# Schelling Games on Graphs

@inproceedings{Elkind2019SchellingGO, title={Schelling Games on Graphs}, author={E. Elkind and Jiarui Gan and Ayumi Igarashi and Warut Suksompong and Alexandros A. Voudouris}, booktitle={IJCAI}, year={2019} }

We consider strategic games that are inspired by Schelling's model of residential segregation. In our model, the agents are partitioned into k types and need to select locations on an undirected graph. Agents can be either stubborn, in which case they will always choose their preferred location, or strategic, in which case they aim to maximize the fraction of agents of their own type in their neighborhood. We investigate the existence of equilibria in these games, study the complexity of… Expand

#### 20 Citations

Swap Stability in Schelling Games on Graphs

- Computer Science
- AAAI
- 2020

This work studies a recently introduced class of strategic games that is motivated by and generalizes Schelling's well-known residential segregation model, and considers a variant of this model that is call swap Schelling games, where the number of agents is equal to thenumber of nodes of the graph, and agents may swap positions with other agents to increase their utility. Expand

Modified Schelling Games

- Computer Science
- SAGT
- 2020

A thorough analysis of the (in)efficiency of equilibria that arise in such modified Schelling games, by bounding the price of anarchy and price of stability for both general graphs and interesting special cases is provided. Expand

Modified Schelling games

- Computer Science
- Theor. Comput. Sci.
- 2021

A thorough analysis of the (in)efficiency of equilibria that arise in such modified Schelling games, by bounding the price of anarchy and price of stability for both general graphs and interesting special cases is provided. Expand

Equilibria in Schelling Games: Computational Complexity and Robustness

- Computer Science
- ArXiv
- 2021

It is proved that deciding the existence of a swap-equilibrium and a jump-Equilibrium in this simplest model of Schelling games is NP-hard, thereby answering questions left open by Agarwal et al. Expand

Modied Schelling Games

- 2020

We introduce the class of modied Schelling games in which there are dierent types of agents who occupy the nodes of a location graph; agents of the same type are friends, and agents of dierent… Expand

Hedonic Diversity Games

- Computer Science
- AAMAS
- 2019

It is shown that a core stable outcome may fail to exist and checking the existence of core stable outcomes is computationally hard, and an efficient algorithm is proposed to find an individually stable outcome under the natural assumption that agents' preferences over fractions of the agents of their own type are single-peaked. Expand

Convergence and Hardness of Strategic Schelling Segregation ( full version )

- 2019

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… Expand

Convergence and Hardness of Strategic Schelling Segregation

- Mathematics, Computer Science
- WINE
- 2019

It is shown that in case of convergence, IRD find an equilibrium in $\mathcal{O}(m)$ steps, where $m$ is the number of edges in the underlying graph and this bound is met in empirical simulations starting from random initial agent placements. Expand

Two Influence Maximization Games on Graphs Made Temporal

- Computer Science
- IJCAI
- 2021

The two main technical results are (algorithmic) proofs for the existence of Nash equilibria in temporal competitive diffusion and temporal Voronoi games when the edges are restricted not to disappear over time. Expand

Topological Influence and Locality in Swap Schelling Games

- Computer Science
- MFCS
- 2020

Improved almost tight bounds on the Price of Anarchy for arbitrary underlying graphs and close bounds for regular graphs, paths and cycles are presented and it is shown that locality has a severe impact on the game dynamics. Expand

#### References

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Schelling Games on Graphs

- Computer Science
- 2019

This work investigates the existence of equilibria in strategic games that are inspired by Schelling's model of residential segregation, study the complexity of finding an equilibrium outcome or an outcome with high social welfare, and also provides upper and lower bounds on the price of anarchy and stability. Expand

Swap Stability in Schelling Games on Graphs

- Computer Science
- AAAI
- 2020

This work studies a recently introduced class of strategic games that is motivated by and generalizes Schelling's well-known residential segregation model, and considers a variant of this model that is call swap Schelling games, where the number of agents is equal to thenumber of nodes of the graph, and agents may swap positions with other agents to increase their utility. Expand

Equilibria in Schelling Games: Computational Complexity and Robustness

- Computer Science
- ArXiv
- 2021

It is proved that deciding the existence of a swap-equilibrium and a jump-Equilibrium in this simplest model of Schelling games is NP-hard, thereby answering questions left open by Agarwal et al. Expand

Hedonic Diversity Games

- Computer Science
- AAMAS
- 2019

It is shown that a core stable outcome may fail to exist and checking the existence of core stable outcomes is computationally hard, and an efficient algorithm is proposed to find an individually stable outcome under the natural assumption that agents' preferences over fractions of the agents of their own type are single-peaked. Expand

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Convergence and Hardness of Strategic Schelling Segregation

- Mathematics, Computer Science
- WINE
- 2019

It is shown that in case of convergence, IRD find an equilibrium in $\mathcal{O}(m)$ steps, where $m$ is the number of edges in the underlying graph and this bound is met in empirical simulations starting from random initial agent placements. Expand

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Topological Influence and Locality in Swap Schelling Games

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- MFCS
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Improved almost tight bounds on the Price of Anarchy for arbitrary underlying graphs and close bounds for regular graphs, paths and cycles are presented and it is shown that locality has a severe impact on the game dynamics. Expand

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