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Combinatorial game associated to the one dimensional Schelling’s model of social segregation

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Abstract

In this paper we consider a finite one-dimensional lattice with \(N = 2n + 1\) sites such that one of them is empty and the others have a black or white token. There are two players (one for each color), such that step by step alternately they move one of their tokens to the empty site trying to obtain a connected configuration. This game is related with the Schelling’s social segregation model, where colors represent two different populations such that each one tries to take up a position with more neighbors as itself (same color). In this work we study strategies to play the game as well as their relation with the associated Schelling’s one-dimensional case (line and cycle graphs).

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References

  • Berlekamp ER, Conway JH, Guy RK (1982) The winning games for your mathematical plays. Academic Press, Cambridge

    MATH  Google Scholar 

  • Castellano C, Fortunato S, Loreto V (2009) Statistical physics for social dynamics. Rev Mod Phys 81:591

    Article  Google Scholar 

  • Clark WAV, Fossett M (2008) Understanding the social context of the Schelling segregation model. PNAS 105:4109–4114

    Article  Google Scholar 

  • Epstein JM, Axtell RL (1996) Growing artificial societies: social science from the bottom up. MIT Press, Cambridge

    Google Scholar 

  • Goles N, Goles E, Rica S (2011) Dynamics and complexity of the Schelling segregation model. Phys Rev E 83:1–13

    Google Scholar 

  • Hatna E, Berenson J (2012) The Schelling model of ethnic residential dynamics beyond the integrated-segregated dichotomy of patterns. J Artif Soc Soc Simul 15:6

    Article  Google Scholar 

  • Hegselmann R, Flache A (1998) Understanding complex social dynamics: a plea for cellular automata based modelling. J Artif Soc Soc Simul 1(3). http://jasss.soc.surrey.ac.uk/1/3/1/1.pdf

  • Pancs R, Vriend NJ (2007) spatial proximity model of segregation revisited. J Public Econ 91:1–24

    Article  Google Scholar 

  • Sandholm WH (2010) Population games and evolutionary dynamics. MIT Press, Cambridge

    MATH  Google Scholar 

  • Schelling TC (1969) Models of segregation. Am Econ Rev 59:488–493

    Google Scholar 

  • Schelling TC (1971) Dynamics of segregation. J Math Sociol 1:1–143

    Article  Google Scholar 

  • Schelling TC (2006) Micromotives and macrobehavior. Norton, New York

    Google Scholar 

  • Vinkovic D, Kirman A (2006) A physical analogue of the Schelling model. PNAS 103:19261–19265

    Article  Google Scholar 

Download references

Acknowledgements

Acknowledgment to the Fondecyt Grant 1140090 (EG), MillenniumNS130017 (EG) and to the CMM-Basal (EG and LG).

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Authors and Affiliations

  1. Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibañez, Diagonal Las Torres 2640, Peñalolén, Santiago, Chile

    Eric Goles & Luis Gómez

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  1. Eric Goles
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  2. Luis Gómez
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Correspondence to Eric Goles.

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Goles, E., Gómez, L. Combinatorial game associated to the one dimensional Schelling’s model of social segregation. Nat Comput 17, 427–436 (2018). https://doi.org/10.1007/s11047-017-9622-5

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  • DOI: https://doi.org/10.1007/s11047-017-9622-5

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