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Efficient two-sided markets with limited information

Authors

Paul Dütting, Federico Fusco, Philip Lazos, Stefano Leonardi, Rebecca Reiffenhäuser
Type: Article
Publication Date: 2021-06-15
Citations: 16
DOI: https://doi.org/10.1145/3406325.3451076

Abstract

A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to relax welfare efficiency and the use of approximation mechanisms. Such mechanisms in general make extensive use of the Bayesian priors. In this work, we investigate a question of increasing theoretical and practical importance: how much prior information is required to design mechanisms with near-optimal approximations?

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  • London School of Economics and Political Science Research Online (London School of Economics and Political Science)
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Efficient Two-Sided Markets with Limited Information

2020-01-01
Paul Dütting , Federico Fusco , Philip Lazos +2 more
A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to … A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to relax welfare efficiency and the use of approximation mechanisms. Such mechanisms in general make extensive use of the Bayesian priors. In this work, we investigate a question of increasing theoretical and practical importance: how much prior information is required to design mechanisms with near-optimal approximations? Our first contribution is a more general impossibility result stating that no meaningful approximation is possible without any prior information, expanding the famous impossibility result of Myerson and Satterthwaite. Our second contribution is that one {\em single sample} (one number per item), arguably a minimum-possible amount of prior information, from each seller distribution is sufficient for a large class of two-sided markets. We prove matching upper and lower bounds on the best approximation that can be obtained with one single sample for subadditive buyers and additive sellers, regardless of computational considerations. Our third contribution is the design of computationally efficient blackbox reductions that turn any one-sided mechanism into a two-sided mechanism with a small loss in the approximation, while using only one single sample from each seller. On the way, our blackbox-type mechanisms deliver several interesting positive results in their own right, often beating even the state of the art that uses full prior information.
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Efficient Two-Sided Markets with Limited Information

2020-03-17
Paul Dütting , Federico Fusco , Philip Lazos +2 more
A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to … A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to relax welfare efficiency and the use of approximation mechanisms. Such mechanisms in general make extensive use of the Bayesian priors. In this work, we investigate a question of increasing theoretical and practical importance: how much prior information is required to design mechanisms with near-optimal approximations? Our first contribution is a more general impossibility result stating that no meaningful approximation is possible without any prior information, expanding the famous impossibility result of Myerson and Satterthwaite. Our second contribution is that one {\em single sample} (one number per item), arguably a minimum-possible amount of prior information, from each seller distribution is sufficient for a large class of two-sided markets. We prove matching upper and lower bounds on the best approximation that can be obtained with one single sample for subadditive buyers and additive sellers, regardless of computational considerations. Our third contribution is the design of computationally efficient blackbox reductions that turn any one-sided mechanism into a two-sided mechanism with a small loss in the approximation, while using only one single sample from each seller. On the way, our blackbox-type mechanisms deliver several interesting positive results in their own right, often beating even the state of the art that uses full prior information.

Approximately Efficient Two-Sided Combinatorial Auctions

2017-06-20
Riccardo Colini-Baldeschi , Paul W. Goldberg , Bart de Keijzer +3 more
We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of … We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases and sales of the items. A mechanism is given prior distributions on the agents' valuations of the items, but not the actual valuations; thus the aim is to maximise the expected social welfare over these distributions. As in previous work, we are interested in the worst-case ratio between the social welfare achieved by a truthful mechanism, and the best social welfare possible.
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The Best of Both Worlds: Asymptotically Efficient Mechanisms with a Guarantee on the Expected Gains-From-Trade

2018-01-01
Moshe Babaioff , Yang Cai , Yannai A. Gonczarowski +1 more
The seminal impossibility result of Myerson and Satterthwaite (1983) states that for bilateral trade, there is no mechanism that is individually rational (IR), incentive compatible (IC), weakly budget balanced, and … The seminal impossibility result of Myerson and Satterthwaite (1983) states that for bilateral trade, there is no mechanism that is individually rational (IR), incentive compatible (IC), weakly budget balanced, and efficient. This has led follow-up work on two-sided trade settings to weaken the efficiency requirement and consider approximately efficient simple mechanisms, while still demanding the other properties. The current state-of-the-art of such mechanisms for two-sided markets can be categorized as giving one (but not both) of the following two types of approximation guarantees on the gains from trade: a constant ex-ante guarantee, measured with respect to the second-best efficiency benchmark, or an asymptotically optimal ex-post guarantee, measured with respect to the first-best efficiency benchmark. Here the second-best efficiency benchmark refers to the highest gains from trade attainable by any IR, IC and weakly budget balanced mechanism, while the first-best efficiency benchmark refers to the maximum gains from trade (attainable by the VCG mechanism, which is not weakly budget balanced). In this paper, we construct simple mechanisms for double-auction and matching markets that simultaneously achieve both types of guarantees: these are ex-post IR, Bayesian IC, and ex-post weakly budget balanced mechanisms that 1) ex-ante guarantee a constant fraction of the gains from trade of the second-best, and 2) ex-post guarantee a realization-dependent fraction of the gains from trade of the first-best, such that this realization-dependent fraction converges to 1 (full efficiency) as the market grows large.

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

2019-03-15
Moshe Babaioff , Kira Goldner , Yannai A. Gonczarowski
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 … 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.

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

2019-01-01
Moshe Babaioff , Kira Goldner , Yannai A. Gonczarowski
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 … 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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Approximately Efficient Two-Sided Combinatorial Auctions

2020-02-29
Riccardo Colini-Baldeschi , Paul W. Goldberg , Bart de Keijzer +3 more
We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of … We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases and sales of the items. A mechanism is given prior distributions on the agents’ valuations of the items, but not the actual valuations; thus, the aim is to maximise the expected social welfare over these distributions. As in previous work, we are interested in the worst-case ratio between the social welfare achieved by a truthful mechanism and the best social welfare possible. Our main result is an incentive compatible and budget balanced constant-factor approximation mechanism in a setting where buyers have XOS valuations and sellers’ valuations are additive. This is the first such approximation mechanism for a two-sided market setting where the agents have combinatorial valuation functions. To achieve this result, we introduce a more general kind of demand query that seems to be needed in this situation. In the simpler case that sellers have unit supply (each having just one item to sell), we give a new mechanism whose welfare guarantee improves on a recent one in the literature. We also introduce a more demanding version of the strong budget balance (SBB) criterion, aimed at ruling out certain “unnatural” transactions satisfied by SBB. We show that the stronger version is satisfied by our mechanisms.
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Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets

2019-12-23
Moshe Babaioff , Kira Goldner , Yannai A. Gonczarowski
Previous chapter Next chapter Full AccessProceedings Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms (SODA)Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided MarketsMoshe Babaioff, Kira Goldner, and Yannai A. GonczarowskiMoshe … Previous chapter Next chapter Full AccessProceedings Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms (SODA)Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided MarketsMoshe Babaioff, Kira Goldner, and Yannai A. GonczarowskiMoshe Babaioff, Kira Goldner, and Yannai A. Gonczarowskipp.2452 - 2471Chapter DOI:https://doi.org/10.1137/1.9781611975994.150PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract We consider the problem of welfare (and gains-from-trade) maximization in two-sided markets using simple mechanisms that are prior-independent. The seminal impossibility result of Myerson and Satterthwaite [1983] shows that even for bilateral trade, there is no feasible (individually rational, truthful, and 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 even worse, it is known to be extremely complex, eluding a precise description. In this paper we present Bulow-Klemperer-style results to circumvent these hurdles in double-auction market settings. We suggest using the Buyer Trade Reduction (BTR) mechanism, a variant of McAfee's mechanism, which is feasible and simple (in particular, it is deterministic, truthful, prior-independent, and anonymous). First, in the setting in which the values of the buyers and of the sellers are sampled independently and identically 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-yet-infeasible VCG mechanism in the original market. We then move to a more general setting in which the values of the buyers are sampled from one distribution, and those of the sellers from another, focusing on the case where the buyers' distribution first-order stochastically dominates the sellers' distribution. We present both upper bounds and lower bounds on the number of buyers that, when added, guarantees that BTR in the augmented market achieve 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 positive and negative 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 (and more precisely, for gains-from-trade approximation) in two-sided markets under the above two settings, which to the best of our knowledge are the first sampling results in this context. Previous chapter Next chapter RelatedDetails Published:2020eISBN:978-1-61197-599-4 https://doi.org/10.1137/1.9781611975994Book Series Name:ProceedingsBook Code:PRDA20Book Pages:xxii + 3011
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Approximately Efficient Two-Sided Combinatorial Auctions

2016-01-01
Riccardo Colini-Baldeschi , Paul W. Goldberg , Bart de Keijzer +3 more
Mechanism design for one-sided markets has been investigated for several decades in economics and in computer science. More recently, there has been an increased attention on mechanisms for two-sided markets, … Mechanism design for one-sided markets has been investigated for several decades in economics and in computer science. More recently, there has been an increased attention on mechanisms for two-sided markets, in which buyers and sellers act strategically. For two-sided markets, an impossibility result of Myerson and Satterthwaite states that no mechanism can simultaneously satisfy individual rationality (IR), incentive compatibility (IC), strong budget-balance (SBB), and be efficient. On the other hand, important applications to web advertisement, stock exchange, and frequency spectrum allocation, require us to consider two-sided combinatorial auctions in which buyers have preferences on subsets of items, and sellers may offer multiple heterogeneous items. No efficient mechanism was known so far for such two-sided combinatorial markets. This work provides the first IR, IC and SBB mechanisms that provides an O(1)-approximation to the optimal social welfare for two-sided markets. An initial construction yields such a mechanism, but exposes a conceptual problem in the traditional SBB notion. This leads us to define the stronger notion of direct trade strong budget balance (DSBB). We then proceed to design mechanisms that are IR, IC, DSBB, and again provide an O(1)-approximation to the optimal social welfare. Our mechanisms work for any number of buyers with XOS valuations - a class in between submodular and subadditive functions - and any number of sellers. We provide a mechanism that is dominant strategy incentive compatible (DSIC) if the sellers each have one item for sale, and one that is bayesian incentive compatible (BIC) if sellers hold multiple items and have additive valuations over them. Finally, we present a DSIC mechanism for the case that the valuation functions of all buyers and sellers are additive.
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The Power of Two-sided Recruitment in Two-sided Markets

2023-01-01
Yang Cai , Christopher Liaw , Aranyak Mehta +1 more
We consider the problem of maximizing the gains from trade (GFT) in two-sided markets. The seminal impossibility result by Myerson and Satterthwaite shows that even for bilateral trade, there is … We consider the problem of maximizing the gains from trade (GFT) in two-sided markets. The seminal impossibility result by Myerson and Satterthwaite shows that even for bilateral trade, there is no individually rational (IR), Bayesian incentive compatible (BIC) and budget balanced (BB) mechanism that can achieve the full GFT. Moreover, the optimal BIC, IR and BB mechanism that maximizes the GFT is known to be complex and heavily depends on the prior. In this paper, we pursue a Bulow-Klemperer-style question, i.e., does augmentation allow for prior-independent mechanisms to compete against the optimal mechanism? Our first main result shows that in the double auction setting with $m$ i.i.d. buyers and $n$ i.i.d. sellers, by augmenting $O(1)$ buyers and sellers to the market, the GFT of a simple, dominant strategy incentive compatible (DSIC), and prior-independent mechanism in the augmented market is at least the optimal in the original market, when the buyers' distribution first-order stochastically dominates the sellers' distribution. Next, we go beyond the i.i.d. setting and study the power of two-sided recruitment in more general markets. Our second main result is that for any $\epsilon > 0$ and any set of $O(1/\epsilon)$ buyers and sellers where the buyers' value exceeds the sellers' value with constant probability, if we add these additional agents into any market with arbitrary correlations, the Trade Reduction mechanism obtains a $(1-\epsilon)$-approximation of the GFT of the augmented market. Importantly, the newly recruited agents are agnostic to the original market.
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A Truthful Cardinal Mechanism for One-Sided Matching

2019-12-23
Rediet Abebe , Richard Cole , Vasilis Gkatzelis +1 more
Previous chapter Next chapter Full AccessProceedings Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms (SODA)A Truthful Cardinal Mechanism for One-Sided MatchingRediet Abebe, Richard Cole, Vasilis Gkatzelis, and Jason D. … Previous chapter Next chapter Full AccessProceedings Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms (SODA)A Truthful Cardinal Mechanism for One-Sided MatchingRediet Abebe, Richard Cole, Vasilis Gkatzelis, and Jason D. HartlineRediet Abebe, Richard Cole, Vasilis Gkatzelis, and Jason D. Hartlinepp.2096 - 2113Chapter DOI:https://doi.org/10.1137/1.9781611975994.129PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract We revisit the well-studied problem of designing mechanisms for one-sided matching markets, where a set of n agents needs to be matched to a set of n heterogeneous items. Each agent i has a value νi,j for each item j, and these values are private information that the agents may misreport if doing so leads to a preferred outcome. Ensuring that the agents have no incentive to misreport requires a careful design of the matching mechanism, and mechanisms proposed in the literature mitigate this issue by eliciting only the ordinal preferences of the agents, i.e., their ranking of the items from most to least preferred. However, the efficiency guarantees of these mechanisms are based only on weak measures that are oblivious to the underlying values. In this paper we achieve stronger performance guarantees by introducing a mechanism that truthfully elicits the full cardinal preferences of the agents, i.e., all of the νi,j values. We evaluate the performance of this mechanism using the much more demanding Nash bargaining solution as a benchmark, and we prove that our mechanism significantly outperforms all ordinal mechanisms (even non-truthful ones). To prove our approximation bounds, we also study the population monotonicity of the Nash bargaining solution in the context of matching markets, providing both upper and lower bounds which are of independent interest. Previous chapter Next chapter RelatedDetails Published:2020eISBN:978-1-61197-599-4 https://doi.org/10.1137/1.9781611975994Book Series Name:ProceedingsBook Code:PRDA20Book Pages:xxii + 3011
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(Almost) Efficient Mechanisms for Bilateral Trading

2016-01-01
Liad Blumrosen , Shahar Dobzinski
We study the bilateral trade problem: one seller, one buyer and a single, indivisible item for sale. It is well known that there is no fully-efficient and incentive compatible mechanism … We study the bilateral trade problem: one seller, one buyer and a single, indivisible item for sale. It is well known that there is no fully-efficient and incentive compatible mechanism for this problem that maintains a balanced budget. We design simple and robust mechanisms that obtain approximate efficiency with these properties. We show that even minimal use of statistical data can yield good approximation results. Finally, we demonstrate how a mechanism for this simple bilateral-trade problem can be used as a "black-box" for constructing mechanisms in more general environments.
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Bayesian Mechanism Design with Efficiency, Privacy, and Approximate Truthfulness

2012-01-01
Samantha Leung , Edward Lui
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Truthful learning mechanisms for multi-slot sponsored search auctions with externalities

2015-06-13
Nicola Gatti , Alessandro Lazaric , Marco Rocco +1 more
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Approximately Efficient Bilateral Trade

2021-01-01
Yuan Deng , Jieming Mao , Balasubramanian Sivan +1 more
We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be … We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be efficient. I.e., no mechanism with these properties can guarantee a trade whenever buyer value exceeds seller cost. Given this, a natural question is whether there exists a mechanism with these properties that guarantees a constant fraction of the first-best gains-from-trade, namely a constant fraction of the gains-from-trade attainable whenever buyer's value weakly exceeds seller's cost. In this work, we positively resolve this long-standing open question on constant-factor approximation, mentioned in several previous works, using a simple mechanism.
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A Truthful Cardinal Mechanism for One-Sided Matching

2019-01-01
Rediet Abebe , Richard Cole , Vasilis Gkatzelis +1 more
We revisit the well-studied problem of designing mechanisms for one-sided matching markets, where a set of $n$ agents needs to be matched to a set of $n$ heterogeneous items. Each … We revisit the well-studied problem of designing mechanisms for one-sided matching markets, where a set of $n$ agents needs to be matched to a set of $n$ heterogeneous items. Each agent $i$ has a value $v_{i,j}$ for each item $j$, and these values are private information that the agents may misreport if doing so leads to a preferred outcome. Ensuring that the agents have no incentive to misreport requires a careful design of the matching mechanism, and mechanisms proposed in the literature mitigate this issue by eliciting only the \emph{ordinal} preferences of the agents, i.e., their ranking of the items from most to least preferred. However, the efficiency guarantees of these mechanisms are based only on weak measures that are oblivious to the underlying values. In this paper we achieve stronger performance guarantees by introducing a mechanism that truthfully elicits the full \emph{cardinal} preferences of the agents, i.e., all of the $v_{i,j}$ values. We evaluate the performance of this mechanism using the much more demanding Nash bargaining solution as a benchmark, and we prove that our mechanism significantly outperforms all ordinal mechanisms (even non-truthful ones). To prove our approximation bounds, we also study the population monotonicity of the Nash bargaining solution in the context of matching markets, providing both upper and lower bounds which are of independent interest.
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Bayesian Mechanism Design for Budget-Constrained Agents

2011-01-01
Shuchi Chawla , David Malec , Azarakhsh Malekian
We study Bayesian mechanism design problems in settings where agents have budgets. Specifically, an agent's utility for an outcome is given by his value for the outcome minus any payment … We study Bayesian mechanism design problems in settings where agents have budgets. Specifically, an agent's utility for an outcome is given by his value for the outcome minus any payment he makes to the mechanism, as long as the payment is below his budget, and is negative infinity otherwise. This discontinuity in the utility function presents a significant challenge in the design of good mechanisms, and classical "unconstrained" mechanisms fail to work in settings with budgets. The goal of this paper is to develop general reductions from budget-constrained Bayesian MD to unconstrained Bayesian MD with small loss in performance. We consider this question in the context of the two most well-studied objectives in mechanism design---social welfare and revenue---and present constant factor approximations in a number of settings. Some of our results extend to settings where budgets are private and agents need to be incentivized to reveal them truthfully.
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Approximately efficient bilateral trade

2022-06-09
Yuan Deng , Jieming Mao , Balasubramanian Sivan +1 more
We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be … We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be efficient. I.e., no mechanism with these properties can guarantee a trade whenever buyer value exceeds seller cost. Given this, a natural question is whether there exists a mechanism with these properties that guarantees a constant fraction of the first-best gains-from-trade, namely a constant fraction of the gains-from-trade attainable whenever buyer's value weakly exceeds seller's cost. In this work, we positively resolve this long-standing open question on constant-factor approximation, mentioned in several previous works, using a simple mechanism that obtains a 1/8.23 ≈ 0.121 fraction of the first-best.
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Optimal Bayesian Mechanisms

1984-12-01
Eric S. Maskin

Bayesian mechanism design for budget-constrained agents

2011-06-05
Shuchi Chawla , David L. Malec , Azarakhsh Malekian
We study Bayesian mechanism design problems in settings where agents have budgets. Specifically, an agent's utility for an outcome is given by his value for the outcome minus any payment … We study Bayesian mechanism design problems in settings where agents have budgets. Specifically, an agent's utility for an outcome is given by his value for the outcome minus any payment he makes to the mechanism, as long as the payment is below his budget, and is negative infinity otherwise. This discontinuity in the utility function presents a significant challenge in the design of good mechanisms, and classical mechanisms fail to work in settings with budgets. The goal of this paper is to develop general reductions from budget-constrained Bayesian MD to unconstrained Bayesian MD with small loss in performance. We consider this question in the context of the two most well-studied objectives in mechanism design---social welfare and revenue---and present constant factor approximations in a number of settings. Some of our results extend to settings where budgets are private and agents need to be incentivized to reveal them truthfully.
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Online revenue maximization for server pricing

2022-01-22
Shant Boodaghians , Federico Fusco , Stefano Leonardi +2 more
Efficient and truthful mechanisms to price resources on servers/machines have been the subject of much work in recent years due to the importance of the cloud market. This paper considers … Efficient and truthful mechanisms to price resources on servers/machines have been the subject of much work in recent years due to the importance of the cloud market. This paper considers revenue maximization in the online stochastic setting with non-preemptive jobs and a unit capacity server. One agent/job arrives at every time step, with parameters drawn from the underlying distribution. We design a posted-price mechanism which can be efficiently computed and is revenue-optimal in expectation and in retrospect, up to additive error. The prices are posted prior to learning the agent's type, and the computed pricing scheme is deterministic, depending only on the length of the allotted time interval and on the earliest time the server is available. We also prove that the proposed pricing strategy is robust to imprecise knowledge of the job distribution and that a distribution learned from polynomially many samples is sufficient to obtain a near-optimal truthful pricing strategy.
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Improved Approximation Ratios of Fixed-Price Mechanisms in Bilateral Trades

2023-05-16
Zhengyang Liu , Zeyu Ren , Zihe Wang
We continue the study of the performance for fixed-price mechanisms in the bilateral trade problem, and improve approximation ratios of welfare-optimal mechanisms in several settings. Specifically, in the case where … We continue the study of the performance for fixed-price mechanisms in the bilateral trade problem, and improve approximation ratios of welfare-optimal mechanisms in several settings. Specifically, in the case where only the buyer distribution is known, we prove that there exists a distribution over different fixed-price mechanisms, such that the approximation ratio lies within the interval of [0.71, 0.7381]. Furthermore, we show that the same approximation ratio holds for the optimal fixed-price mechanism, when both buyer and seller distributions are known. As a result, the previously best-known (1 − 1/e+0.0001)-approximation can be improved to 0.71. Additionally, we examine randomized fixed-price mechanisms when we receive just one single sample from the seller distribution, for both symmetric and asymmetric settings. Our findings reveal that posting the single sample as the price remains optimal among all randomized fixed-price mechanisms.
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A Regret Analysis of Bilateral Trade

2021-07-18
Nicolò Cesa‐Bianchi , Tommaso Cesari , Roberto Colomboni +2 more
Bilateral trade, a fundamental topic in economics, models the problem of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold … Bilateral trade, a fundamental topic in economics, models the problem of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. Despite the simplicity of this problem, a classical result by Myerson and Satterthwaite (1983) affirms the impossibility of designing a mechanism which is simultaneously efficient, incentive compatible, individually rational, and budget balanced. This impossibility result fostered an intense investigation of meaningful trade-offs between these desired properties. Much work has focused on approximately efficient fixed-price mechanisms, i.e., Blumrosen and Dobzinski (2014; 2016), Colini-Baldeschi et al. (2016), which have been shown to fully characterize strong budget balanced and ex-post individually rational direct revelation mechanisms. All these results, however, either assume some knowledge on the priors of the seller/buyer valuations, or a black box access to some samples of the distributions, as in D{\"u}tting et al. (2021). In this paper, we cast for the first time the bilateral trade problem in a regret minimization framework over rounds of seller/buyer interactions, with no prior knowledge on the private seller/buyer valuations. Our main contribution is a complete characterization of the regret regimes for fixed-price mechanisms with different models of feedback and private valuations, using as benchmark the best fixed price in hindsight. More precisely, we prove the following bounds on the regret: $\bullet$ $\widetilde{\Theta}(\sqrt{T})$ for full-feedback (i.e., direct revelation mechanisms); $\bullet$ $\widetilde{\Theta}(T^{2/3})$ for realistic feedback (i.e., posted-price mechanisms) and independent seller/buyer valuations with bounded densities; $\bullet$ $\Theta(T)$ for realistic feedback and seller/buyer valuations with bounded densities; $\bullet$ $\Theta(T)$ for realistic feedback and independent seller/buyer valuations; $\bullet$ $\Theta(T)$ for the adversarial setting.
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Single-Sample Prophet Inequalities via Greedy-Ordered Selection

2022-01-01
Constantine Caramanis , Paul Dütting , Matthew Faw +6 more
Previous chapter Next chapter Full AccessProceedings Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Single-Sample Prophet Inequalities via Greedy-Ordered SelectionConstantine Caramanis, Paul Dütting, Matthew Faw, Federico Fusco, Philip … Previous chapter Next chapter Full AccessProceedings Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Single-Sample Prophet Inequalities via Greedy-Ordered SelectionConstantine Caramanis, Paul Dütting, Matthew Faw, Federico Fusco, Philip Lazos, Stefano Leonardi, Orestis Papadigenopoulos, Emmanouil Pountourakis, and Rebecca ReiffenhäuserConstantine Caramanis, Paul Dütting, Matthew Faw, Federico Fusco, Philip Lazos, Stefano Leonardi, Orestis Papadigenopoulos, Emmanouil Pountourakis, and Rebecca Reiffenhäuserpp.1298 - 1325Chapter DOI:https://doi.org/10.1137/1.9781611977073.54PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available. Besides a direct, and optimal, SSPI for the basic single choice problem [Rubinstein et al., 2020], most existing SSPI results were obtained via an elegant, but inherently lossy reduction to order-oblivious secretary (OOS) policies [Azar et al., 2014]. Motivated by this discrepancy, we develop an intuitive and versatile greedy-based technique that yields SSPIs directly rather than through the reduction to OOSs. Our results can be seen as generalizing and unifying a number of existing results in the area of prophet and secretary problems. Our algorithms significantly improve on the competitive guarantees for a number of interesting scenarios (including general matching with edge arrivals, bipartite matching with vertex arrivals, and certain matroids), and capture new settings (such as budget additive combinatorial auctions). Complementing our algorithmic results, we also consider mechanism design variants. Finally, we analyze the power and limitations of different SSPI approaches by providing a partial converse to the reduction from SSPI to OOS given by Azar et al. Previous chapter Next chapter RelatedDetails Published:2022eISBN:978-1-61197-707-3 https://doi.org/10.1137/1.9781611977073Book Series Name:ProceedingsBook Code:PRDA22Book Pages:xvii + 3771
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Truthful Mechanisms for Two-Sided Markets via Prophet Inequalities

2022-12-05
Alexander Braun , Thomas Keßelheim
We design novel mechanisms for welfare maximization in two-sided markets. That is, there are buyers willing to purchase items and sellers holding items initially, both acting rationally and strategically in … We design novel mechanisms for welfare maximization in two-sided markets. That is, there are buyers willing to purchase items and sellers holding items initially, both acting rationally and strategically in order to maximize utility. Our mechanisms are designed based on a powerful correspondence between two-sided markets and prophet inequalities. They satisfy individual rationality, dominant-strategy incentive compatibility, and budget balance constraints and give constant factor approximations to the optimal social welfare. We improve previous results in several settings. Our main focus is on matroid double auctions. Here, sellers hold identical items, and the set of buyers that obtain an item needs to be independent in a matroid. We construct two mechanisms, the first being a 1/3 approximation of the optimal social welfare-satisfying strong budget balance and requiring the agents to trade in a customized order and the second being a 1/2 approximation weakly budget balanced and able to deal with online arrival determined by an adversary. In addition, we construct constant factor approximations in two-sided markets with identical items when buyers need to fulfill a knapsack constraint. Also, in combinatorial double auctions with heterogeneous items, where buyers have valuation functions over item bundles instead of being interested in only one item, using similar techniques, we design a mechanism that is a 1/2 approximation of the optimal social welfare, is strongly budget balanced, and can deal with the online arrival of agents in an adversarial order. Funding: A. Braun was funded by the Deutsche Forschungsgemeinschaft [Grant 437739576].
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Bayesian and Randomized Clock Auctions

2022-07-12
Michal Feldman , Vasilis Gkatzelis , Nick Gravin +1 more
In a single-parameter mechanism design problem, a provider is looking to sell some service to a group of potential buyers. Each buyer i has a private value vi for receiving … In a single-parameter mechanism design problem, a provider is looking to sell some service to a group of potential buyers. Each buyer i has a private value vi for receiving this service, and some feasibility constraint restricts which subsets of buyers can be served simultaneously. Recent work in economics introduced (deferred-acceptance) clock auctions as a superior class of auctions for this problem, due to their transparency, simplicity, and very strong incentive guarantees. Subsequent work in computer science focused on evaluating these auctions with respect to their social welfare approximation guarantees, leading to strong impossibility results: in the absence of prior information regarding the buyers' values, no deterministic clock auction can achieve a bounded approximation, even for simple feasibility constraints with only two maximal feasible sets.
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No-Regret Learning in Bilateral Trade via Global Budget Balance

2024-06-10
Martino Bernasconi , Matteo Castiglioni , Andrea Celli +1 more
Bilateral trade models the problem of intermediating between two rational agents — a seller and a buyer — both characterized by a private valuation for an item they want to … Bilateral trade models the problem of intermediating between two rational agents — a seller and a buyer — both characterized by a private valuation for an item they want to trade. We study the online learning version of the problem, in which at each time step a new seller and buyer arrive and the learner has to set prices for them without any knowledge about their (adversarially generated) valuations.
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Fixed-Price Approximations in Bilateral Trade.

2021-07-29
Zi Yang Kang , Francisco Pernice , Jan Vondrák
We consider the bilateral trade problem, in which two agents trade a single indivisible item. It is known that the only dominant-strategy truthful mechanism is the fixed-price mechanism: given commonly … We consider the bilateral trade problem, in which two agents trade a single indivisible item. It is known that the only dominant-strategy truthful mechanism is the fixed-price mechanism: given commonly known distributions of the buyer's value $B$ and the seller's value $S$, a price $p$ is offered to both agents and trade occurs if $S \leq p < B$. The objective is to maximize either expected welfare $\mathbb{E}[S + (B-S) \mathbf{1}_{S \leq p < B}]$ or expected gains from trade $\mathbb{E}[(B-S) \mathbf{1}_{S \leq p < B}]$. We determine the optimal approximation ratio for several variants of the problem. When the agents' distributions are identical, we show that the optimal approximation ratio for welfare is $\frac{2+\sqrt{2}}{4}$. The optimal approximation for gains from trade in this case was known to be $1/2$; we show that this can be achieved even with just $1$ sample from the common distribution. We also show that a $3/4$-approximation to welfare can be achieved with $1$ sample from the common distribution. When agents' distributions are not required to be identical, we show that a previously best-known $(1-1/e)$-approximation can be strictly improved, but $1-1/e$ is optimal if only the seller's distribution is known.

Interactive Communication in Bilateral Trade

2021-01-01
Jieming Mao , Renato Paes Leme , Kangning Wang
We define a model of interactive communication where two agents with private types can exchange information before a game is played. The model contains Bayesian persuasion as a special case … We define a model of interactive communication where two agents with private types can exchange information before a game is played. The model contains Bayesian persuasion as a special case of a one-round communication protocol. We define message complexity corresponding to the minimum number of interactive rounds necessary to achieve the best possible outcome. Our main result is that for bilateral trade, agents don't stop talking until they reach an efficient outcome: Either agents achieve an efficient allocation in finitely many rounds of communication; or the optimal communication protocol has infinite number of rounds. We show an important class of bilateral trade settings where efficient allocation is achievable with a small number of rounds of communication.
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Approximately efficient bilateral trade

2022-06-09
Yuan Deng , Jieming Mao , Balasubramanian Sivan +1 more
We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be … We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be efficient. I.e., no mechanism with these properties can guarantee a trade whenever buyer value exceeds seller cost. Given this, a natural question is whether there exists a mechanism with these properties that guarantees a constant fraction of the first-best gains-from-trade, namely a constant fraction of the gains-from-trade attainable whenever buyer's value weakly exceeds seller's cost. In this work, we positively resolve this long-standing open question on constant-factor approximation, mentioned in several previous works, using a simple mechanism that obtains a 1/8.23 ≈ 0.121 fraction of the first-best.
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Prophet Inequalities for Matching with a Single Sample.

2021-04-05
Paul Dütting , Federico Fusco , Philip Lazos +2 more
We consider the prophet inequality problem for (not necessarily bipartite) matching problems with independent edge values, under both edge arrivals and vertex arrivals. We show constant-factor prophet inequalities for the … We consider the prophet inequality problem for (not necessarily bipartite) matching problems with independent edge values, under both edge arrivals and vertex arrivals. We show constant-factor prophet inequalities for the case where the online algorithm has only limited access to the value distributions through samples. First, we give a $16$-approximate prophet inequality for matching in general graphs under edge arrivals that uses only a single sample from each value distribution as prior information. Then, for bipartite matching and (one-sided) vertex arrivals, we show an improved bound of $8$ that also uses just a single sample from each distribution. Finally, we show how to turn our $16$-approximate single-sample prophet inequality into a truthful single-sample mechanism for online bipartite matching with vertex arrivals.

Concurrent Auctions Across The Supply Chain

2004-05-01
Moshe Babaioff , Noam Nisan
With the recent technological feasibility of electronic commerce over the Internet, much attention has been given to the design of electronic markets for various types of electronically-tradable goods. Such markets, … With the recent technological feasibility of electronic commerce over the Internet, much attention has been given to the design of electronic markets for various types of electronically-tradable goods. Such markets, however, will normally need to function in some relationship with markets for other related goods, usually those downstream or upstream in the supply chain. Thus, for example, an electronic market for rubber tires for trucks will likely need to be strongly influenced by the rubber market as well as by the truck market. In this paper we design protocols for exchange of information between a sequence of markets along a single supply chain. These protocols allow each of these markets to function separately, while the information exchanged ensures efficient global behavior across the supply chain. Each market that forms a link in the supply chain operates as a double auction, where the bids on one side of the double auction come from bidders in the corresponding segment of the industry, and the bids on the other side are synthetically generated by the protocol to express the combined information from all other links in the chain. The double auctions in each of the markets can be of several types, and we study several variants of incentive compatible double auctions, comparing them in terms of their efficiency and of the market revenue.
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Simple and Near-Optimal Mechanisms for Market Intermediation

2014-01-01
Rad Niazadeh , Yuan Yang , Robert Kleinberg
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The sample complexity of revenue maximization

2014-05-31
Richard Cole , Tim Roughgarden
In the design and analysis of revenue-maximizing auctions, auction performance is typically measured with respect to a prior distribution over inputs. The most obvious source for such a distribution is … In the design and analysis of revenue-maximizing auctions, auction performance is typically measured with respect to a prior distribution over inputs. The most obvious source for such a distribution is past data. The goal of this paper is to understand how much data is necessary and sufficient to guarantee near-optimal expected revenue.
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Breaking the logarithmic barrier for truthful combinatorial auctions with submodular bidders

2016-06-10
Shahar Dobzinski
We study a central problem in Algorithmic Mechanism Design: constructing truthful mechanisms for welfare maximization in combinatorial auctions with submodular bidders. Dobzinski, Nisan, and Schapira provided the first mechanism that … We study a central problem in Algorithmic Mechanism Design: constructing truthful mechanisms for welfare maximization in combinatorial auctions with submodular bidders. Dobzinski, Nisan, and Schapira provided the first mechanism that guarantees a non-trivial approximation ratio of O(log^2 m) [STOC'06], where m is the number of items. This was subsequently improved to O( log m log log m) [Dobzinski, APPROX'07] and then to O(m) [Krysta and Vocking, ICALP'12]. In this paper we develop the first mechanism that breaks the logarithmic barrier. Specifically, the mechanism provides an approximation ratio of O( m). Similarly to previous constructions, our mechanism uses polynomially many value and demand queries, and in fact provides the same approximation ratio for the larger class of XOS (a.k.a. fractionally subadditive) valuations. We also develop a computationally efficient implementation of the mechanism for combinatorial auctions with budget additive bidders. Although in general computing a demand query is NP-hard for budget additive valuations, we observe that the specific form of demand queries that our mechanism uses can be efficiently computed when bidders are budget additive.
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Almost) Efficient Mechanisms for Bilateral Trading

2016-04-17
Liad Blumrosen , Shahar Dobzinski
We study the bilateral trade problem: one seller, one buyer and a single, indivisible item for sale. It is well known that there is no fully-efficient and incentive compatible mechanism … We study the bilateral trade problem: one seller, one buyer and a single, indivisible item for sale. It is well known that there is no fully-efficient and incentive compatible mechanism for this problem that maintains a balanced budget. We design simple and robust mechanisms that obtain approximate efficiency with these properties. We show that even minimal use of statistical data can yield good approximation results. Finally, we demonstrate how a mechanism for this simple bilateral-trade problem can be used as a black-box for constructing mechanisms in more general environments.

SBBA: A Strongly-Budget-Balanced Double-Auction Mechanism

2016-01-01
Erel Segal-Halevi , Avinatan Hassidim , Yonatan Aumann
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Approximately Efficient Two-Sided Combinatorial Auctions

2017-06-20
Riccardo Colini-Baldeschi , Paul W. Goldberg , Bart de Keijzer +3 more
We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of … We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases and sales of the items. A mechanism is given prior distributions on the agents' valuations of the items, but not the actual valuations; thus the aim is to maximise the expected social welfare over these distributions. As in previous work, we are interested in the worst-case ratio between the social welfare achieved by a truthful mechanism, and the best social welfare possible.
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Approximating Gains from Trade in Two-sided Markets via Simple Mechanisms

2017-06-20
Johannes Brustle , Yang Cai , Fa Wu +1 more
We design simple mechanisms to approximate the Gains from Trade (GFT) in two-sided markets with multiple unit-supply sellers and multiple unit-demand buyers. A classical impossibility result by Myerson and Satterthwaite … We design simple mechanisms to approximate the Gains from Trade (GFT) in two-sided markets with multiple unit-supply sellers and multiple unit-demand buyers. A classical impossibility result by Myerson and Satterthwaite showed that even with only one seller and one buyer, no Bayesian Incentive Compatible (BIC), Individually Rational (IR), and Budget-Balanced (BB) mechanism can achieve full GFT (trade whenever buyer's value is higher than the seller's cost). The same paper also proposed the ``second-best'' mechanism that maximizes the GFT subject to BIC, IR, and BB constraints, which is unfortunately rather complex for even the single-seller single-buyer case. Our mechanism is simple, BIC, IR, and BB and achieves 1/2 of the optimal GFT among all BIC, IR, and BB mechanisms. The result holds for arbitrary distributions of the buyers' and sellers' values and can accommodate any downward-closed feasibility constraints over the allocations. The analysis of our mechanism is facilitated by extending the Cai-Weinberg-Devanur duality framework to two-sided markets.
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Fixed Price Approximability of the Optimal Gain from Trade

2017-01-01
Riccardo Colini-Baldeschi , Paul W. Goldberg , Bart de Keijzer +2 more
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Reallocation mechanisms

2014-05-30
Liad Blumrosen , Shahar Dobzinski
We consider reallocation problems in settings where the initial endowment of each agent consists of a subset of the resources. The private information of the players is their value for … We consider reallocation problems in settings where the initial endowment of each agent consists of a subset of the resources. The private information of the players is their value for every possible subset of the resources. The goal is to redistribute resources among agents to maximize efficiency. Monetary transfers are allowed, but participation is voluntary.
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Prophet Inequalities for I.I.D. Random Variables from an Unknown Distribution

2019-06-17
José R. Correa , Paul Dütting , Felix Fischer +1 more
A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: given a sequence of random variables X1, ..., Xn drawn independently from … A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: given a sequence of random variables X1, ..., Xn drawn independently from a distribution F, the goal is to choose a stopping time τ so as to maximize α such that for all distributions F we have E[Xτ]≥α•E[maxt Xt]. What makes this problem challenging is that the decision whether τ=t may only depend on the values of the random variables X1, ..., Xt and on the distribution F. For a long time the best known bound for the problem had been α≥1-1/e≅0.632, but quite recently a tight bound of α≅0.745 was obtained. The case where F is unknown, such that the decision whether τ=t may depend only on the values of the random variables X1, ..., Xt, is equally well motivated but has received much less attention. A straightforward guarantee for this case of α≥1-1/e≅0.368 can be derived from the solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from~F, and show that even with o(n) samples α≥1/e. On the other hand, n samples allow for a significant improvement, while O(n2) samples are equivalent to knowledge of the distribution: specifically, with n samples α≥1-1/e≅0.632 and α≥ln(2)≅0.693, and with O(n2) samples α≥0.745-ε for any ε>0.
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Prophet Inequalities with Limited Information

2013-12-18
Pablo Azar , Robert Kleinberg , S. Matthew Weinberg
Previous chapter Next chapter Full AccessProceedings Proceedings of the 2014 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Prophet Inequalities with Limited InformationPablo D. Azar, Robert Kleinberg, and S. Matthew WeinbergPablo D. … Previous chapter Next chapter Full AccessProceedings Proceedings of the 2014 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Prophet Inequalities with Limited InformationPablo D. Azar, Robert Kleinberg, and S. Matthew WeinbergPablo D. Azar, Robert Kleinberg, and S. Matthew Weinbergpp.1358 - 1377Chapter DOI:https://doi.org/10.1137/1.9781611973402.100PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract In the classical prophet inequality, a gambler observes a sequence of stochastic rewards V1, …, Vn and must decide, for each reward Vi, whether to keep it and stop the game or to forfeit the reward forever and reveal the next value Vi. The gambler's goal is to obtain a constant fraction of the expected reward that the optimal offline algorithm would get. Recently, prophet inequalities have been generalized to settings where the gambler can choose k items, and, more generally, where he can choose any independent set in a matroid. However, all the existing algorithms require the gambler to know the distribution from which the rewards V1, …, Vn are drawn. The assumption that the gambler knows the distribution from which V1, …, Vn are drawn is very strong. Instead, we work with the much simpler assumption that the gambler only knows a few samples from this distribution. We construct the first single-sample prophet inequalities for many settings of interest, whose guarantees all match the best possible asymptotically, even with full knowledge of the distribution. Specifically, we provide a novel single-sample algorithm when the gambler can choose any k elements whose analysis is based on random walks with limited correlation. In addition, we provide a black-box method for converting specific types of solutions to the related secretary problem to single-sample prophet inequalities, and apply it to several existing algorithms. Finally, we provide a constant-sample prophet inequality for constant-degree bipartite matchings. In addition, we apply these results to design the first posted-price and multi-dimensional auction mechanisms with limited information in settings with asymmetric bidders. Connections between prophet inequalities and posted-price mechanisms are already known, but applying the existing framework requires knowledge of the underlying distributions, as well as the so-called "virtual values" even when the underlying prophet inequalities do not. We therefore provide an extension of this framework that bypasses virtual values altogether, allowing our mechanisms to take full advantage of the limited information required by our new prophet inequalities. Previous chapter Next chapter RelatedDetails Published:2014ISBN:978-1-61197-338-9eISBN:978-1-61197-340-2 https://doi.org/10.1137/1.9781611973402Book Series Name:ProceedingsBook Code:PRDA14Book Pages:viii + 1885
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Improved Truthful Mechanisms for Combinatorial Auctions with Submodular Bidders

2019-11-01
Sepehr Assadi , Sahil Singla
A longstanding open problem in Algorithmic Mechanism Design is to design computationally-efficient truthful mechanisms for (approximately) maximizing welfare in combinatorial auctions with submodular bidders. The first such mechanism was obtained … A longstanding open problem in Algorithmic Mechanism Design is to design computationally-efficient truthful mechanisms for (approximately) maximizing welfare in combinatorial auctions with submodular bidders. The first such mechanism was obtained by Dobzinski, Nisan, and Schapira [STOC'06] who gave an O(log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> m)-approximation where m is number of items. This problem has been studied extensively since, culminating in an O(√log m)-approximation mechanism by Dobzinski [STOC'16]. We present a computationally-efficient truthful mechanism with approximation ratio that improves upon the state-of-the-art by an exponential factor. In particular, our mechanism achieves an O((log log m) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> )-approximation in expectation, uses only O(n) demand queries, and has universal truthfulness whether Θ(√log m) is the best approximation ratio in this guarantee. This settles an open question of Dobzinski on setting in negative.
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Optimal Single-Choice Prophet Inequalities from Samples

2019-11-18
Aviad Rubinstein , Jack Z. Wang , S. Matthew Weinberg
We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of $1/2$ can be achieved with a single … We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of $1/2$ can be achieved with a single sample from each distribution. When the distributions are identical, we show that for any constant $\varepsilon > 0$, $O(n)$ samples from the distribution suffice to achieve the optimal competitive ratio ($\approx 0.745$) within $(1+\varepsilon)$, resolving an open problem of Correa, Dutting, Fischer, and Schewior.

The two-sided game of googol and sample-based prophet inequalities

2020-01-05
José R. Correa , Andrés Cristi , Boris Epstein +1 more
The secretary problem or the game of Googol are classic models for online selection problems that have received significant attention in the last five decades. In this paper we consider … The secretary problem or the game of Googol are classic models for online selection problems that have received significant attention in the last five decades. In this paper we consider a variant of the problem and explore its connections to data-driven online selection. Specifically, we are given n cards with arbitrary nonnegative numbers written on both sides. The cards are randomly placed on n consecutive positions on a table, and for each card, the visible side is also selected at random. The player sees the visible side of all cards and wants to select the card with the maximum hidden value. To this end, the player flips the first card, sees its hidden value and decides whether to pick it or drop it and continue with the next card. We study algorithms for two natural objectives. In the first one, similar to the secretary problem, the player wants to maximize the probability of selecting the maximum hidden value. We show that this can be done with probability at least 0.45292. In the second objective, similar to the prophet inequality, the player wants to maximize the expectation of the selected hidden value. Here we show a guarantee of at least 0.63518 with respect to the expected maximum hidden value. Our algorithms result from combining three basic strategies. One is to stop whenever we see a value larger than the initial n visible numbers. The second one is to stop the first time the last flipped card's value is the largest of the currently n visible numbers in the table. And the third one is similar to the latter but to stop it additionally requires that the last flipped value is larger than the value on the other side of its card. We apply our results to the prophet secretary problem with unknown distributions, but with access to a single sample from each distribution. In particular, our guarantee improves upon 1 − 1/e for this problem, which is the currently best known guarantee and only works for the i.i.d. prophet inequality with samples.

Online Trading as a Secretary Problem

2018-01-01
Ηλίας Κουτσουπιάς , Philip Lazos
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Improved Truthful Mechanisms for Subadditive Combinatorial Auctions: Breaking the Logarithmic Barrier

2021-01-01
Sepehr Assadi , Thomas Keßelheim , Sahil Singla
We present a computationally-efficient truthful mechanism for combinatorial auctions with subadditive bidders that achieves an $O((\log\!\log{m})^3)$-approximation to the maximum welfare in expectation using $O(n)$ demand queries; here $m$ and $n$ … We present a computationally-efficient truthful mechanism for combinatorial auctions with subadditive bidders that achieves an $O((\log\!\log{m})^3)$-approximation to the maximum welfare in expectation using $O(n)$ demand queries; here $m$ and $n$ are the number of items and bidders, respectively. This breaks the longstanding logarithmic barrier for the problem dating back to the $O(\log{m}\cdot\log\!\log{m})$-approximation mechanism of Dobzinski from 2007. Along the way, we also improve and considerably simplify the state-of-the-art mechanisms for submodular bidders.
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Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets

2019-12-23
Moshe Babaioff , Kira Goldner , Yannai A. Gonczarowski
Previous chapter Next chapter Full AccessProceedings Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms (SODA)Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided MarketsMoshe Babaioff, Kira Goldner, and Yannai A. GonczarowskiMoshe … Previous chapter Next chapter Full AccessProceedings Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms (SODA)Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided MarketsMoshe Babaioff, Kira Goldner, and Yannai A. GonczarowskiMoshe Babaioff, Kira Goldner, and Yannai A. Gonczarowskipp.2452 - 2471Chapter DOI:https://doi.org/10.1137/1.9781611975994.150PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract We consider the problem of welfare (and gains-from-trade) maximization in two-sided markets using simple mechanisms that are prior-independent. The seminal impossibility result of Myerson and Satterthwaite [1983] shows that even for bilateral trade, there is no feasible (individually rational, truthful, and 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 even worse, it is known to be extremely complex, eluding a precise description. In this paper we present Bulow-Klemperer-style results to circumvent these hurdles in double-auction market settings. We suggest using the Buyer Trade Reduction (BTR) mechanism, a variant of McAfee's mechanism, which is feasible and simple (in particular, it is deterministic, truthful, prior-independent, and anonymous). First, in the setting in which the values of the buyers and of the sellers are sampled independently and identically 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-yet-infeasible VCG mechanism in the original market. We then move to a more general setting in which the values of the buyers are sampled from one distribution, and those of the sellers from another, focusing on the case where the buyers' distribution first-order stochastically dominates the sellers' distribution. We present both upper bounds and lower bounds on the number of buyers that, when added, guarantees that BTR in the augmented market achieve 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 positive and negative 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 (and more precisely, for gains-from-trade approximation) in two-sided markets under the above two settings, which to the best of our knowledge are the first sampling results in this context. Previous chapter Next chapter RelatedDetails Published:2020eISBN:978-1-61197-599-4 https://doi.org/10.1137/1.9781611975994Book Series Name:ProceedingsBook Code:PRDA20Book Pages:xxii + 3011
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An Optimal Truthful Mechanism for the Online Weighted Bipartite Matching Problem

2019-01-01
Rebecca Reiffenhäuser
In the weighted bipartite matching problem, the goal is to find a maximum-weight matching in a bipartite graph with nonnegative edge weights. We consider its online version where the first … In the weighted bipartite matching problem, the goal is to find a maximum-weight matching in a bipartite graph with nonnegative edge weights. We consider its online version where the first vertex set is known beforehand, but vertices of the second set appear one after another. Vertices of the first set are interpreted as items, and those of the second set as bidders. On arrival, each bidder vertex reveals the weights of all adjacent edges and the algorithm has to decide which of those to add to the matching. We introduce an optimal, e-competitive truthful mechanism under the assumption that bidders arrive in random order (secretary model).It has been shown that the upper and lower bound of e for the original secretary problem extends to various other problems even with rich combinatorial structure, one of them being weighted bipartite matching. But truthful mechanisms so far fall short of reasonable competitive ratios once respective algorithms deviate from the original, simple threshold form. The best known mechanism for weighted bipartite matching by Krysta and Vöcking [19] offers only a ratio logarithmic in the number of online vertices. We close this gap, showing that truthfulness does not impose any additional bounds. The proof technique is new in this surrounding, and based on the observation of an independency inherent to the mechanism. The insights provided hereby are interesting in their own right and appear to offer promising tools for other problems, with or without truthfulness.
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The Two-Sided Game of Googol and Sample-Based Prophet Inequalities

2019-12-23
José R. Correa , Andrés Cristi , Boris Epstein +1 more
Previous chapter Next chapter Full AccessProceedings Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms (SODA)The Two-Sided Game of Googol and Sample-Based Prophet InequalitiesJosé R. Correa, Andrés Cristi, Boris Epstein, … Previous chapter Next chapter Full AccessProceedings Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms (SODA)The Two-Sided Game of Googol and Sample-Based Prophet InequalitiesJosé R. Correa, Andrés Cristi, Boris Epstein, and José A. SotoJosé R. Correa, Andrés Cristi, Boris Epstein, and José A. Sotopp.2066 - 2081Chapter DOI:https://doi.org/10.1137/1.9781611975994.127PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract The secretary problem or the game of Googol are classic models for online selection problems that have received significant attention in the last five decades. In this paper we consider a variant of the problem and explore its connections to data-driven online selection. Specifically, we are given n cards with arbitrary nonnegative numbers written on both sides. The cards are randomly placed on n consecutive positions on a table, and for each card, the visible side is also selected at random. The player sees the visible side of all cards and wants to select the card with the maximum hidden value. To this end, the player flips the first card, sees its hidden value and decides whether to pick it or drop it and continue with the next card. We study algorithms for two natural objectives. In the first one, similar to the secretary problem, the player wants to maximize the probability of selecting the maximum hidden value. We show that this can be done with probability at least 0.45292. In the second objective, similar to the prophet inequality, the player wants to maximize the expectation of the selected hidden value. Here we show a guarantee of at least 0.63518 with respect to the expected maximum hidden value. Our algorithms result from combining three basic strategies. One is to stop whenever we see a value larger than the initial n visible numbers. The second one is to stop the first time the last flipped card's value is the largest of the currently n visible numbers in the table. And the third one is similar to the latter but to stop it additionally requires that the last flipped value is larger than the value on the other side of its card. We apply our results to the prophet secretary problem with unknown distributions, but with access to a single sample from each distribution. In particular, our guarantee improves upon 1 – 1/e for this problem, which is the currently best known guarantee and only works for the i.i.d. prophet inequality with samples. Previous chapter Next chapter RelatedDetails Published:2020eISBN:978-1-61197-599-4 https://doi.org/10.1137/1.9781611975994Book Series Name:ProceedingsBook Code:PRDA20Book Pages:xxii + 3011
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