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Consider the six-page mini-Web drawn below. Each page is named after its author. PageRank computes the following rankings (using a damping factor of 0.85) for this mini-Web:  | Rankings:- Leslie (1.929)
- Sarah (1.542)
- Chris (1.345)
- Jess (0.722)
- Will (0.243)
- Alex (0.219)
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We assume that each of these Web builders wants to improve his/her rank and will do what s/he can to change the network to that end. We also assume no new Web builders join the network. Below are steps that each person in the top-ranked trio (Leslie, Sarah, Chris) might consider in order to win the top ranking: - Leslie is in first place. She can do nothing (for now).
- Sarah can take first place by deleting her link to Leslie. Sadly for Sarah, Leslie can retaliate and still win by deleting her links to Sarah and Chris. Sarah ends up dropping to third place.
 Sarah deletes her link to Leslie - Sarah (0.608)
- Chris (0.596)
- Leslie (0.483)
- Jess (0.403)
- Will (0.243)
- Alex (0.219)
|  Leslie retaliates - Leslie (0.438)
- Chris (0.345)
- Sarah (0.297)
- Jess (0.297)
- Will (0.243)
- Alex (0.219)
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- Chris can take first place with Sarah's help (i.e., if Sarah links to Chris). Sarah may be happy to help Chris, because Chris is already linking to Sarah, and Sarah does not lose anything by helping Chris.
Below we see the initial alliance of Sarah and Chris, followed by retaliation from Leslie. Leslie's return to first place lasts only until Sarah strikes back and deletes her link to Leslie. Thanks to Sarah's unswerving loyalty to Chris, the Chris & Sarah alliance ultimately keeps Chris in first place.
 Sarah agrees to help Chris - Chris (1.805)
- Sarah (1.483)
- Leslie (1.332)
- Jess (0.917)
- Will (0.243)
- Alex (0.219)
| Leslie deletes her links to Sarah and Chris - Leslie (0.635)
- Chris (0.542)
- Sarah (0.380)
- Jess (0.380)
- Will (0.243)
- Alex (0.219)
|  Sarah deletes her link to Leslie - Chris (0.895)
- Leslie (0.537)
- Sarah (0.530)
- Jess (0.530)
- Will (0.243)
- Alex (0.219
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- Surprise ending: Leslie recognizes that she needs her own alliance to defeat the combined forces of Chris & Sarah. Leslie teams up with Alex, because Alex has already linked to Leslie but not to Chris. Leslie catapults Alex from last place to first, with one link (below). Alex may be trusted to share the spoils of his victory with Leslie, because Leslie can put Alex back into last place anytime she wants.
 Leslie & Alex defeat Chris & Sarah - Alex (1.435)
- Leslie (1.258)
- Chris (1.215)
- Will (0.760)
- Sarah (0.666)
- Jess (0.666)
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