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Hedonic Diversity Games Revisited

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Algorithmic Decision Theory (ADT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13023))

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Abstract

A hedonic diversity game (HDG) is a coalition formation problem, where the set of agents is partitioned into two types of agents (say red and blue agents), and each agent has preferences over the relative number (fraction) of agents of her own type in her coalition. In a dichotomous hedonic diversity game (DHDG) each agent partitions the set of possible fractions into a set of approved and a set of disapproved fractions. The solution concepts for these games considered in the literature so far are concerned with stability notions such as core and Nash stability. We add to the existing literature by providing NP-completeness results for the decision problems whether a DHDG admits (i) a Nash stable outcome and (ii) a strictly core stable outcome respectively, in restricted settings with only two (and three, respectively) approved fractions per agent. In addition, applying approval and Borda scores from voting theory we aim at outcomes that maximize social welfare (i.e., the sum of scores) in (dichotomous) hedonic diversity games. In that context we provide an NP-completeness result for HDGs under the use of Borda scores. For DHDGs with approval scores, we draw the sharp separation line between polynomially solvable and NP-complete cases with respect to the number of approved fractions per agent.

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Notes

  1. 1.

    Also known as two-dimensional knapsack problem (the latter notion, however, often refers to the geometric variant of that problem).

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Acknowledgments

The author would like to thank Edith Elkind for useful discussion and is grateful for the valuable comments provided by the reviewers.

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Authors and Affiliations

  1. Department of Operations and Information Systems, University of Graz, Graz, Austria

    Andreas Darmann

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  1. Andreas Darmann
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Correspondence to Andreas Darmann .

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Editors and Affiliations

  1. National Technical University of Athens, Athens, Greece

    Dimitris Fotakis

  2. Consejo Superior de Investigaciones Cientificas, Madrid, Madrid, Spain

    David Ríos Insua

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Darmann, A. (2021). Hedonic Diversity Games Revisited. In: Fotakis, D., Ríos Insua, D. (eds) Algorithmic Decision Theory. ADT 2021. Lecture Notes in Computer Science(), vol 13023. Springer, Cham. https://doi.org/10.1007/978-3-030-87756-9_23

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  • DOI: https://doi.org/10.1007/978-3-030-87756-9_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-87755-2

  • Online ISBN: 978-3-030-87756-9

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