many real-world applications such as data centers and cloud computing, the systems often consist of multiple frontends (routers) that receive job requests and backends (servers) that process these jobs. Efficient resource management is becoming increasingly important given the growing demand for serving machine learning inference queries, which incur high latencies and require expensive computational resources.

Budget pacing is a popular service that has been offered by major internet advertising platforms since their inception. In the past few years, autobidding products that provide real-time bidding as a service to advertisers have seen a prominent rise in adoption. A popular autobidding stategy is value maximization subject to return-on-spend (ROS) constraints. For historical or business reasons, the systems that govern these two services, namely budget pacing and ROS pacing, are not necessarily always a single unified and coordinated entity that optimizes a global objective subject to both constraints. The purpose of this work is to theoretically and empirically compare algorithms with different degrees of coordination between these two pacing systems. In particular, we compare (a) a fully-decoupled sequential algorithm; (b) a minimally-coupled min-pacing algorithm; (c) a fully-coupled dual-based algorithm. Our main contribution is to theoretically analyze the min-pacing algorithm and show that it attains similar guarantees to the fully-coupled canonical dual-based algorithm. On the other hand, we show that the sequential algorithm, even though appealing by virtue of being fully decoupled, could badly violate the constraints. We validate our theoretical findings empirically by showing that the min-pacing algorithm performs almost as well as the canonical dual-based algorithm on a semi-synthetic dataset that was generated from a large online advertising platform's auction data.

Motivated by the increased adoption of autobidding algorithms in internet advertising markets, we study the design of optimal mechanisms for selling an item to a value-maximizing buyer with a return-on-spend constraint. The buyer's values and target ratio in the return-on-spend constraint are private. We restrict attention to deterministic sequential screening mechanisms that can be implemented as a menu of two-part tariffs. The main result of this paper is to provide a characterization of an optimal mechanism. Surprisingly, we show that the optimal mechanism does not require target screening, i.e., offering a single two-part tariff is optimal for the seller. The optimal mechanism is a subsidized two-part tariff that provides a lump-sum subsidy to the buyer to encourage participation and then charges a fixed unit price for each item sold. The seller's problem is a challenging non-linear mechanism design problem, and a key technical contribution of our work is to provide a novel approach to analyzing non-linear pricing contracts for constrained buyers. Our results have valuable implications for advertising platforms seeking to personalize pricing decisions based on advertisers' characteristics.

Major Internet advertising platforms offer budget pacing tools as a standard service for advertisers to manage their ad campaigns. Given the inherent non-stationarity in an advertiser’s value and also competing advertisers’ values over time, a commonly used approach is to learn a target expenditure plan that specifies a target spend as a function of time, and then run a controller that tracks this plan. This raises the question: how many historical samples are required to learn a good expenditure plan? We study this question by considering an advertiser repeatedly participating in $T$ second-price auctions, where the tuple of her value and the highest competing bid is drawn from an unknown time-varying distribution. The advertiser seeks to maximize her total utility subject to her budget constraint. Prior work has shown the sufficiency of $T\log T$ samples per distribution to achieve the optimal $O(\sqrt{T})$-regret. We dramatically improve this state-of-the-art and show that just one sample per distribution is enough to achieve the near-optimal $\tilde O(\sqrt{T})$-regret, while still being robust to noise in the sampling distributions.

A seller wants to sell an indivisible item to n buyers. The buyer valuations are drawn i.i.d. from a distribution, but the seller does not know this distribution; the seller only knows the support [a, b]. To be robust against the lack of knowledge of the environment and buyers' behavior, the seller optimizes over dominant strategy incentive compatible (DSIC) mechanisms, and measures the worst-case performance relative to an oracle with complete knowledge of buyers' valuations. Our analysis encompasses both the regret and the approximation ratio objectives.

Single-leg revenue management is a foundational problem of revenue management that has been particularly impactful in the airline and hotel industry: Given n units of a resource, e.g. flight seats, and a stream of sequentially-arriving customers segmented by fares, what is the optimal online policy for allocating the resource. Previous work focused on designing algorithms when forecasts are available, which are not robust to inaccuracies in the forecast, or online algorithms with worst-case performance guarantees, which can be too conservative in practice. In this work, we look at the single-leg revenue management problem through the lens of the algorithms-with-advice framework, which attempts to harness the increasing prediction accuracy of machine learning methods by optimally incorporating advice about the future into online algorithms. In particular, we develop online algorithms which optimally trade-off consistency (performance when advice is accurate) and competitiveness (performance when advice is inaccurate) for every advice. Our results extend to other unit-cost online allocations problems such as the display advertising and the multiple secretary problem together with more general variable-cost problems such as the online knapsack problem.

Classical Bayesian mechanism design relies on the common prior assumption, but the common prior is often not available in practice. We study the design of prior-independent mechanisms that relax this assumption: the seller is selling an indivisible item to n buyers such that the buyers' valuations are drawn from a joint distribution that is unknown to both the buyers and the seller; buyers do not need to form beliefs about competitors, and the seller assumes the distribution is adversarially chosen from a specified class. We measure performance through the worst-caseregret, or the difference between the expected revenue achievable with perfect knowledge of buyers' valuations and the actual mechanism revenue.

We study the design of revenue-maximizing mechanisms for value-maximizing agents with budget constraints. Agents have return-on-spend constraints requiring a minimum amount of value per unit of payment made and budget constraints limiting their total payments. The agents' only private information are the minimum admissible ratios on the return-on-spend constraint, referred to as the target ratios.

The internet advertising market is a multi-billion dollar industry, in which advertisers buy thousands of ad placements every day by repeatedly participating in auctions. In recent years, the industry has shifted to first-price auctions as the preferred paradigm for selling advertising slots. Another important and ubiquitous feature of these auctions is the presence of campaign budgets, which specify the maximum amount the advertisers are willing to pay over a specified time period. In this paper, we present a new model to study the equilibrium bidding strategies in standard auctions, a large class of auctions that includes first- and second-price auctions, for advertisers who satisfy budget constraints on average. Our model dispenses with the common, yet unrealistic assumption that advertisers' values are independent and instead assumes a contextual model in which advertisers determine their values using a common feature vector. We show the existence of a natural value-pacing-based Bayes-Nash equilibrium under very mild assumptions. Furthermore, we prove a revenue equivalence showing that all standard auctions yield the same revenue even in the presence of budget constraints. Leveraging this equivalence, we prove Price of Anarchy bounds for liquid welfare and structural properties of pacing-based equilibria that hold for all standard auctions. Our work takes an important step toward understanding the implications of the shift to first-price auctions in internet advertising markets.

Online allocation problems with resource constraints have a rich history in computer science and operations research. In this paper, we introduce the regularized online allocation problem, a variant that includes a non-linear regularizer acting on the total resource consumption. In this problem, requests repeatedly arrive over time and, for each request, a decision maker needs to take an action that generates a reward and consumes resources. The objective is to simultaneously maximize total rewards and the value of the regularizer subject to the resource constraints. Our primary motivation is the online allocation of internet advertisements wherein firms seek to maximize additive objectives such as the revenue or efficiency of the allocation. By introducing a regularizer, firms can account for the fairness of the allocation or, alternatively, punish under-delivery of advertisements—two common desiderata in internet advertising markets. We design an algorithm when arrivals are drawn independently from a distribution that is unknown to the decision maker. Our algorithm is simple, fast, and attains the optimal order of sub-linear regret compared to the optimal allocation with the benefit of hindsight. Numerical experiments confirm the effectiveness of the proposed algorithm and of the regularizers in an internet advertising application.

In classic auction theory, reserve prices are known to be effective for improving revenue for the auctioneer against quasi-linear utility maximizing bidders. The introduction of reserve prices, however, usually do not help improve total welfare of the auctioneer and the bidders. In this paper, we focus on value maximizing bidders with return on spend constraints---a paradigm that has drawn considerable attention recently as more advertisers adopt auto-bidding algorithms in advertising platforms---and show that the introduction of reserve prices has a novel impact on the market. Namely, by choosing reserve prices appropriately the auctioneer can improve not only the total revenue but also the total welfare. Our results also demonstrate that reserve prices are robust to bidder types, i.e., reserve prices work well for different bidder types, such as value maximizers and utility maximizers, without using bidder type information. We generalize these results for a variety of auction mechanisms such as VCG, GSP, and first-price auctions. Moreover, we show how to combine these results with additive boosts to improve the welfare of the outcomes of the auction further. Finally, we complement our theoretical observations with an empirical study confirming the effectiveness of these ideas using data from online advertising auctions.

Internet advertisers are increasingly adopting automated bidders to buy advertising opportunities. Automated bidders simplify the procurement process by allowing advertisers to specify their goals and then bidding on their behalf in the auctions that are used to sell advertising slots. One popular goal adopted by advertisers is to maximize their clicks (or conversions) subject to a return on spend (RoS) constraint, which imposes that the ratio of total value to total spend is greater than a target ratio specified by the advertisers. The emergence of automated bidders brings into question whether the standard mechanisms used to sell ads are still effective in this new landscape. Thus motivated, in this paper, we study the problem of characterizing optimal mechanisms for selling an item to one of multiple agents with return on spend constraints when either the values or target ratios are private. We consider two objectives for the agents: value maximization, which is becoming the prevalent objective in advertising markets, and utility maximization, which is the de facto paradigm in economic theory. Our goal is to understand the impact of the agents' private information and their objectives on the seller's revenue, and determine whether the first-best revenue, which is the optimal revenue when all the private information is public, is achievable. We show that first-best revenue is achievable for value-maximizing buyers when either the target ratio or the values are private, but not when both are private. In the case of utility-maximizing buyers, first-best is never achievable and we characterize revenue-maximizing mechanisms.

Dynamic mechanism design expands the scope of allocations that can be implemented and the performance that can be attained compared to static mechanisms. Even under stringent participation constraints and restrictions on transfers, recent work demonstrated that it is possible for a designer to extract the surplus of all players as revenue when players have quasilinear utilities and the number of interactions is large. Much of the analysis has focused on excludable environments (i.e., any player can be excluded from trade without affecting the utilities of others). The mechanisms presented in the literature, however, do not extend to non-excludable environments. Two prototypical examples of such environments are: (i) public projects, where all players must have the same allocation; and (ii) non-disposable goods, where each item must be allocated to some player. We show a general mechanism that can asymptotically extract full surplus as revenue in such environments. Moreover, we provide a tight characterization for general environments, and identify necessary and sufficient conditions on the possibility of asymptotic full surplus extraction. Our characterization is based on the geometry of achievable utility sets – convex sets that delineate the expected utilities that can be implemented by static mechanisms. Our results provide a reduction from dynamic to static mechanism design: the geometry of the achievable utility set of static mechanisms determines whether it is possible to fully extract surplus in the limit.

We consider online allocation problems with concave revenue functions and resource constraints, which are central problems in revenue management and online advertising. In these settings, requests arrive sequentially during a finite horizon and, for each request, a decision maker needs to choose an action that consumes a certain amount of resources and generates revenue. The revenue function and resource consumption of each request are drawn independently and at random from a probability distribution that is unknown to the decision maker. The objective is to maximize cumulative revenues subject to a constraint on the total consumption of resources. We design a general class of algorithms that achieve sub-linear expected regret compared to the hindsight optimal allocation. Our algorithms operate in the Lagrangian dual space: they maintain a dual multiplier for each resource that is updated using online mirror descent. By choosing the reference function accordingly, we recover dual sub-gradient descent and dual exponential weights algorithm. The resulting algorithms are simple, efficient, and shown to attain the optimal order of regret when the length of the horizon and the initial number of resources are scaled proportionally. We discuss applications to online bidding in repeated auctions with budget constraints and online proportional matching with high entropy.

Motivated by online advertising applications, we study incentive properties of stationary mechanisms that satisfy budget constraints in expectation at a stationary equilibrium. We consider a general repeated auction setting where a seller sells identical items to buyers with budget constraints and the buyers' value distributions can be arbitrarily correlated. We introduce the novel notion of budget-constrained incentive compatibility (BCIC) under which each buyer chooses an optimal bidding strategy among stationary budget-feasible bidding strategies. Armed with the notion of BCIC, we characterize Bayesian optimal mechanisms that satisfy the budget constraints in expectation with respect to the profit, utility and welfare objectives in the restricted setting where the buyers' value distributions are independent. Furthermore, in the general setting where the buyers' value distributions are correlated, we provide the first systematic study on the incentive properties of different budget management mechanisms, including those studied in the literature and, to the best of our knowledge, used in the industry. We explore the following mechanisms and show some popular mechanisms are not incentive compatible even when restricting attention to stationary budget-feasible deviations: throttling, thresholding, bid shading, reserve pricing and two versions of multiplicative boosting.

In the classical contextual bandits problem, in each round $t$, a learner observes some context $c$, chooses some action $a$ to perform, and receives some reward $r_{a,t}(c)$. We consider the variant of this problem where in addition to receiving the reward $r_{a,t}(c)$, the learner also learns the values of $r_{a,t}(c')$ for all other contexts $c'$; i.e., the rewards that would have been achieved by performing that action under different contexts. This variant arises in several strategic settings, such as learning how to bid in non-truthful repeated auctions (in this setting the context is the decision maker's private valuation for each auction). We call this problem the contextual bandits problem with cross-learning. The best algorithms for the classical contextual bandits problem achieve $\tilde{O}(\sqrt{CKT})$ regret against all stationary policies, where $C$ is the number of contexts, $K$ the number of actions, and $T$ the number of rounds. We demonstrate algorithms for the contextual bandits problem with cross-learning that remove the dependence on $C$ and achieve regret $\tilde{O}(\sqrt{KT})$ (when contexts are stochastic with known distribution), $\tilde{O}(K^{1/3}T^{2/3})$ (when contexts are stochastic with unknown distribution), and $\tilde{O}(\sqrt{KT})$ (when contexts are adversarial but rewards are stochastic). We simulate our algorithms on real auction data from an ad exchange running first-price auctions (showing that they outperform traditional contextual bandit algorithms).

We study the problem of designing dynamic double auctions for two-sided markets in which a platform intermediates the trade between one seller offering independent items to multiple buyers, repeatedly over a finite horizon, when agents have private values. Motivated by online advertising and ride-hailing markets, we seek to design mechanisms satisfying the following properties: no positive transfers, i.e., the platform never asks the seller to make payments nor buyers are ever paid and periodic individual rationality, i.e., every agent should derive a non-negative utility from every trade opportunity. We provide mechanisms satisfying these requirements that are asymptotically efficient and budget-balanced with high probability as the number of trading opportunities grows. Moreover, we show that the average expected profit obtained by the platform under these mechanisms asymptotically approaches first best (the maximum possible welfare generated by the market).

Many online platforms act as intermediaries between a seller and a set of buyers. Examples of such settings include online retailers (such as Ebay) selling items on behalf of sellers to buyers, or advertising exchanges (such as AdX) selling pageviews on behalf of publishers to advertisers. In such settings, revenue sharing is a central part of running such a marketplace for the intermediary, and fixed-percentage revenue sharing schemes are often used to split the revenue among the platform and the sellers. In particular, such revenue sharing schemes require the platform to (i) take at most a constant fraction \alpha of the revenue from auctions and (ii) pay the seller at least the seller declared opportunity cost c for each item sold. A straightforward way to satisfy the constraints is to set a reserve price at c / (1 - \alpha) for each item, but it is not the optimal solution on maximizing the profit of the intermediary. While previous studies (by Mirrokni and Gomes, and by Niazadeh et al) focused on revenue-sharing schemes in static double auctions, in this paper, we take advantage of the repeated nature of the auctions. In particular, we introduce dynamic revenue sharing schemes where we balance the two constraints over different auctions to achieve higher profit and seller revenue. This is directly motivated by the practice of advertising exchanges where the fixed-percentage revenue-share should be met across all auctions and not in each auction. In this paper, we characterize the optimal revenue sharing scheme that satisfies both constraints in expectation. Finally, we empirically evaluate our revenue sharing scheme on real data.

In online advertising markets, advertisers often purchase ad placements through bidding in repeated auctions based on realized viewer information. We study how budget-constrained advertisers may bid in the presence of competition, when there is uncertainty about future bidding opportunities as well as competitors' heterogenous preferences and budgets. We formulate this problem as a sequential game of incomplete information, where bidders know neither their own valuation distribution, nor the budgets and valuation distributions of their competitors. We introduce a family of dynamic bidding strategies we refer to as "adaptive pacing" strategies, in which advertisers adjust their bids throughout the campaign according to the sample path of observed expenditures. We analyze the performance of this class of strategies under different assumptions on competitors' behavior. Under arbitrary competitors' bids, we establish through matching lower and upper bounds the asymptotic optimality of this class of strategies as the number of auctions grows large. When adopted by all the bidders, the dynamics converge to a tractable and meaningful steady state. Moreover, we show that these strategies constitute an approximate Nash equilibrium in dynamic strategies: The benefit of unilaterally deviating to other strategies, including ones with access to complete information, becomes negligible as the number of auctions and competitors grows large. This establishes a connection between regret minimization and market stability, by which advertisers can essentially follow equilibrium bidding strategies that also ensure the best performance that can be guaranteed off-equilibrium.

We study the dynamic mechanism design problem of a seller who repeatedly sells independent items to a buyer with private values. In this setting, the seller could potentially extract the entire buyer surplus by running efficient auctions and charging an upfront participation fee at the beginning of the horizon. In some markets, such as internet advertising, participation fees are not practical since buyers expect to inspect items before purchasing them. This motivates us to study the design of dynamic mechanisms under successively more stringent requirements that capture the implicit business constraints of these markets. We first consider a periodic individual rationality constraint, which limits the mechanism to charge at most the buyer's value in each period. While this prevents large upfront participation fees, the seller can still design mechanisms that spread a participation fee across the first few auctions. These mechanisms have the unappealing feature that they provide close-to-zero buyer utility in earlier auctions in exchange for higher utility in later auctions. To address this problem, we introduce a {martingale utility constraint, which imposes the requirement that from the perspective of the buyer, the next item's expected utility is equal to the present one's. Our main result is providing a dynamic auction satisfying martingale utility and periodic individual rationality whose loss in profit with respect to first-best (full extraction of buyer surplus) is optimal up to polylogarithmic factors. The proposed mechanism is a dynamic two-tier auction with a hard floor and a soft floor that allocates the item whenever the buyer's bid is above the hard floor and charges the minimum of the bid and the soft floor.

In online advertising, advertisers purchase ad placements by participating in a long sequence of repeated auctions. One of the most important features advertising platforms often provide, and advertisers often use, is budget management, which allows advertisers to control their cumulative expenditures. Advertisers typically declare the maximum daily amount they are willing to pay, and the platform adjusts allocations and payments to guarantee that cumulative expenditures do not exceed budgets. There are multiple ways to achieve this goal, and each one, when applied to all budget-constrained advertisers simultaneously, steers the system toward a different equilibrium. While previous research focused on online stochastic optimization techniques or game-theoretic equilibria of such settings, our goal in this paper is to compare the ``system equilibria'' of a range of budget management strategies in terms of the seller's profit and buyers' utility. In particular, we consider six different budget management strategies including probabilistic throttling, thresholding, bid shading, reserve pricing, and multiplicative boosting. We show these methods admit a system equilibrium in a rather general setting, and prove dominance relations between them in a simplified setting. Our study sheds light on the impact of budget management strategies on the tradeoff between the seller's profit and buyers' utility. Finally, we also empirically compare the system equilibria of these strategies using real ad auction data in sponsored search and randomly generated bids. The empirical study confirms our theoretical findings about the relative performances of budget management strategies.

We study the dynamic mechanism design problem of a seller who repeatedly auctions independent items over a discrete time horizon to buyers who face a cumulative budget constraint. A driving motivation behind our model is the emergence of real-time bidding markets for online display advertising in which such budgets are prevalent. We assume the seller has a strong form of limited commitment: she commits to the rules of the current auction but cannot commit to those of future auctions. We show that the celebrated Myersonian approach that leverages the envelope theorem fails in this setting, and therefore, characterizing the dynamic optimal mechanism seems intractable. Despite these challenges, we derive and characterize a near-optimal dynamic mechanism. To do so, we show that the Myersonian approach is recovered in a corresponding fluid continuous time model in which the time interval between consecutive items becomes negligible. Then we leverage this approach to characterize the optimal dynamic direct-revelation mechanism, highlighting novel incentives at play in settings with buyers’ budget constraints and seller’s limited commitment. We show through a combination of theoretical and numerical results that the optimal mechanism arising from the fluid continuous time model approximately satisfies incentive compatibility for the buyers and is approximately sequentially rational for the seller in the original discrete time model. Supplemental material is available at https://doi.org/10.1287/opre.2018.1830 .

Ad Exchanges are emerging Internet markets where advertisers may purchase display ad placements, in real-time and based on specific viewer information, directly from publishers via a simple auction mechanism. Advertisers join these markets with a prespecified budget and participate in multiple second-price auctions over the length of a campaign. This paper studies the competitive landscape that arises in Ad Exchanges and the implications for publishers' decisions.

In light of the growing market of Ad Exchanges for the real-time sale of advertising slots, publishers face new challenges in choosing between the allocation of contract-based reservation ads and spot market ads. In this setting, the publisher should take into account the tradeoff between short-term revenue from an Ad Exchange and quality of allocating reservation ads. In this paper, we formalize this combined optimization problem as a stochastic control problem and derive an efficient policy for online ad allocation in settings with general joint distribution over placement quality and exchange bids. Ad Exchanges like RightMedia, AdECN or DoubleClick are an emerging market for the real-time sale of display advertising slots in publishing sites on the Internet. While exchanges differ in their implementations, in a generic Ad Exchange (AdX), publishers post an ad slot with a reservation price, advertisers post bids, and an auction is run; this happens between the time a user visits a page and the ad is displayed.