arXiv subjects

Sophie Klumper

Publications and source records attributed to Sophie Klumper.

7 recordsLinked to original sources

arXiv2026

Improved Lower Bounds and Output Augmentation for Facility Location Mechanisms

We study the strategic facility location problem under the egalitarian objective, where a mechanism uses the reported locations of a set of agents in Euclidean space to select a facility location that minimizes the maximum distance to any agent. We restrict our attention to strategyproof mechanisms, ensuring that no agent can benefit from misreporting their location. As our main results, we prove an asymptotic lower bound of $1 + \sqrt{d/(2(d+1))}$ on the approximation ratio of any mechanism that is strategyproof in expectation in $\mathbb{R}^d$. We show that this barrier is driven by large populations by providing a randomized $\sqrt{2}$-approximate mechanism for the two-agent case. We then consider an output-augmented framework, which allows the facility to be placed outside the agents' restricted domain. For the setting where agents are restricted to a line but the facility can be anywhere in the plane, we design a deterministic strategyproof $\sqrt{2}$-approximate mechanism with a matching lower bound, showing that output augmentation can replace the need for randomness. For the setting where the agents' reports lie on the unit circle but the facility can be placed anywhere in $\mathbb{R}^2$ we introduce a randomized $3/2$-approximate mechanism that is group-strategyproof in expectation.

cs.GT↗

arXiv2026

Beyond Stability: Improved Efficiency Guarantees for $α$-Stable Matchings

Stable matching mechanisms are fundamental to market design but face an inherent tension between stability and social welfare optimality. We study a natural relaxation of stability, termed $α$-stability, which models agents as willing to deviate only when the potential improvement is sufficiently large. Under $α$-stability, no pair of agents can deviate and improve their valuations by more than a factor of $1/α$, with $α\in (0,1]$. We provide a complete characterization of the stability-efficiency tradeoff under asymmetric valuations. This tradeoff depends on the degree of asymmetry $μ\in (0,1]$, which bounds the ratio between agents' valuations for any pair. Our results show that relaxing stability can substantially improve achievable efficiency guarantees. We further present a polynomial-time algorithm that computes an $α$-stable matching attaining the best possible efficiency guarantee. For $α\le μ/(μ+1)$, our algorithm achieves 1-efficiency; for larger $α$, it computes an $α$-stable matching achieving at least $(1/α)\cdot μ/(μ+1)$ of the optimal social welfare. Remarkably, our algorithm inflates the values of an optimal matching and then applies the Gale-Shapley algorithm to the modified instance. Finally, we show that computing an optimal $α$-stable matching is NP-hard, even under slight relaxations of stability, i.e., for $α$ close to 1.

cs.GT↗

arXiv2025

Optimal Type-Dependent Liquid Welfare Guarantees for Autobidding Agents with Budgets

Online advertising systems have recently transitioned to autobidding, allowing advertisers to delegate bidding decisions to automated agents. Each advertiser directs their agent to optimize an objective function subject to return-on-investment (ROI) and budget constraints. Given their practical relevance, this shift has spurred a surge of research on the liquid welfare price of anarchy (POA) of fundamental auction formats under autobidding, most notably simultaneous first-price auctions (FPA). One of the main challenges is to understand the efficiency of FPA in the presence of heterogeneous agent types. We introduce {type-dependent smoothness framework that enables a unified analysis of the POA in such complex autobidding environments. In our approach, we derive type-dependent smoothness parameters which we carefully balance to obtain POA bounds. This balancing gives rise to a POA-revealing mathematical program, which we use to determine tight bounds on the POA of coarse correlated equilibria (CCE). Our framework is versatile enough to handle heterogeneous agent types and extends to the general class of fractionally subadditive valuations. Additionally, we develop a novel reduction technique that transforms budget-constrained agents into budget-unconstrained ones. Combining this reduction technique with our smoothness framework enables us to derive tight bounds on the POA of CCE in the general hybrid agent model with both ROI and budget constraints. Among other results, our bounds uncover an intriguing threshold phenomenon showing that the POA depends intricately on the smallest and largest agent types. We also extend our study to FPAs with reserve prices, which can be interpreted as predictions of agents' values, to further improve efficiency guarantees.

cs.GT↗

arXiv2025

Mechanism Design with Outliers and Predictions

We initiate the study of mechanism design with outliers, where the designer can discard $z$ agents from the social cost objective. This setting is particularly relevant when some agents exhibit extreme or atypical preferences. As a natural case study, we consider facility location on the line: $n$ strategic agents report their preferred locations, and a mechanism places a facility to minimize a social cost function. In our setting, the $z$ agents farthest from the chosen facility are excluded from the social cost. While it may seem intuitive that discarding outliers improves efficiency, our results reveal that the opposite can hold. We derive tight bounds for deterministic strategyproof mechanisms under the two most-studied objectives: utilitarian and egalitarian social cost. Our results offer a comprehensive view of the impact of outliers. We first show that when $z \ge n/2$, no strategyproof mechanism can achieve a bounded approximation for either objective. For egalitarian cost, selecting the $(z + 1)$-th order statistic is strategyproof and 2-approximate. In fact, we show that this is best possible by providing a matching lower bound. Notably, this lower bound of 2 persists even when the mechanism has access to a prediction of the optimal location, in stark contrast to the setting without outliers. For utilitarian cost, we show that strategyproof mechanisms cannot effectively exploit outliers, leading to the counterintuitive outcome that approximation guarantees worsen as the number of outliers increases. However, in this case, access to a prediction allows us to design a strategyproof mechanism achieving the best possible trade-off between consistency and robustness. Finally, we also establish lower bounds for randomized mechanisms that are truthful in expectation.

cs.GT↗

arXiv2025

Partial Allocations in Budget-Feasible Mechanism Design: Bridging Multiple Levels of Service and Divisible Agents

Budget-feasible procurement has been a major paradigm in mechanism design since its introduction by Singer (2010). An auctioneer (buyer) with a strict budget constraint is interested in buying goods or services from a group of strategic agents (sellers). In many scenarios it makes sense to allow the auctioneer to only partially buy what an agent offers, e.g., an agent might have multiple copies of an item to sell, they might offer multiple levels of a service, or they may be available to perform a task for any fraction of a specified time interval. Nevertheless, the focus of the related literature has been on settings where each agent's services are either fully acquired or not at all. The main reason for this, is that in settings with partial allocations like the ones mentioned, there are strong inapproximability results. Under the mild assumption of being able to afford each agent entirely, we are able to circumvent such results in this work. We design a polynomial-time, deterministic, truthful, budget-feasible $(2+\sqrt{3})$-approximation mechanism for the setting where each agent offers multiple levels of service and the auctioneer has a discrete separable concave valuation function. We then use this result to design a deterministic, truthful and budget-feasible $O(1)$-approximation mechanism for the setting where any fraction of a service can be acquired and the auctioneer's valuation function is separable concave (i.e., the sum of concave functions). For the special case of a linear valuation function, we improve the best known approximation ratio for the problem from $1+ϕ$ (by Klumper & Schäfer (2022)) to $2$. This establishes a separation between this setting and its indivisible counterpart.

cs.GT↗

arXiv2024

To Trust or Not to Trust: Assignment Mechanisms with Predictions in the Private Graph Model

The realm of algorithms with predictions has led to the development of several new algorithms that leverage (potentially erroneous) predictions to enhance their performance guarantees. The challenge is to devise algorithms that achieve optimal approximation guarantees as the prediction quality varies from perfect (consistency) to imperfect (robustness). This framework is particularly appealing in mechanism design contexts, where predictions might convey private information about the agents. In this paper, we design strategyproof mechanisms that leverage predictions to achieve improved approximation guarantees for several variants of the Generalized Assignment Problem (GAP) in the private graph model. In this model, first introduced by Dughmi & Ghosh (2010), the set of resources that an agent is compatible with is private information. For the Bipartite Matching Problem (BMP), we give a deterministic group-strategyproof (GSP) mechanism that is $(1 +1/γ)$-consistent and $(1 + γ)$-robust, where $γ\ge 1$ is some confidence parameter. We also prove that this is best possible. Remarkably, our mechanism draws inspiration from the renowned Gale-Shapley algorithm, incorporating predictions as a crucial element. Additionally, we give a randomized mechanism that is universally GSP and improves on the guarantees in expectation. The other GAP variants that we consider all make use of a unified greedy mechanism that adds edges to the assignment according to a specific order. Our universally GSP mechanism randomizes over the greedy mechanism, our mechanism for BMP and the predicted assignment, leading to $(1+3/γ)$-consistency and $(3+γ)$-robustness in expectation. All our mechanisms also provide more fine-grained approximation guarantees that interpolate between the consistency and the robustness, depending on some natural error measure of the prediction.

cs.GT↗

arXiv2022

Budget Feasible Mechanisms for Procurement Auctions with Divisible Agents

We consider budget feasible mechanisms for procurement auctions with additive valuation functions. For the divisible case, where agents can be allocated fractionally, there exists an optimal mechanism with approximation guarantee $e/(e-1)$ under the small bidder assumption. We study the divisible case without the small bidder assumption, but assume that the true costs of the agents are bounded by the budget. This setting lends itself to modeling economic situations in which the goods represent time and the agents' true costs are not necessarily small compared to the budget. Non-trivially, we give a mechanism with an approximation guarantee of 2.62, improving the result of 3 for the indivisible case. Additionally, we give a lower bound on the approximation guarantee of 1.25. We then study the problem in more competitive markets and assume that the agents' value over cost efficiencies are bounded by some $θ\ge 1$. For $θ\le 2$, we give a mechanism with an approximation guarantee of 2 and a lower bound of 1.18. Both results can be extended to settings with different agent types with a linear capped valuation function for each type. Finally, if each agent type has a concave valuation, we give a mechanism for which the approximation guarantee grows linearly with the number of agent types.

cs.GT↗