Convergence and Hardness of Strategic Schelling Segregation WINE - PowerPoint PPT Presentation

Convergence and Hardness of Strategic Schelling Segregation WINE Conference 2019 Algorithm Engineering Research Group H. Echzell, T. Friedrich, P . Lenzner, L. Molitor, M. Pappik , F . Schöne, F . Sommer, D. Stangl

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Schelling Segregation Thomas Schelling (1921-2016) "economics Nobel prize" winner Micromotives and Macrobehavior (1978) https://www.bostonglobe.com/ Convergence and Hardness of Strategic Schelling Segregation 1

Schelling Segregation Thomas Schelling (1921-2016) "economics Nobel prize" winner Micromotives and Macrobehavior (1978) https://www.bostonglobe.com/ Convergence and Hardness of Strategic Schelling Segregation 1

Schelling Segregation Thomas Schelling (1921-2016) "economics Nobel prize" winner Micromotives and Macrobehavior (1978) agents https://www.bostonglobe.com/ Convergence and Hardness of Strategic Schelling Segregation 1

Schelling Segregation Thomas Schelling (1921-2016) "economics Nobel prize" winner Micromotives and Macrobehavior (1978) agents https://www.bostonglobe.com/ neighborhood Convergence and Hardness of Strategic Schelling Segregation 1

Schelling Segregation Thomas Schelling (1921-2016) "economics Nobel prize" winner Micromotives and Macrobehavior (1978) agents https://www.bostonglobe.com/ neighborhood "I am happy if at least a fraction τ of my neighborhood is of my type." Convergence and Hardness of Strategic Schelling Segregation 1

Schelling Segregation Thomas Schelling (1921-2016) "economics Nobel prize" winner Micromotives and Macrobehavior (1978) agents https://www.bostonglobe.com/ neighborhood "I am happy if at least a fraction τ of my neighborhood is of my type." e.g. τ = 1 4 Convergence and Hardness of Strategic Schelling Segregation 1

Schelling Segregation Thomas Schelling (1921-2016) "economics Nobel prize" winner Micromotives and Macrobehavior (1978) agents https://www.bostonglobe.com/ neighborhood "I am happy if at least a fraction τ of my neighborhood is of my type." e.g. τ = 1 4 Convergence and Hardness of Strategic Schelling Segregation 1

Schelling Segregation Thomas Schelling (1921-2016) "economics Nobel prize" winner Micromotives and Macrobehavior (1978) agents https://www.bostonglobe.com/ neighborhood "I am happy if at least a fraction τ of my neighborhood is of my type." e.g. τ = 1 4 Convergence and Hardness of Strategic Schelling Segregation 1

Schelling Segregation Thomas Schelling (1921-2016) "economics Nobel prize" winner Micromotives and Macrobehavior (1978) https://www.bostonglobe.com/ Convergence and Hardness of Strategic Schelling Segregation 1

Theoretical Approaches Stochastic Models Young et al. (2001) Barmpalias et al. (FOCS 2014) Brandt et al. (STOC 2012) Immorlica et al. (SODA 2017) Bhakta et al. (SODA 2014) Omidvar et al. (PODC 2017) many more... Convergence and Hardness of Strategic Schelling Segregation 2

Theoretical Approaches Stochastic Models Young et al. (2001) Barmpalias et al. (FOCS 2014) Brandt et al. (STOC 2012) Immorlica et al. (SODA 2017) Bhakta et al. (SODA 2014) Omidvar et al. (PODC 2017) many more... Game Theoretic Models Chauhan et al. (SAGT 2018) Elkind et al. (IJCAI 2019) Brederek et al. (AAMAS 2019) Agarwal et al. (AAAI 2020) Convergence and Hardness of Strategic Schelling Segregation 2

Theoretical Approaches Stochastic Models Young et al. (2001) Barmpalias et al. (FOCS 2014) Brandt et al. (STOC 2012) Immorlica et al. (SODA 2017) Bhakta et al. (SODA 2014) Omidvar et al. (PODC 2017) many more... Game Theoretic Models Chauhan et al. (SAGT 2018) Elkind et al. (IJCAI 2019) Brederek et al. (AAMAS 2019) Agarwal et al. (AAAI 2020) Convergence and Hardness of Strategic Schelling Segregation 2

Strategic Schelling Segregation undirected (simple) graph G = ( V , E ) Convergence and Hardness of Strategic Schelling Segregation 3

Strategic Schelling Segregation undirected (simple) graph G = ( V , E ) set of agents A with partitioning P ( A ) Convergence and Hardness of Strategic Schelling Segregation 3

Strategic Schelling Segregation undirected (simple) graph G = ( V , E ) set of agents A with partitioning P ( A ) placement p G : A → V (injective) neighborhood N p G ( a ) := adjacent agents Convergence and Hardness of Strategic Schelling Segregation 3

Strategic Schelling Segregation undirected (simple) graph G = ( V , E ) set of agents A with partitioning P ( A ) placement p G : A → V (injective) neighborhood N p G ( a ) := adjacent agents intolerance threshold τ ∈ [0, 1] Convergence and Hardness of Strategic Schelling Segregation 3

Strategic Schelling Segregation N + p G ( a ), N − p G ( a ) ⊆ N p G ( a ) cost  | N + τ pG ( a ) | max(0, τ − pG ( a ) | ) if N p G ( a ) � = ∅  | N + pG ( a ) | + | N − cost p G ( a ) τ else  τ pnr Convergence and Hardness of Strategic Schelling Segregation 4

Strategic Schelling Segregation N + p G ( a ), N − p G ( a ) ⊆ N p G ( a ) cost  | N + τ pG ( a ) | max(0, τ − pG ( a ) | ) if N p G ( a ) � = ∅  | N + pG ( a ) | + | N − cost p G ( a ) τ else  τ pnr always: N + p G ( a ) := neighbors with same type as a Convergence and Hardness of Strategic Schelling Segregation 4

Strategic Schelling Segregation N + p G ( a ), N − p G ( a ) ⊆ N p G ( a ) cost  | N + τ pG ( a ) | max(0, τ − pG ( a ) | ) if N p G ( a ) � = ∅  | N + pG ( a ) | + | N − cost p G ( a ) τ else  τ pnr always: N + p G ( a ) := neighbors with same type as a 1 vs. all Schelling Game (1-k-SG) a Convergence and Hardness of Strategic Schelling Segregation 4

Strategic Schelling Segregation N + p G ( a ), N − p G ( a ) ⊆ N p G ( a ) cost  | N + τ pG ( a ) | max(0, τ − pG ( a ) | ) if N p G ( a ) � = ∅  | N + pG ( a ) | + | N − cost p G ( a ) τ else  τ pnr always: N + p G ( a ) := neighbors with same type as a 1 vs. all Schelling Game (1-k-SG) a N + p G ( a ) = N − p G ( a ) = Convergence and Hardness of Strategic Schelling Segregation 4

Strategic Schelling Segregation N + p G ( a ), N − p G ( a ) ⊆ N p G ( a ) cost  | N + τ pG ( a ) | max(0, τ − pG ( a ) | ) if N p G ( a ) � = ∅  | N + pG ( a ) | + | N − cost p G ( a ) τ else  τ pnr always: N + p G ( a ) := neighbors with same type as a 1 vs. all Schelling Game (1-k-SG) a N + p G ( a ) = N − p G ( a ) = 1 vs. 1 Schelling Game (1-1-SG) a Convergence and Hardness of Strategic Schelling Segregation 4

Strategic Schelling Segregation N + p G ( a ), N − p G ( a ) ⊆ N p G ( a ) cost  | N + τ pG ( a ) | max(0, τ − pG ( a ) | ) if N p G ( a ) � = ∅  | N + pG ( a ) | + | N − cost p G ( a ) τ else  τ pnr always: N + p G ( a ) := neighbors with same type as a 1 vs. all Schelling Game (1-k-SG) a N + p G ( a ) = N − p G ( a ) = 1 vs. 1 Schelling Game (1-1-SG) N + a p G ( a ) = N − p G ( a ) = Convergence and Hardness of Strategic Schelling Segregation 4

Strategic Schelling Segregation N + p G ( a ), N − p G ( a ) ⊆ N p G ( a ) cost  | N + τ pG ( a ) | max(0, τ − pG ( a ) | ) if N p G ( a ) � = ∅  | N + pG ( a ) | + | N − cost p G ( a ) τ else  τ pnr always: N + p G ( a ) := neighbors with same type as a τ = 1 1 vs. all Schelling Game (1-k-SG) 3 a N + p G ( a ) = cost p G ( a ) = 1 12 N − p G ( a ) = 1 vs. 1 Schelling Game (1-1-SG) N + a p G ( a ) = cost p G ( a ) = 0 N − p G ( a ) = Convergence and Hardness of Strategic Schelling Segregation 4

Strategic Schelling Segregation N + p G ( a ), N − p G ( a ) ⊆ N p G ( a ) cost  | N + τ pG ( a ) | max(0, τ − pG ( a ) | ) if N p G ( a ) � = ∅  | N + pG ( a ) | + | N − cost p G ( a ) τ else  τ pnr always: N + p G ( a ) := neighbors with same type as a τ = 1 1 vs. all Schelling Game (1-k-SG) 3 a N + p G ( a ) = cost p G ( a ) = 1 12 N − p G ( a ) = 1 vs. 1 Schelling Game (1-1-SG) N + a p G ( a ) = cost p G ( a ) = 0 N − p G ( a ) = Convergence and Hardness of Strategic Schelling Segregation 4

Strategic Schelling Segregation What do discontent agents do? Convergence and Hardness of Strategic Schelling Segregation 5

Strategic Schelling Segregation What do discontent agents do? Jump Schelling Game (JSG): "jump to empty node to decrease costs" p G → p ′ G if cost p G ( a ) > cost p ′ G ( a ) Convergence and Hardness of Strategic Schelling Segregation 5

Strategic Schelling Segregation What do discontent agents do? Jump Schelling Game (JSG): "jump to empty node to decrease costs" p G → p ′ G if cost p G ( a ) > cost p ′ G ( a ) Swap Schelling Game (SSG): "swap position to decrease costs" p G → p ′ G if cost p G ( a ) > cost p ′ G ( a ) and cost p G ( b ) > cost p ′ G ( b ) Convergence and Hardness of Strategic Schelling Segregation 5