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Stochastic Stability in Schelling’s Segregation Model with Markovian Asynchronous Update

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Cellular Automata (ACRI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11115))

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Abstract

We investigate the dependence of steady-state properties of Schelling’s segregation model on the agents’ activation order. Our basic formalism is the Pollicott-Weiss version of Schelling’s segregation model. Our main result modifies this baseline scenario by incorporating contagion in the decision to move: (pairs of) agents are connected by a second, agent influence network. Pair activation is specified by a random walk on this network.

The considered schedulers choose the next pair nonadaptively. We can complement this result by an example of adaptive scheduler (even one that is quite fair) that is able to preclude maximal segregation. Thus scheduler nonadaptiveness seems to be required for the validity of the original result under arbitrary asynchronous scheduling. The analysis (and our result) are part of an adversarial scheduling approach we are advocating to evolutionary games and social simulations.

This work was supported by a grant of the Ministry of Research and Innovation, CNCS - UEFISCDI, project number PN-III-P4-ID-PCE-2016-0842, within PNCDI III.

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Notes

  1. 1.

    This translates, intuitively, to the following condition: we always give the participants in a swap the chance to immediately reevaluate their last move.

  2. 2.

    This is where we use a property specific to our model of Schelling segregation, as opposed to proving a result valid for general potential game: the property that we employ is that in Schelling’s model any move m “can be undone”. This means that there is a move n using the same pair of vertices as m that brings the system back to where it was before. Move n simply “swaps back” the two agents if they were swapped by m, and leaves them in place otherwise.

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Authors and Affiliations

  1. Department of Computer Science, West University of Timişoara, Bd. V. Pârvan 4, Timişoara, Romania

    Gabriel Istrate

  2. e-Austria Research Institute, Bd. V. Pârvan 4, cam. 045 B, Timişoara, Romania

    Gabriel Istrate

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  1. Gabriel Istrate
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Correspondence to Gabriel Istrate .

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Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Giancarlo Mauri

  2. University of Perpignan, Perpignan, France

    Samira El Yacoubi

  3. University of Milano-Bicocca, Milan, Italy

    Alberto Dennunzio

  4. University of Tokyo, Tokyo, Japan

    Katsuhiro Nishinari

  5. University of Milano-Bicocca, Milan, Italy

    Luca Manzoni

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Istrate, G. (2018). Stochastic Stability in Schelling’s Segregation Model with Markovian Asynchronous Update. In: Mauri, G., El Yacoubi, S., Dennunzio, A., Nishinari, K., Manzoni, L. (eds) Cellular Automata. ACRI 2018. Lecture Notes in Computer Science(), vol 11115. Springer, Cham. https://doi.org/10.1007/978-3-319-99813-8_38

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  • DOI: https://doi.org/10.1007/978-3-319-99813-8_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99812-1

  • Online ISBN: 978-3-319-99813-8

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