Convergence and Hardness of Strategic Schelling Segregation

  • Hagen Echzell
  • Tobias Friedrich
  • Pascal LenznerEmail author
  • Louise Molitor
  • Marcus Pappik
  • Friedrich Schöne
  • Fabian Sommer
  • David Stangl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11920)


The phenomenon of residential segregation was captured by Schelling’s famous segregation model where two types of agents are placed on a grid and an agent is content with her location if the fraction of her neighbors which have the same type as her is at least \(\tau \), for some \(0<\tau <1\). Discontent agents simply swap their location with a randomly chosen other discontent agent or jump to a random empty cell.

We analyze a generalized game-theoretic model of Schelling segregation which allows more than two agent types and more general underlying graphs modeling the residential area. For this we show that both aspects heavily influence the dynamic properties and the tractability of finding an optimal placement. We map the boundary of when improving response dynamics (IRD) are guaranteed to converge and we prove several sharp threshold results where guaranteed IRD convergence suddenly turns into a strong non-convergence result: a violation of weak acyclicity. In particular, we show threshold results also for Schelling’s original model, which is in contrast to the standard assumption in many empirical papers. In case of convergence we show that IRD find equilibria quickly.


Schelling segregation Convergence of improving response dynamics Potential games Computational hardness 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Hagen Echzell
    • 1
  • Tobias Friedrich
    • 1
  • Pascal Lenzner
    • 1
    Email author
  • Louise Molitor
    • 1
  • Marcus Pappik
    • 1
  • Friedrich Schöne
    • 1
  • Fabian Sommer
    • 1
  • David Stangl
    • 1
  1. 1.Hasso Plattner InstituteUniversity of PotsdamPotsdamGermany

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