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DOI: 10.4230/LIPIcs.MFCS.2022.60

Not All Strangers Are the Same: The Impact of Tolerance in Schelling Games

Authors: Panagiotis Kanellopoulos, Maria Kyropoulou, and Alexandros A. Voudouris

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract

Schelling’s famous model of segregation assumes agents of different types, who would like to be located in neighborhoods having at least a certain fraction of agents of the same type. We consider natural generalizations that allow for the possibility of agents being tolerant towards other agents, even if they are not of the same type. In particular, we consider an ordering of the types, and make the realistic assumption that the agents are in principle more tolerant towards agents of types that are closer to their own according to the ordering. Based on this, we study the strategic games induced when the agents aim to maximize their utility, for a variety of tolerance levels. We provide a collection of results about the existence of equilibria, and their quality in terms of social welfare.

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Panagiotis Kanellopoulos, Maria Kyropoulou, and Alexandros A. Voudouris. Not All Strangers Are the Same: The Impact of Tolerance in Schelling Games. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 60:1-60:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kanellopoulos_et_al:LIPIcs.MFCS.2022.60,
  author =	{Kanellopoulos, Panagiotis and Kyropoulou, Maria and Voudouris, Alexandros A.},
  title =	{{Not All Strangers Are the Same: The Impact of Tolerance in Schelling Games}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{60:1--60:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.60},
  URN =		{urn:nbn:de:0030-drops-168589},
  doi =		{10.4230/LIPIcs.MFCS.2022.60},
  annote =	{Keywords: Schelling games, Equilibria, Price of anarchy, Price of stability}
}

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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2020.71

Obviously Strategyproof Single-Minded Combinatorial Auctions

Authors: Bart de Keijzer, Maria Kyropoulou, and Carmine Ventre

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract

We consider the setting of combinatorial auctions when the agents are single-minded and have no contingent reasoning skills. We are interested in mechanisms that provide the right incentives to these imperfectly rational agents, and therefore focus our attention to obviously strategyproof (OSP) mechanisms. These mechanisms require that at each point during the execution where an agent is queried to communicate information, it should be "obvious" for the agent what strategy to adopt in order to maximise her utility. In this paper we study the potential of OSP mechanisms with respect to the approximability of the optimal social welfare. We consider two cases depending on whether the desired bundles of the agents are known or unknown to the mechanism. For the case of known-bundle single-minded agents we show that OSP can actually be as powerful as (plain) strategyproofness (SP). In particular, we show that we can implement the very same algorithm used for SP to achieve a √m-approximation of the optimal social welfare with an OSP mechanism, m being the total number of items. Restricting our attention to declaration domains with two values, we provide a 2-approximate OSP mechanism, and prove that this approximation bound is tight. We also present a randomised mechanism that is universally OSP and achieves a finite approximation of the optimal social welfare for the case of arbitrary size finite domains. This mechanism also provides a bounded approximation ratio when the valuations lie in a bounded interval (even if the declaration domain is infinitely large). For the case of unknown-bundle single-minded agents, we show how we can achieve an approximation ratio equal to the size of the largest desired set, in an OSP way. We remark this is the first known application of OSP to multi-dimensional settings, i.e., settings where agents have to declare more than one parameter. Our results paint a rather positive picture regarding the power of OSP mechanisms in this context, particularly for known-bundle single-minded agents. All our results are constructive, and even though some known strategyproof algorithms are used, implementing them in an OSP way is a non-trivial task.

Cite as

Bart de Keijzer, Maria Kyropoulou, and Carmine Ventre. Obviously Strategyproof Single-Minded Combinatorial Auctions. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 71:1-71:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dekeijzer_et_al:LIPIcs.ICALP.2020.71,
  author =	{de Keijzer, Bart and Kyropoulou, Maria and Ventre, Carmine},
  title =	{{Obviously Strategyproof Single-Minded Combinatorial Auctions}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{71:1--71:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.71},
  URN =		{urn:nbn:de:0030-drops-124781},
  doi =		{10.4230/LIPIcs.ICALP.2020.71},
  annote =	{Keywords: OSP Mechanisms, Extensive-form Mechanisms, Single-minded Combinatorial Auctions, Greedy algorithms}
}

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Not All Strangers Are the Same: The Impact of Tolerance in Schelling Games

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Obviously Strategyproof Single-Minded Combinatorial Auctions

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