Schelling games on graphs

Agarwal, Aishwarya; Elkind, Edith; Gan, Jiarui; Igarashi, Ayumi; Suksompong, Warut; Voudouris, Alexandros A.

doi:10.1016/j.artint.2021.103576

Cited by 15 publications

(40 citation statements)

References 32 publications

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“…Moreover, for Λ = 1 2 swap equilibria exist on the broad class of graphs that admit an independent set that is large enough to accommodate the minority type agents. In particular, this implies equilibrium existence and efficient computability on bipartite graphs, including trees, which is in contrast to the non-existence results by Agarwal et al [2021].…”

Section: Our Contributionmentioning

confidence: 79%

“…On general graphs we prove an tight bound on the PoA that depends on b, the number of agents of the minority color, and we give a bound of ∆(G) on all graphs G, that is asymptotically tight even on δ-regular graphs. Also for the PoS we get stronger positive results compared to [Agarwal et al, 2021].…”

Section: Our Contributionmentioning

confidence: 80%

“…Our main findings shed light on the existence of equilibrium states and their quality in terms of the recently defined degree of integration [Agarwal et al, 2021] that measures the number of agents that live in a heterogeneous neighborhood. Model We consider a strategic game played on a given underlying connected graph G = (V, E), with |V | = n and |E| = m. For any node v ∈ V , let the closed neighborhood of v in G be N [v] = {v} ∪ {u ∈ V : {v, u} ∈ E} where δ(v) = |N [v]| − 1 denotes the degree of v, and δ(G) and ∆(G) denote the minimum and the maximum degree over all nodes in G, respectively.…”

Section: Introductionmentioning

confidence: 90%

“…Later, Echzell et al [2019] significantly extended these results and generalized them to games with more than two agent types. Agarwal et al [2021] introduce a simplified model without individual node preferences and with τ = 1. They prove results on the existence of equilibria, in particular that equilbria are not guaranteed to exist on trees, and on the complexity of deciding equilibrium existence.…”

Section: Related Workmentioning

confidence: 99%

“…But only in the last decade progress has been made to understand the involved random process from a theoretical point of view. Even more recently, the Algorithmic Game Theory and the AI communities became interested in residential segregation and game-theoretic variants of Schelling's model were studied [Chauhan et al, 2018;Echzell et al, 2019;Bilò et al, 2020;Agarwal et al, 2021; Kanellopoulos et al, 2021a;Bullinger et al, 2021]. In these strategic games the agents do not perform random moves but rather jump or swap to positions that maximize their utility.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Tolerance is Necessary for Stability: Single-Peaked Swap Schelling Games

Bilò¹,

Bilò²,

Lenzner³

et al. 2022

Preprint

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Residential segregation in metropolitan areas is a phenomenon that can be observed all over the world. It is characterized by the emergence of large regions populated by residents that are homogeneous in terms of ethnicity or other traits. In a recent research trend in the AI community this phenomenon was investigated via game-theoretic models. There, selfish agents of two types are equipped with a monotone utility function that ensures higher utility if an agent has more same-type neighbors. The agents strategically choose their location on a given graph that serves as residential area to maximize their utility. However, sociological polls suggest that real-world agents are actually favoring mixed-type neighborhoods, and hence should be modeled via non-monotone utility functions. We study Swap Schelling Games with nonmonotone utility functions that are single-peaked. In these games pairs of agents may improve their utility by swapping their locations. Our main finding is that tolerance, i.e., that the agents favor fiftyfifty neighborhoods or even being in the minority, is necessary for equilibrium existence on almost regular or bipartite graphs. We show equilibrium existence on almost regular graphs via a potential function argument and we prove that this approach is impossible on arbitrary graphs even with tolerant agents. Regarding the quality of equilibria, we consider the recently introduced degree of integration, that counts the number of agents that live in a heterogeneous neighborhood, as social welfare function. We derive (almost) tight bounds on the Price of Anarchy and the Price of Stability. In particular, we show that the latter is constant on bipartite and almost regular graphs. Moreover, we prove that computing approximations of the social optimum placement and the equilibrium with maximum social welfare is NP-hard even on cubic graphs.

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Section: Our Contributionmentioning

confidence: 79%

Section: Our Contributionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 90%

Section: Related Workmentioning

confidence: 99%