arXiv subjects

Kira Goldner

Publications and source records attributed to Kira Goldner.

17 recordsLinked to original sources

arXiv2026

From Welfare to Utility: Generalized Objectives in Budget-Feasible Procurement

We study mechanism design for the budget-feasible procurement problem, a natural problem that arises when a buyer wants to procure goods or services from multiple strategic sellers who each have a cost to provide that service, the buyer has a value for each service procured, but is constrained by a budget. In contrast to prior work, which has focused on buyer value maximization for this problem, we solve for optimal and approximately-optimal mechanisms for the objectives of buyer utility (value of procured services minus payments), welfare (value minus production costs), and generalizations of the two. For welfare, we design a simple mechanism that obtains a constant-factor approximation for the prior-free (worst-case) setting. As prior-free mechanisms fail to provide any guarantee for utility, even for a single seller, we consider Bayesian settings, where the buyer has distributional knowledge over sellers' costs. We first provide a utility-optimal mechanism that satisfies the buyer's budget constraint in expectation, then we show how to modify the mechanism to satisfy the budget constraint ex-post, for every realization of seller costs, while still obtaining near-optimal utility guarantees. Finally, we generalize our mechanisms to other objectives.

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arXiv2026

Knowing Who, Not How Much: Learning-Augmented Mechanisms for Consumer Utility Maximization

We study consumer utility maximization in an online random-order model where strategic agents arrive sequentially. To circumvent strong impossibility results for utility maximization, we turn to the framework of learning-augmented mechanism design. Crucially, we show that the types of predictions commonly used in learning-augmented mechanism design (such as predictions of agent values or the optimal value) are not useful for utility maximization, where payments are directly at odds with the objective. Instead, we identify that a qualitatively different kind of prediction suffices: the identity of the highest-valued agent. First, we provide a deterministic truthful mechanism for our online setting by adapting offline randomized techniques. Then, we augment our mechanism with predictions. When the predictions are correct, we achieve a constant approximation to the optimal solution under full information (consistency), and even when predictions are arbitrarily bad, we guarantee a constant approximation to the best implementable solution (robustness).

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arXiv2025

Interdependent Bilateral Trade: Information vs Approximation

Welfare maximization in bilateral trade has been extensively studied in recent years. Previous literature obtained incentive-compatible approximation mechanisms only for the private values case. In this paper, we study welfare maximization in bilateral trade with interdependent values. Designing mechanisms for interdependent settings is much more challenging because the values of the players depend on the private information of the others, requiring complex belief updates and strategic inference. We propose to classify information structures by quantifying the influence that a player's private signal has on their own valuation. We then paint a picture of where approximations are possible and impossible based on these information structures. Finally, we also study the possible approximation ratios for a natural family of information structures.

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arXiv2024

Multidimensional Bayesian Utility Maximization: Tight Approximations to Welfare

We initiate the study of multidimensional Bayesian utility maximization, focusing on the unit-demand setting where values are i.i.d. across both items and buyers. The seminal result of Hartline and Roughgarden '08 studies simple, information-robust mechanisms that maximize utility for $n$ i.i.d. agents and $m$ identical items via an approximation to social welfare as an upper bound, and they prove this gap between optimal utility and social welfare is $\Theta(1+\log{n/m})$ in this setting. We extend these results to the multidimensional setting. To do so, we develop simple, prior-independent, approximately-optimal mechanisms, targeting the simplest benchmark of optimal welfare. We give a $(1- 1/e)$-approximation when there are more items than buyers, and a $\Theta(\log{n/m})$-approximation when there are more buyers than items, and we prove that this bound is tight in both $n$ and $m$ by reducing the i.i.d. unit-demand setting to the identical items setting. Finally, we include an extensive discussion section on why Bayesian utility maximization is a promising research direction. In particular, we characterize complexities in this setting that defy our intuition from the welfare and revenue literature, and motivate why coming up with a better benchmark than welfare is a hard problem itself.

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arXiv2023

Constant Approximation for Private Interdependent Valuations

The celebrated model of auctions with interdependent valuations, introduced by Milgrom and Weber in 1982, has been studied almost exclusively under private signals $s_1, \ldots, s_n$ of the $n$ bidders and public valuation functions $v_i(s_1, \ldots, s_n)$. Recent work in TCS has shown that this setting admits a constant approximation to the optimal social welfare if the valuations satisfy a natural property called submodularity over signals (SOS). More recently, Eden et al. (2022) have extended the analysis of interdependent valuations to include settings with private signals and private valuations, and established $O(\log^2 n)$-approximation for SOS valuations. In this paper we show that this setting admits a constant factor approximation, settling the open question raised by Eden et al. (2022).

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arXiv2022

On Multi-Dimensional Gains from Trade Maximization

We study gains from trade in multi-dimensional two-sided markets. Specifically, we focus on a setting with $n$ heterogeneous items, where each item is owned by a different seller $i$, and there is a constrained-additive buyer with feasibility constraint $\mathcal{F}$. Multi-dimensional settings in one-sided markets, e.g. where a seller owns multiple heterogeneous items but also is the mechanism designer, are well-understood. In addition, single-dimensional settings in two-sided markets, e.g. where a buyer and seller each seek or own a single item, are also well-understood. Multi-dimensional two-sided markets, however, encapsulate the major challenges of both lines of work: optimizing the sale of heterogeneous items, ensuring incentive-compatibility among both sides of the market, and enforcing budget balance. We present, to the best of our knowledge, the first worst-case approximation guarantee for gains from trade in a multi-dimensional two-sided market. Our first result provides an $O(\log (1/r))$-approximation to the first-best gains from trade for a broad class of downward-closed feasibility constraints (such as matroid, matching, knapsack, or the intersection of these). Here $r$ is the minimum probability over all items that a buyer's value for the item exceeds the seller's cost. Our second result removes the dependence on $r$ and provides an unconditional $O(\log n)$-approximation to the second-best gains from trade. We extend both results for a general constrained-additive buyer, losing another $O(\log n)$-factor en-route.

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arXiv2021

Private Interdependent Valuations

We consider the single-item interdependent value setting, where there is a monopolist, $n$ buyers, and each buyer has a private signal $s_i$ describing a piece of information about the item. Each bidder $i$ also has a valuation function $v_i(s_1,\ldots,s_n)$ mapping the (private) signals of all buyers to a positive real number representing their value for the item. This setting captures scenarios where the item's information is asymmetric or dispersed among agents, such as in competitions for oil drilling rights, or in auctions for art pieces. Due to the increased complexity of this model compared to standard private values, it is generally assumed that each bidder's valuation function $v_i$ is public knowledge. But in many situations, the seller may not know how a bidder aggregates signals into a valuation. In this paper, we design mechanisms that guarantee approximately-optimal social welfare while satisfying ex-post incentive compatibility and individual rationality for the case where the valuation functions are private to the bidders. When the valuations are public, it is possible for optimal social welfare to be attained by a deterministic mechanism under a single-crossing condition. In contrast, when the valuations are the bidders' private information, we show that no finite bound can be achieved by any deterministic mechanism even under single-crossing. Moreover, no randomized mechanism can guarantee better than an $n$-approximation. We thus consider valuation functions that are submodular over signals (SOS), introduced in the context of combinatorial auctions in a recent breakthrough paper by Eden et al. [EC'19]. Our main result is an $O(\log^2 n)$-approximation for buyers with private signals and valuations under the SOS condition. We also give a tight $Θ(k)$-approximation for the case each agent's valuation depends on at most $k$ other signals even for unknown $k$.

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arXiv2020

Non-Adaptive Matroid Prophet Inequalities

We investigate non-adaptive algorithms for matroid prophet inequalities. Matroid prophet inequalities have been considered resolved since 2012 when [KW12] introduced thresholds that guarantee a tight 2-approximation to the prophet; however, this algorithm is adaptive. Other approaches of [CHMS10] and [FSZ16] have used non-adaptive thresholds with a feasibility restriction; however, this translates to adaptively changing an item's threshold to infinity when it cannot be taken with respect to the additional feasibility constraint, hence the algorithm is not truly non-adaptive. A major application of prophet inequalities is in auction design, where non-adaptive prices possess a significant advantage: they convert to order-oblivious posted pricings, and are essential for translating a prophet inequality into a truthful mechanism for multi-dimensional buyers. The existing matroid prophet inequalities do not suffice for this application. We present the first non-adaptive constant-factor prophet inequality for graphic matroids.

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arXiv2020

When to Limit Market Entry under Mandatory Purchase

We study a problem inspired by regulated health insurance markets, such as those created by the government in the Affordable Care Act Exchanges or by employers when they contract with private insurers to provide plans for their employees. The market regulator can choose to do nothing, running a Free Market, or can exercise her regulatory power by limiting the entry of providers (decreasing consumer welfare by limiting options, but also decreasing revenue via enhanced competition). We investigate whether limiting entry increases or decreases the utility (welfare minus revenue) of the consumers who purchase from the providers, specifically in settings where the outside option of "purchasing nothing" is prohibitively undesirable. We focus primarily on the case where providers are symmetric. We propose a sufficient condition on the distribution of consumer values for (a) a unique symmetric equilibrium to exist in both markets and (b) utility to be higher with limited entry. (We also establish that these conclusions do not necessarily hold for all distributions, and therefore some condition is necessary.) Our techniques are primarily based on tools from revenue maximization, and in particular Myerson's virtual value theory. We also consider extensions to settings where providers have identical costs for providing plans, and to two providers with an asymmetric distribution.

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arXiv2020

Optimal Mechanism Design for Single-Minded Agents

We consider revenue-optimal mechanism design in the interdimensional setting, where one dimension is the 'value' of the buyer, and one is a 'type' that captures some auxiliary information. One setting is the FedEx Problem, for which FGKK [2016] characterize the optimal mechanism for a single agent. We ask: how far can such characterizations go? In particular, we consider single-minded agents. A seller has heterogenous items. A buyer has a value v for a specific subset of items S, and obtains value v iff he gets (at least) all the items in S. We show: 1. Deterministic mechanisms are optimal for distributions that satisfy the "declining marginal revenue" (DMR) property; we give an explicit construction of the optimal mechanism. 2. Without DMR, the result depends on the structure of the directed acyclic graph (DAG) representing the partial order among types. When the DAG has out-degree at most 1, we characterize the optimal mechanism a la FedEx. 3. Without DMR, when the DAG has some node with out-degree at least 2, we show that in this case the menu complexity is unbounded: for any M, there exist distributions over (v,S) pairs such that the menu complexity of the optimal mechanism is at least M. 4. For the case of 3 types, we show that for all distributions there exists an optimal mechanism of finite menu complexity. This is in contrast to 2 additive heterogenous items or which the menu complexity could be uncountable [MV07; DDT15]. In addition, we prove that optimal mechanisms for Multi-Unit Pricing (without DMR) can have unbounded menu complexity. We also propose an extension where the menu complexity of optimal mechanisms can be countable but not uncountable. Together these results establish that optimal mechanisms in interdimensional settings are both much richer than single-dimensional settings, yet also vastly more structured than multi-dimensional settings.

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arXiv2019

Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets

We consider the problem of welfare maximization in two-sided markets using simple mechanisms that are prior-independent. The Myerson-Satterthwaite impossibility theorem shows that even for bilateral trade, there is no feasible (IR, truthful, budget balanced) mechanism that has welfare as high as the optimal-yet-infeasible VCG mechanism, which attains maximal welfare but runs a deficit. On the other hand, the optimal feasible mechanism needs to be carefully tailored to the Bayesian prior, and is extremely complex, eluding a precise description. We present Bulow-Klemperer-style results to circumvent these hurdles in double-auction markets. We suggest using the Buyer Trade Reduction (BTR) mechanism, a variant of McAfee's mechanism, which is feasible and simple (in particular, deterministic, truthful, prior-independent, anonymous). First, in the setting where buyers' and sellers' values are sampled i.i.d. from the same distribution, we show that for any such market of any size, BTR with one additional buyer whose value is sampled from the same distribution has expected welfare at least as high as the optimal in the original market. We then move to a more general setting where buyers' values are sampled from one distribution and sellers' from another, focusing on the case where the buyers' distribution first-order stochastically dominates the sellers'. We present bounds on the number of buyers that, when added, guarantees that BTR in the augmented market have welfare at least as high as the optimal in the original market. Our lower bounds extend to a large class of mechanisms, and all of our results extend to adding sellers instead of buyers. In addition, we present positive results about the usefulness of pricing at a sample for welfare maximization in two-sided markets under the above two settings, which to the best of our knowledge are the first sampling results in this context.

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arXiv2019

Reducing Inefficiency in Carbon Auctions with Imperfect Competition

We study auctions for carbon licenses, a policy tool used to control the social cost of pollution. Each identical license grants the right to produce a unit of pollution. Each buyer (i.e., firm that pollutes during the manufacturing process) enjoys a decreasing marginal value for licenses, but society suffers an increasing marginal cost for each license distributed. The seller (i.e., the government) can choose a number of licenses to put up for auction, and wishes to maximize the societal welfare: the total economic value of the buyers minus the social cost. Motivated by emission license markets deployed in practice, we focus on uniform price auctions with a price floor and/or price ceiling. The seller has distributional information about the market, and their goal is to tune the auction parameters to maximize expected welfare. The target benchmark is the maximum expected welfare achievable by any such auction under truth-telling behavior. Unfortunately, the uniform price auction is not truthful, and strategic behavior can significantly reduce (even below zero) the welfare of a given auction configuration. We describe a subclass of "safe-price'" auctions for which the welfare at any Bayes-Nash equilibrium will approximate the welfare under truth-telling behavior. We then show that the better of a safe-price auction, or a truthful auction that allocates licenses to only a single buyer, will approximate the target benchmark. In particular, we show how to choose a number of licenses and a price floor so that the worst-case welfare, at any equilibrium, is a constant approximation to the best achievable welfare under truth-telling after excluding the welfare contribution of a single buyer.

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arXiv2019

Simple and Approximately Optimal Pricing for Proportional Complementarities

We study a new model of complementary valuations, which we call "proportional complementarities." In contrast to common models, such as hypergraphic valuations, in our model, we do not assume that the extra value derived from owning a set of items is independent of the buyer's base valuations for the items. Instead, we model the complementarities as proportional to the buyer's base valuations, and these proportionalities are known market parameters. Our goal is to design a simple pricing scheme that, for a single buyer with proportional complementarities, yields approximately optimal revenue. We define a new class of mechanisms where some number of items are given away for free, and the remaining items are sold separately at inflated prices. We find that the better of such a mechanism and selling the grand bundle earns a 12-approximation to the optimal revenue for pairwise proportional complementarities. This confirms the intuition that items should not be sold completely separately in the presence of complementarities. In the more general case, a buyer has a maximum of proportional positive hypergraphic valuations, where a hyperedge in a given hypergraph describes the boost to the buyer's value for item $i$ given by owning any set of items $T$ in addition. The maximum-out-degree of such a hypergraph is $d$, and $k$ is the positive rank of the hypergraph. For valuations given by these parameters, our simple pricing scheme is an $O(\min\{d,k\})$-approximation.

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arXiv2019

Combinatorial Auctions with Interdependent Valuations: SOS to the Rescue

We study combinatorial auctions with interdependent valuations. In such settings, each agent $i$ has a private signal $s_i$ that captures her private information, and the valuation function of every agent depends on the entire signal profile, ${\bf s}=(s_1,\ldots,s_n)$. The literature in economics shows that the interdependent model gives rise to strong impossibility results, and identifies assumptions under which optimal solutions can be attained. The computer science literature provides approximation results for simple single-parameter settings (mostly single item auctions, or matroid feasibility constraints). Both bodies of literature focus largely on valuations satisfying a technical condition termed {\em single crossing} (or variants thereof). We consider the class of {\em submodular over signals} (SOS) valuations (without imposing any single-crossing type assumption), and provide the first welfare approximation guarantees for multi-dimensional combinatorial auctions, achieved by universally ex-post IC-IR mechanisms. Our main results are: $(i)$ 4-approximation for any single-parameter downward-closed setting with single-dimensional signals and SOS valuations; $(ii)$ 4-approximation for any combinatorial auction with multi-dimensional signals and {\em separable}-SOS valuations; and $(iii)$ $(k+3)$- and $(2\log(k)+4)$-approximation for any combinatorial auction with single-dimensional signals, with $k$-sized signal space, for SOS and strong-SOS valuations, respectively. All of our results extend to a parameterized version of SOS, $d$-SOS, while losing a factor that depends on $d$.

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arXiv2018

Mechanism Design for Social Good

Across various domains--such as health, education, and housing--improving societal welfare involves allocating resources, setting policies, targeting interventions, and regulating activities. These solutions have an immense impact on the day-to-day lives of individuals, whether in the form of access to quality healthcare, labor market outcomes, or how votes are accounted for in a democratic society. Problems that can have an out-sized impact on individuals whose opportunities have historically been limited often pose conceptual and technical challenges, requiring insights from many disciplines. Conversely, the lack of interdisciplinary approach can leave these urgent needs unaddressed and can even exacerbate underlying socioeconomic inequalities. To realize the opportunities in these domains, we need to correctly set objectives and reason about human behavior and actions. Doing so requires a deep grounding in the field of interest and collaboration with domain experts who understand the societal implications and feasibility of proposed solutions. These insights can play an instrumental role in proposing algorithmically-informed policies. In this article, we describe the Mechanism Design for Social Good (MD4SG) research agenda, which involves using insights from algorithms, optimization, and mechanism design to improve access to opportunity. The MD4SG research community takes an interdisciplinary, multi-stakeholder approach to improve societal welfare. We discuss three exciting research avenues within MD4SG related to improving access to opportunity in the developing world, labor markets and discrimination, and housing. For each of these, we showcase ongoing work, underline new directions, and discuss potential for implementing existing work in practice.

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arXiv2018

Interdependent Values without Single-Crossing

We consider a setting where an auctioneer sells a single item to $n$ potential agents with {\em interdependent values}. That is, each agent has her own private signal, and the valuation of each agent is a known function of all $n$ private signals. This captures settings such as valuations for artwork, oil drilling rights, broadcast rights, and many more. In the interdependent value setting, all previous work has assumed a so-called {\sl single-crossing condition}. Single-crossing means that the impact of agent $i$'s private signal, $s_i$, on her own valuation is greater than the impact of $s_i$ on the valuation of any other agent. It is known that without the single-crossing condition an efficient outcome cannot be obtained. We study welfare maximization for interdependent valuations through the lens of approximation. We show that, in general, without the single-crossing condition, one cannot hope to approximate the optimal social welfare any better than the approximation given by assigning the item to a random bidder. Consequently, we introduce a relaxed version of single-crossing, {\sl $c$-single-crossing}, parameterized by $c\geq 1$, which means that the impact of $s_i$ on the valuation of agent $i$ is at least $1/c$ times the impact of $s_i$ on the valuation of any other agent ($c=1$ is single-crossing). Using this parameterized notion, we obtain a host of positive results. We propose a prior-free deterministic mechanism that gives an $(n-1)c$-approximation guarantee to welfare. We then show that a random version of the proposed mechanism gives a prior-free universally truthful $2c$-approximation to the optimal welfare for any concave $c$-single crossing setting (and a $2\sqrt{n}c^{3/2}$-approximation in the absence of concavity). We extend this mechanism to a universally truthful mechanism that gives $O(c^2)$-approximation to the optimal revenue.

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arXiv2018

Revenue Maximization with an Uncertainty-Averse Buyer

Most work in mechanism design assumes that buyers are risk neutral; some considers risk aversion arising due to a non-linear utility for money. Yet behavioral studies have established that real agents exhibit risk attitudes which cannot be captured by any expected utility model. We initiate the study of revenue-optimal mechanisms under buyer behavioral models beyond expected utility theory. We adopt a model from prospect theory which arose to explain these discrepancies and incorporates agents under-weighting uncertain outcomes. In our model, an event occurring with probability $x < 1$ is worth strictly less to the agent than $x$ times the value of the event when it occurs with certainty. In contrast to the risk-neutral setting, the optimal mechanism may be randomized and appears challenging to find, even for a single buyer and a single item for sale. Nevertheless, we give a characterization of the optimal mechanism which enables positive approximation results. In particular, we show that under a reasonable bounded-risk-aversion assumption, posted pricing obtains a constant approximation. Notably, this result is "risk-robust" in that it does not depend on the details of the buyer's risk attitude. Finally, we examine a dynamic setting in which the buyer is uncertain about his future value. In contrast to positive results for a risk-neutral buyer, we show that the buyer's risk aversion may prevent the seller from approximating the optimal revenue in a risk-robust manner.

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