Schelling Games on Graphs

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

doi:10.24963/ijcai.2019/38

Cited by 24 publications

(68 citation statements)

References 19 publications

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“…However, we remark that even if we change this definition into summing up the cost of all agents, i.e., cost p G (A) = a∈A cost p G (a), like social cost, the above hardness results still hold. This relates to the hardness results from Elkind et al [15] which hold for the JSG with τ = 1 in the presence of stubborn agents which are unwilling to move.…”

Section: Hardness Properties For Two Typesmentioning

confidence: 64%

“…Very recently, Elkind et al [15] studied a variant of the model by Chauhan et al [11], where the agents are partitioned into stubborn and strategic agents. The former agents do not move and the latter agents try to maximize the fraction of same-type agents in their neighborhood by jumping to a suitable empty location.…”

Section: Related Workmentioning

confidence: 99%

“…All mentioned works, with SimSeg [18] and the work by Elkind et al [15] as exceptions, assume that exactly two types of agents exist. In SimSeg and [15], agents only differentiate between agents of their own type and agents of other types. As we will discuss later, this is a very restricted point of view and this will correspond to our "one-versus-all" version.…”

Section: Related Workmentioning

confidence: 99%

“…Since most versions are not guaranteed to converge via IRD, the existence of stable placements for all graph types is not given. Elkind et al [15] showed that for the 1-k-JSG that stable placements exist if the underlying network is a star or a graph with maximum degree 2 and τ = 1. Furthermore they proved that if the underlying network is a tree the existence of a stable placement may fail to exist for τ = 1 in the 1-k-JSG.…”

Section: Conclusion and Open Questionsmentioning

confidence: 99%

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Convergence and Hardness of Strategic Schelling Segregation

Echzell

Friedrich

Lenzner

et al. 2019

Web and Internet Economics

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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 τ , for some 0 < τ < 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), i.e., the natural approach for finding equilibrium states, are guaranteed to converge. For this we prove several sharp threshold results where guaranteed IRD convergence suddenly turns into the strongest possible non-convergence result: a violation of weak acyclicity. In particular, we show such threshold results also for Schelling's original model, which is in contrast to the standard assumption in many empirical papers. Furthermore, we show that in case of convergence, IRD find an equilibrium in O(m) steps, where m is the number of edges in the underlying graph and show that this bound is met in empirical simulations starting from random initial agent placements.

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Section: Hardness Properties For Two Typesmentioning

confidence: 64%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Conclusion and Open Questionsmentioning

confidence: 99%

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Convergence and Hardness of Strategic Schelling Segregation

Echzell

Friedrich

Lenzner

et al. 2019

Web and Internet Economics

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“…Recent work in theoretical computer science [4,19] has shown that the expected size of these segregated communities can be exponential in the size of the local neighbourhoods in some social network graphs. The Schelling model has also been studied from a games perspective, where neighborhood formation is determined by agents that can be selfish, strategic [6,13] or form coalitions [5].…”

Section: Introductionmentioning

confidence: 99%

Distributed Pattern Formation in a Ring

Ehresmann

Lafond

Narayanan

et al. 2019

Structural Information and Communication Complexity

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Motivated by concerns about diversity in social networks, we consider the following pattern formation problems in rings. Assume n mobile agents are located at the nodes of an n-node ring network. Each agent is assigned a colour from the set {c 1 , c 2 , . . . , c q }. The ring is divided into k contiguous blocks or neighbourhoods of length p. The agents are required to rearrange themselves in a distributed manner to satisfy given diversity requirements: in each block j and for each colour c i , there must be exactly n i (j) > 0 agents of colour c i in block j. Agents are assumed to be able to see agents in adjacent blocks, and move to any position in adjacent blocks in one time step.When the number of colours q = 2, we give an algorithm that terminates in time N 1 /n * 1 + k + 4 where N 1 is the total number of agents of colour c 1 and n * 1 is the minimum number of agents of colour c 1 required in any block. When the diversity requirements are the same in every block, our algorithm requires 3k + 4 steps, and is asymptotically optimal. Our algorithm generalizes for an arbitrary number of colours, and terminates in O(nk) steps. We also show how to extend it to achieve arbitrary specific final patterns, provided there is at least one agent of every colour in every pattern.

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Evolving Shelah‐Spencer graphs

Elwes

2021

Mathematical Logic Qtrly

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We define an evolving Shelah‐Spencer process as one by which a random graph grows, with at each time τ∈N a new node incorporated and attached to each previous node with probability τ−α, where α∈(0,1)∖Q is fixed. We analyse the graphs that result from this process, including the infinite limit, in comparison to Shelah‐Spencer sparse random graphs discussed in [21] and throughout the model‐theoretic literature. The first order axiomatisation for classical Shelah‐Spencer graphs comprises a Generic Extension axiom scheme and a No Dense Subgraphs axiom scheme. We show that in our context Generic Extension continues to hold. While No Dense Subgraphs fails, a weaker Few Rigid Subgraphs property holds.

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Schelling Games on Graphs

Cited by 24 publications

References 19 publications

Convergence and Hardness of Strategic Schelling Segregation

Convergence and Hardness of Strategic Schelling Segregation

Distributed Pattern Formation in a Ring

Evolving Shelah‐Spencer graphs

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