Engineering Agreement: The Naming Game wit ith Asymmetric and - - PowerPoint PPT Presentation

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Engineering Agreement: The Naming Game wit ith Asymmetric and - - PowerPoint PPT Presentation

Aug 28, 2022 147 likes •663 views

Engineering Agreement: The Naming Game wit ith Asymmetric and Heterogeneous Agents Jie Gao, Bo Li, Grant Schoenebeck, Fan ang-Yi i Yu Social Convention Conventions are universally adopted from two or more alternatives. Language,

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Engineering Agreement: The Naming Game wit ith Asymmetric and Heterogeneous Agents

Jie Gao, Bo Li, Grant Schoenebeck, Fan ang-Yi i Yu

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SLIDE 2

Social Convention

  • Conventions are universally

adopted from two or more alternatives.

  • Language, etiquette, or custom.
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SLIDE 3

Agreement on Convention

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SLIDE 4

Engineering Agreement

  • What can help or harm convergence?

– Homogeneity or heterogeneity – Community structure

  • How robust are the dynamics to possible manipulations?
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SLIDE 5

Naming Game [Baronchelli 06] 06]

  • A agent-based process on a network
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Naming Game

  • A agent-based process on a network

– Each agent has inventory of names

Soft drink coke

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SLIDE 7

Naming Game

  • A agent-based process on a network

– Each agent has inventory of names

Soft drink coke coke Soda Soda pop coke coke pop

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SLIDE 8

Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random

Soft drink coke Soda pop coke coke pop coke Soda

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SLIDE 9

Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random, and one is speaker and the other is listener.

Soft drink coke Soda pop coke coke pop coke Soda

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SLIDE 10

Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random, and one is speaker and the other is listener.

Soft drink coke Soda pop coke coke pop coke Soda

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SLIDE 11

Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random, and one is speaker and the other is listener.

  • Failure

Soft drink coke Soda pop coke coke pop coke Soda

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SLIDE 12

Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random, and one is speaker and the other is listener.

  • Failure: listener adds the new name

Soft drink coke coke Soda Soda pop coke Soft drink coke pop

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Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random, and one is speaker and the other is listener.

  • Failure: listener adds the new name

Soft drink coke Soda pop coke Soft drink coke Soda coke pop

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SLIDE 14

Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random, and one is speaker and the other is listener.

  • Failure: listener adds the new name

Soft drink coke Soda pop coke Soft drink coke Soda coke pop

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SLIDE 15

Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random, and one is speaker and the other is listener.

  • Failure: listener adds the new name
  • Success

Soft drink coke Soda pop coke Soft drink coke Soda coke pop

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Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random, and one is speaker and the other is listener.

  • Failure: listener adds the new name
  • Success: both remove all other names

Soft drink coke Soda pop coke Soft drink coke coke

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SLIDE 17

Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random, and one is speaker and the other is listener.

  • Failure: listener adds the new name
  • Success: both remove all other names
  • Empty

Soft drink coke Soda pop coke Soft drink coke coke

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SLIDE 18

Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random, and one is speaker and the other is listener.

  • Failure: listener adds the new name
  • Success: both remove all other names
  • Empty: speaker invent a new word

Soft drink coke Soda pop coke Soft drink coke coke Cola

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Naming Game

  • A agent-based process on a network

– Each agent has inventory of names – At each time an edge is selected at random, and one is speaker and the other is listener.

  • Failure: listener adds the new name
  • Success: both remove all other names
  • Empty: speaker invent a new word

– Convergence

coke coke coke coke coke coke

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Different initial states

Empty in initia itial states Segregated in initi itial l states

coke Soda coke coke Soda Soda

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Motivating Questions

  • What can help or harm convergence?

– Homogeneity or heterogeneity – Community structure

  • How robust are the dynamics to possible manipulations?
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SLIDE 22

Different graphs

d-ary tree star grid Kleinberg complete regular Watts-Strogatz disjoint cliques

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Fast and Slo low Convergence

2000000 4000000 6000000 8000000 10000000 12000000 5000 10000 15000 20000 25000 30000 35000 40000

Consensus time # nodes grid complete graph regular graph Star

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Fast and Slo low Convergence

2000000 4000000 6000000 8000000 10000000 12000000 5000 10000 15000 20000 25000 30000 35000 40000

Consensus time # nodes grid complete graph regular graph Star Local structure

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SLIDE 25

Fast and Slo low Convergence

2000000 4000000 6000000 8000000 10000000 12000000 5000 10000 15000 20000 25000 30000 35000 40000

Consensus time # nodes grid complete graph regular graph Star Homogeneous Local structure

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Fast and Slo low Convergence

2000000 4000000 6000000 8000000 10000000 12000000 5000 10000 15000 20000 25000 30000 35000 40000

Consensus time # nodes grid complete graph regular graph Star Homogeneous Local structure Heterogeneous

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Heterogeneous

0.5 1 1.5 2 2.5 3 0.1 0.2 0.3 0.4 0.5

Normalized consensus time R/(R+L)

10000 5000

R=1 L = 7 R/(R+L) = 1/8

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Heterogeneous

0.5 1 1.5 2 2.5 3 0.1 0.2 0.3 0.4 0.5

Normalized consensus time R/(R+L)

10000 5000

R=2 L = 6 R/(R+L) = 2/8

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Heterogeneous

0.5 1 1.5 2 2.5 3 0.1 0.2 0.3 0.4 0.5

Normalized consensus time R/(R+L)

10000 5000

R=3 L = 5 R/(R+L) = 3/8

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Motivating Questions

  • What can help or harm convergence?

– Homogeneity or heterogeneity – Community structure

  • How robust are the dynamics to possible manipulations?
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Community Structure

Few edges between groups Many edges within groups

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Disjoint cliques

Few edges between groups Many edges within groups

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Tree Structure

Few edges between groups Many edges within groups

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Tree Structure

Few edges between groups Many edges within groups

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SLIDE 35

Adding Homogeneity

1 − 𝑞 𝑞

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Community Structure

Empty in initia itial states Segregated in initi itial l states 1 − 𝑞 𝑞 1 − 𝑞 𝑞

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Simulation on Disjo joint Cliques

Empty in initia itial states Segregated in initi itial l states

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5

Fraction of non- consensus p

emp-1000: emp-5000: emp-10000: 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5

Fraction of non- consensus p

seg-1000: seg-5000: seg-10000:

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SLIDE 38

Simulation on Disjo joint Cliques

Empty in initia itial states Segregated in initi itial l states

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5

Fraction of non- consensus p

emp-1000: emp-5000: emp-10000: 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5

Fraction of non- consensus p

seg-1000: seg-5000: seg-10000:

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Theoretical Analysis

  • Segregated start: for 𝑞 < 𝑞0 ≈ 0.110, consensus time=

exp(Ω(𝑜))

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5

Fraction of non- consensus p

seg-1000: seg-5000: seg-10000: 𝑞0

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Theoretical Analysis

  • Segregated start: for 𝑞 < 𝑞0 ≈ 0.110, consensus time=

exp(Ω(𝑜))

1 − 𝑞 𝑞

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Theoretical Analysis

  • Segregated start: for 𝑞 < 𝑞0 ≈ 0.110, consensus time=

exp(Ω(𝑜))

– Mean field approximation

1 − 𝑞 𝑞

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SLIDE 42

Theoretical Analysis

  • Segregated start: for 𝑞 < 𝑞0 ≈ 0.110, consensus time=

exp(Ω(𝑜))

– Mean field approximation – Stability of autonomous system

  • Local stability
  • Global stability

1 − 𝑞 𝑞

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SLIDE 43

Motivating Questions

  • What can help or harm convergence?

– Homogeneity or heterogeneity – Community structure

  • How robust are the dynamics to possible manipulations?
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SLIDE 44

Robustness

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Stubborn nodes

  • How and when can such nodes affect the name to which the

dynamics converge?

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Stubborn nodes

  • How and when can such nodes affect the name to which the

dynamics converge?

– The network topology – The time when the stubborn nodes are activated

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Stubborn nodes and network

Gr Graph si size = 10 1000 00 Gr Graph si size = 10 1000 000

0.2 0.4 0.6 0.8 1 1.2 2 4 6 8 10

Fraction of stubborn

  • pinion

Number of stubborn nodes

Grid Complete graph Regular star 0.2 0.4 0.6 0.8 1 1.2 2 4 6 8 10 Fraction of stubborn opinion Number of stubborn nodes Complete graph Regular Grid star

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Adding stubborn nodes aft fter consensus

  • After consensus: with 𝑞 < 𝑞0 ≈ 0.108 fraction of stubborn

nodes, the consensus time = exp(Ω(𝑜)).

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 1024 10000

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SLIDE 49

Engineering Agreement

  • What can help or harm convergence?

– Homogeneity or heterogeneity – Community structure

  • How robust are the dynamics to possible manipulations?
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SLIDE 50

QUESTIONS?