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Residential segregation is a wide-spread phenomenon that can be observed inalmost every major city. In these urban areas residents with different racialor socioeconomic background tend to form homogeneous clusters. Schelling'sfamous agent-based model for residential segregation explains how such clusterscan form even if all agents are tolerant, i.e., if they agree to live in mixedneighborhoods. For segregation to occur, all it needs is a slight bias towardsagents preferring similar neighbors. Very recently, Schelling's model has beeninvestigated from a game-theoretic point of view with selfish agents thatstrategically select their residential location. In these games, agents canimprove on their current location by performing a location swap with anotheragent who is willing to swap. We significantly deepen these investigations bystudying the influence of the underlying topology modeling the residential areaon the existence of equilibria, the Price of Anarchy and on the dynamicproperties of the resulting strategic multi-agent system. Moreover, as a newconceptual contribution, we also consider the influence of locality, i.e., ifthe location swaps are restricted to swaps of neighboring agents. We giveimproved almost tight bounds on the Price of Anarchy for arbitrary underlyinggraphs and we present (almost) tight bounds for regular graphs, paths andcycles. Moreover, we give almost tight bounds for grids, which are commonlyused in empirical studies. For grids we also show that locality has a severeimpact on the game dynamics.

Topological Influence and Locality in Swap Schelling Games