compcontagion11

vs vs vs vs vs a compeve contagion model two

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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...
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