Topological influence and locality in swap schelling games

Abstract

Residential segregation is a wide-spread phenomenon that can be observed in almost every major city. In these urban areas residents with different racial or socioeconomic background tend to form homogeneous clusters. Schelling’s famous agent-based model for residential segregation explains how such clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slight bias towards agents preferring similar neighbors. Very recently, Schelling’s model has been investigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight bounds on the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, which are commonly used in empirical studies. For grids we also show that locality has a severe impact on the game dynamics.

Schelling games on graphs

“…Later, in eorem 5.11), we will show that the bound holds even in the presence of stubborn agents. We should note that a er the conference version of our paper, Bilò et al [2020] improved the bound to 3 for the fully-strategic case. eorem 5.8. e social price of anarchy of fully-strategic balanced 2-swap games with at least two agents per type and connected topology is between 667/324 ≈ 2.…”

“…A similar se ing with agents that derive linear utility both from their location as well as their nearby friends, was recently studied by Elkind et al [2020b]. Bilò et al [2020] examined the in uence of the topology and locality on the existence of equilibria and the price of anarchy in swap games. Chan et al [2020] introduced an alternative model wherein multiple agents can occupy the same location and, similarly to our social Schelling games (Section 7.1), there is a friendship network.…”

Welfare Guarantees in Schelling Segregation

“…For this setting, the authors showed results similar to those of Elkind et al (2019). Bilò et al (2020) improved some of the price of anarchy bounds of Agarwal et al (2020), and also studied a variation of the model in which the agents have a restricted view of the topology and can only swap with their neighbors. Finally, Kanellopoulos, Kyropoulou, and Voudouris (2020) investigated the price of anarchy and stability in jump Schelling games, but with a slightly different utility function according to which an agent considers herself as part of her set of neighbors.…”

“…Most related to our present work are the papers (Elkind et al 2019;Agarwal et al 2020;Bilò et al 2020;Kanellopoulos, Kyropoulou, and Voudouris 2020), which studied game-theoretic and complexity questions related to the social welfare in Schelling games. In particular, Elkind et al ( 2019) considered jump Schelling games in which there are k ≥ 2 types of agents, and the topology is a graph with more nodes than agents so that there are empty nodes to which unhappy agents can jump.…”

“…Given that the agents are willing to relocate to be close to other agents of the same type, another natural question is whether the resulting assignments satisfy some sort of efficiency. This has been considered in part by a recent array of papers (Chauhan, Lenzner, and Molitor 2018;Echzell et al 2019;Elkind et al 2019;Agarwal et al 2020;Bilò et al 2020;Chan, Irfan, and Than 2020;Kanellopoulos, Kyropoulou, and Voudouris 2020), which have studied Schelling's model from a game-theoretic perspective. In particular, instead of randomly relocating, the agents are assumed to be strategic and each of them aims to select a location that maximizes her utility, defined as the fraction of same-type agents in her neighborhood.…”