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# Networked Influencers and Victims

iteration.

📗 Game

➭ Number of influencers

n

➭ Number of victims

m

➭ Influencer network

I \in {[0, 1]}^{n \times n}

➭ Influence weights

W \in {[0, 1]}^{n \times m}

➭ Victim network

V \in {[0, 1]}^{m \times m}

➭ Victim weights

U \in {[0, 1]}^{m \times n}

➭ Influencer targets

t

📗 Equilibrium

➭ Influencers positions

x

➭ Victims positions

y

➭ Influencers best response dynamics:

➭ Victims best response dynamics:

📗 Parameters

➭ Influencer

i

's payoff given action

x_{i}

\sum_{j^{'}} W (i, j^{'}) {‖ t_{i} - y_{j^{'}} ‖}^{2} + λ \sum_{i^{'}} I (i, i^{'}) {‖ x_{i} - x_{i^{'}} ‖}^{2}

➭ Victim

j

's payoff given action

y_{j}

\sum_{i^{'}} U (j, i^{'}) {‖ y_{j} - x_{i^{'}} ‖}^{2} + ρ \sum_{j^{'}} V (j, j^{'}) {‖ y_{j} - y_{j^{'}} ‖}^{2}

➭ Influencer weight on neighbors

λ

➭ Victim weight on neighbors

ρ

Last Updated: August 28, 2024 at 6:28 AM