This preview shows page 1. Sign up to view the full content.
Unformatted text preview: etplace) • Cell phone service providers Stronger infec0ousness (can call landlines) Moderate plaIorm eﬀects (friends and family programs) • Television sets Strong infec0ousness (immediate content) Weak plaIorm eﬀects (know what your friends own?) vs. vs. vs. vs. vs. A Compe&&ve Contagion Model •
•
•
• Two compe0ng companies oﬀering similar underlying products: R(ed) and B(lue) Underlying, known social network or graph G of consumers R and B respec0vely have K_R and K_B ini&al infec&ons; assume K_R >= K_B R and B play a one
shot, two
player game: – Simultaneously choose ini0al infec0ons in G – Local, stochas0c infec0on dynamics over G determine subsequent infec0ons – Payoﬀs are total infec0ons for R and B respec0vely • The infec0on dynamics over G are determined by two func0ons f and g • Let v be a vertex in G with frac&ons x_R and x_B of infected (R or B) neighbors • Switching func&on f: [0,1] [0,1]: f(x_R+x_B) = probability v is infected (R or B) – Models how infec0ous the product/service is regardless of company • Selec&on func&on g: [0,1] [0,1]: g(x_R/(x_R + x_B)) = condi&onal probability of R – Models how strong/weak plaIorm eﬀects are • For some number of...
View Full
Document
 Spring '14

Click to edit the document details