4 Search Results for "Dobzinski, Shahar"

Document
DOI: 10.4230/LIPIcs.ITCS.2023.44
Rigidity in Mechanism Design and Its Applications

Authors: Shahar Dobzinski and Ariel Shaulker

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We introduce the notion of rigidity in auction design and use it to analyze some fundamental aspects of mechanism design. We focus on the setting of a single-item auction where the values of the bidders are drawn from some (possibly correlated) distribution F. Let f be the allocation function of an optimal mechanism for F. Informally, S is (linearly) rigid in F if for every mechanism M' with an allocation function f' where f and f' agree on the allocation of at most x-fraction of the instances of S, it holds that the expected revenue of M' is at most an x fraction of the optimal revenue. We start with using rigidity to explain the singular success of Cremer and McLean’s auction assuming interim individual rationality. Recall that the revenue of Cremer and McLean’s auction is the optimal welfare if the distribution obeys a certain "full rank" conditions, but no analogous constructions are known if this condition does not hold. We show that the allocation function of the Cremer and McLean auction has logarithmic (in the size of the support) Kolmogorov complexity, whereas we use rigidity to show that there exist distributions that do not obey the full rank condition for which the allocation function of every mechanism that provides a constant approximation is almost linear. We further investigate rigidity assuming different notions of individual rationality. Assuming ex-post individual rationality, if there exists a rigid set then the structure of the optimal mechanism is relatively simple: the player with the highest value "usually" wins the item and contributes most of the revenue. In contrast, assuming interim individual rationality, there are distributions with a rigid set S where the optimal mechanism has no obvious allocation pattern (in the sense that its Kolmogorov complexity is high). Since the existence of rigid sets essentially implies that the hands of the designer are tied, our results help explain why we have little hope of developing good, simple and generic approximation mechanisms in the interim individual rationality world.
Cite as

Shahar Dobzinski and Ariel Shaulker. Rigidity in Mechanism Design and Its Applications. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 44:1-44:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dobzinski_et_al:LIPIcs.ITCS.2023.44,
  author =	{Dobzinski, Shahar and Shaulker, Ariel},
  title =	{{Rigidity in Mechanism Design and Its Applications}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{44:1--44:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.44},
  URN =		{urn:nbn:de:0030-drops-175479},
  doi =		{10.4230/LIPIcs.ITCS.2023.44},
  annote =	{Keywords: Revenue Maximization, Auctions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.55
Mechanism Design with Moral Bidders

Authors: Shahar Dobzinski and Sigal Oren

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
A rapidly growing literature on lying in behavioral economics and psychology shows that individuals often do not lie even when lying maximizes their utility. In this work, we attempt to incorporate these findings into the theory of mechanism design. We consider players that have a preference for truth-telling and will only lie if their benefit from lying is sufficiently larger than the loss of the others. To accommodate such players, we introduce α-moral mechanisms, in which the gain of a player from misreporting his true value, comparing to truth-telling, is at most α times the loss that the others incur due to misreporting. Note that a 0-moral mechanism is a truthful mechanism. We develop a theory of moral mechanisms in the canonical setting of single-item auctions within the "reasonable" range of α, 0 ≤ α ≤ 1. We identify similarities and disparities to the standard theory of truthful mechanisms. In particular, we show that the allocation function does not uniquely determine the payments and is unlikely to admit a simple characterization. In contrast, recall that monotonicity characterizes the allocation function of truthful mechanisms. Our main technical effort is invested in determining whether the auctioneer can exploit the preference for truth-telling of the players to extract more revenue comparing to truthful mechanisms. We show that the auctioneer can indeed extract more revenue when the values of the players are correlated, even when there are only two players. However, we show that truthful mechanisms are revenue-maximizing even among moral ones when the values of the players are independently drawn from certain identical distributions (e.g., the uniform and exponential distributions). A by-product of our proof that optimal moral mechanisms are truthful is an alternative proof to Myerson’s optimal truthful mechanism characterization in the settings that we consider. We flesh out this approach by providing an alternative proof that does not involve moral mechanisms to Myerson’s characterization of optimal truthful mechanisms to all settings in which the values are independently drawn from regular distributions (not necessarily identical).
Cite as

Shahar Dobzinski and Sigal Oren. Mechanism Design with Moral Bidders. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dobzinski_et_al:LIPIcs.ITCS.2022.55,
  author =	{Dobzinski, Shahar and Oren, Sigal},
  title =	{{Mechanism Design with Moral Bidders}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{55:1--55:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.55},
  URN =		{urn:nbn:de:0030-drops-156513},
  doi =		{10.4230/LIPIcs.ITCS.2022.55},
  annote =	{Keywords: Mechanism Design, Cognitive Biases, Revenue Maximization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.92
On Fairness and Stability in Two-Sided Matchings

Authors: Gili Karni, Guy N. Rothblum, and Gal Yona

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
There are growing concerns that algorithms, which increasingly make or influence important decisions pertaining to individuals, might produce outcomes that discriminate against protected groups. We study such fairness concerns in the context of a two-sided market, where there are two sets of agents, and each agent has preferences over the other set. The goal is producing a matching between the sets. Throughout this work, we use the example of matching medical residents (who we call "doctors") to hospitals. This setting has been the focus of a rich body of work. The seminal work of Gale and Shapley formulated a stability desideratum, and showed that a stable matching always exists and can be found in polynomial time. With fairness concerns in mind, it is natural to ask: might a stable matching be discriminatory towards some of the doctors? How can we obtain a fair matching? The question is interesting both when hospital preferences might be discriminatory, and also when each hospital’s preferences are fair. We study this question through the lens of metric-based fairness notions (Dwork et al. [ITCS 2012] and Kim et al. [ITCS 2020]). We formulate appropriate definitions of fairness and stability in the presence of a similarity metric, and ask: does a fair and stable matching always exist? Can such a matching be found in polynomial time? Can classical Gale-Shapley algorithms find such a matching? Our contributions are as follows: - Composition failures for classical algorithms. We show that composing the Gale-Shapley algorithm with fair hospital preferences can produce blatantly unfair outcomes. - New algorithms for finding fair and stable matchings. Our main technical contributions are efficient new algorithms for finding fair and stable matchings when: (i) the hospitals' preferences are fair, and (ii) the fairness metric satisfies a strong "proto-metric" condition: the distance between every two doctors is either zero or one. In particular, these algorithms also show that, in this setting, fairness and stability are compatible. - Barriers for finding fair and stable matchings in the general case. We show that if the hospital preferences can be unfair, or if the metric fails to satisfy the proto-metric condition, then no algorithm in a natural class can find a fair and stable matching. The natural class includes the classical Gale-Shapley algorithms and our new algorithms.
Cite as

Gili Karni, Guy N. Rothblum, and Gal Yona. On Fairness and Stability in Two-Sided Matchings. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 92:1-92:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{karni_et_al:LIPIcs.ITCS.2022.92,
  author =	{Karni, Gili and Rothblum, Guy N. and Yona, Gal},
  title =	{{On Fairness and Stability in Two-Sided Matchings}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{92:1--92:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.92},
  URN =		{urn:nbn:de:0030-drops-156880},
  doi =		{10.4230/LIPIcs.ITCS.2022.92},
  annote =	{Keywords: algorithmic fairness}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.61
Implementation in Advised Strategies: Welfare Guarantees from Posted-Price Mechanisms When Demand Queries Are NP-Hard

Authors: Linda Cai, Clay Thomas, and S. Matthew Weinberg

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
State-of-the-art posted-price mechanisms for submodular bidders with m items achieve approximation guarantees of O((log log m)^3) [Sepehr Assadi and Sahil Singla, 2019]. Their truthfulness, however, requires bidders to compute an NP-hard demand-query. Some computational complexity of this form is unavoidable, as it is NP-hard for truthful mechanisms to guarantee even an m^(1/2-ε)-approximation for any ε > 0 [Shahar Dobzinski and Jan Vondrák, 2016]. Together, these establish a stark distinction between computationally-efficient and communication-efficient truthful mechanisms. We show that this distinction disappears with a mild relaxation of truthfulness, which we term implementation in advised strategies. Specifically, advice maps a tentative strategy either to that same strategy itself, or one that dominates it. We say that a player follows advice as long as they never play actions which are dominated by advice. A poly-time mechanism guarantees an α-approximation in implementation in advised strategies if there exists advice (which runs in poly-time) for each player such that an α-approximation is achieved whenever all players follow advice. Using an appropriate bicriterion notion of approximate demand queries (which can be computed in poly-time), we establish that (a slight modification of) the [Sepehr Assadi and Sahil Singla, 2019] mechanism achieves the same O((log log m)^3)-approximation in implementation in advised strategies.
Cite as

Linda Cai, Clay Thomas, and S. Matthew Weinberg. Implementation in Advised Strategies: Welfare Guarantees from Posted-Price Mechanisms When Demand Queries Are NP-Hard. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 61:1-61:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cai_et_al:LIPIcs.ITCS.2020.61,
  author =	{Cai, Linda and Thomas, Clay and Weinberg, S. Matthew},
  title =	{{Implementation in Advised Strategies: Welfare Guarantees from Posted-Price Mechanisms When Demand Queries Are NP-Hard}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{61:1--61:32},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.61},
  URN =		{urn:nbn:de:0030-drops-117464},
  doi =		{10.4230/LIPIcs.ITCS.2020.61},
  annote =	{Keywords: Combinatorial auctions, Posted-Price mechanisms, Submodular valuations, Incentive compatible}
}
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