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Opinion Formation Games with Aggregation and Negative Influence

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Algorithmic Game Theory (SAGT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10504))

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Abstract

We study continuous opinion formation games with aggregation aspects. In many domains, expressed opinions of people are not only affected by local interaction and personal beliefs, but also by influences that stem from global properties of the opinions in the society. To capture the interplay of such global and local effects, we propose a model of opinion formation games with aggregation, where we concentrate on the average public opinion as a natural way to represent a global trend in the society. While the average alone does not have good strategic properties as an aggregation rule, we show that with a reasonable influence of the average public opinion, the good properties of opinion formation models are preserved. More formally, we prove that a unique equilibrium exists in average-oriented opinion formation games. Simultaneous best-response dynamics converge to within distance \(\varepsilon \) of equilibrium in \(O(n^2 \ln (n/\varepsilon ))\) rounds, even in a model with outdated information on the average public opinion. For the Price of Anarchy, we show a small bound of \(9/8 + o(1)\), almost matching the tight bound for games without aggregation. Moreover, some of the results apply to a general class of opinion formation games with negative influences, and we extend our results to the case where expressed opinions come from a restricted domain.

This work was supported by DFG Cluster of Excellence MMCI at Saarland University. Stratis Skoulakis is supported by a scholarship from the Onassis Foundation.

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Authors and Affiliations

  1. Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, USA

    Markos Epitropou

  2. School of Electrical and Computer Engineering, NTU Athens, Zografou, Greece

    Dimitris Fotakis & Stratis Skoulakis

  3. Institut Für Informatik, Goethe-Universität Frankfurt/Main, Frankfurt, Germany

    Martin Hoefer

Authors
  1. Markos Epitropou
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  2. Dimitris Fotakis
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  3. Martin Hoefer
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  4. Stratis Skoulakis
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Correspondence to Dimitris Fotakis .

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Editors and Affiliations

  1. University of Salento, Lecce, Italy

    Vittorio Bilò

  2. University of L'Aquila, L'Aquila, Italy

    Michele Flammini

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Epitropou, M., Fotakis, D., Hoefer, M., Skoulakis, S. (2017). Opinion Formation Games with Aggregation and Negative Influence. In: Bilò, V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_14

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  • DOI: https://doi.org/10.1007/978-3-319-66700-3_14

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