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Documents authored by Ezra, Tomer


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On the (In)approximability of Combinatorial Contracts

Authors: Tomer Ezra, Michal Feldman, and Maya Schlesinger

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
We study two recent combinatorial contract design models, which highlight different sources of complexity that may arise in contract design, where a principal delegates the execution of a costly project to others. In both settings, the principal cannot observe the choices of the agent(s), only the project’s outcome (success or failure), and incentivizes the agent(s) using a contract, a payment scheme that specifies the payment to the agent(s) upon a project’s success. We present results that resolve open problems and advance our understanding of the computational complexity of both settings. In the multi-agent setting, the project is delegated to a team of agents, where each agent chooses whether or not to exert effort. A success probability function maps any subset of agents who exert effort to a probability of the project’s success. For the family of submodular success probability functions, Dütting et al. [2023] established a poly-time constant factor approximation to the optimal contract, and left open whether this problem admits a PTAS. We answer this question on the negative, by showing that no poly-time algorithm guarantees a better than 0.7-approximation to the optimal contract. For XOS functions, they give a poly-time constant approximation with value and demand queries. We show that with value queries only, one cannot get any constant approximation. In the multi-action setting, the project is delegated to a single agent, who can take any subset of a given set of actions. Here, a success probability function maps any subset of actions to a probability of the project’s success. Dütting et al. [2021a] showed a poly-time algorithm for computing an optimal contract for gross substitutes success probability functions, and showed that the problem is NP-hard for submodular functions. We further strengthen this hardness result by showing that this problem does not admit any constant factor approximation. Furthermore, for the broader class of XOS functions, we establish the hardness of obtaining a n^{-1/2+ε}-approximation for any ε > 0.

Cite as

Tomer Ezra, Michal Feldman, and Maya Schlesinger. On the (In)approximability of Combinatorial Contracts. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 44:1-44:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{ezra_et_al:LIPIcs.ITCS.2024.44,
  author =	{Ezra, Tomer and Feldman, Michal and Schlesinger, Maya},
  title =	{{On the (In)approximability of Combinatorial Contracts}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{44:1--44:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.44},
  URN =		{urn:nbn:de:0030-drops-195724},
  doi =		{10.4230/LIPIcs.ITCS.2024.44},
  annote =	{Keywords: algorithmic contract design, combinatorial contracts, moral hazard}
}
Document
Pricing Social Goods

Authors: Alon Eden, Tomer Ezra, and Michal Feldman

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)


Abstract
Social goods are goods that grant value not only to their owners but also to the owners' surroundings, be it their families, friends or office mates. The benefit a non-owner derives from the good is affected by many factors, including the type of the good, its availability, and the social status of the non-owner. Depending on the magnitude of the benefit and on the price of the good, a potential buyer might stay away from purchasing the good, hoping to free ride on others' purchases. A revenue-maximizing seller who sells social goods must take these considerations into account when setting prices for the good. The literature on optimal pricing has advanced considerably over the last decade, but little is known about optimal pricing schemes for selling social goods. In this paper, we conduct a systematic study of revenue-maximizing pricing schemes for social goods: we introduce a Bayesian model for this scenario, and devise nearly-optimal pricing schemes for various types of externalities, both for simultaneous sales and for sequential sales.

Cite as

Alon Eden, Tomer Ezra, and Michal Feldman. Pricing Social Goods. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{eden_et_al:LIPIcs.ESA.2017.35,
  author =	{Eden, Alon and Ezra, Tomer and Feldman, Michal},
  title =	{{Pricing Social Goods}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{35:1--35:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.35},
  URN =		{urn:nbn:de:0030-drops-78717},
  doi =		{10.4230/LIPIcs.ESA.2017.35},
  annote =	{Keywords: Public Goods, Posted Prices, Revenue Maximization, Externalities}
}
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