07-cascades_annot

07-cascades_annot -...

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CS224W: Social and Information Network Analysis re eskovec tanford University Jure Leskovec, Stanford University http://cs224w.stanford.edu
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[Morris 2000] ased on 2 player coordination game Based on 2 player coordination game 2 players–each chooses technology A or B 10/11/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 2
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If both v and w adopt behavior A, they each get payoff a>0 If v and w adopt behavior B, they reach get payoff b>0 If v and w adopt the pposite behaviors opposite behaviors, they each get 0 10/11/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 3
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Let v have d neighbors If fraction p of v ’s neighbors adopt A , then: v chooses A if: a p d> b (1 p) d 10/11/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 4
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ayoffs: =3 b=2 reshold: Payoffs: a3 , b2 Everyone is adopting B v and w are initial adopters q b p Threshold: Does the adoption spread? b a Fact: When a node switches from B to A it never wants to switch back to B . 10/11/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 5
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onsider infinite graph Consider infinite graph G (but each node has finite number of neighbors) e say that a finite set uses a cascade We say that a finite set S causes a cascade in G with threshold q if, when S adopts A, ventually very node adopts eventually every node adopts A Example: Path 10/11/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 6
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ee:
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This note was uploaded on 01/11/2011 for the course CS 224 at Stanford.

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07-cascades_annot -...

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