Understanding Scale-Free Networks and Their Impact on Online Worlds, Lecture notes of Game Theory

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Raph Koster Creative Director Sony Online Entertainment Austin

Competitive and Cooperative Structures in Online Worlds

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We’re

going to

go very

very fast.

Be

warned.

What we‘re going to cover

• Graph theory
  • What are scale-free networks and why care?
• Social networks
  • What is the structure of social networks?
• Game theory
  • How do people in social networks interact?
• Pareto‘s Law
  • How does skill affect networks?
• Conclusions and recommendations
  • Concrete advice.
• Bibliography
  • Many many pages long!

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How do we get there from here?

• The Seven Bridges problem: can you walk the whole city but cross every bridge only once?

The City of Königsberg

The Pregel River Kneiphof Island

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There is a path! Well, sort of.

• Leonhard Euler creates graph theory and proves that you can‘t cross each bridge only once.

a (^) b

c d

f

g

e

A

B

C

D

The City of Königsberg

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The Internet, 2001

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The Internet, 2002

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Random graph theory

• If you take a set of nodes, like say people, and link them randomly…

k= 1

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Random graph theory

• …you end up with a complex graph where anyone can reach anyone.

k= 2

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Six degrees of separation gets famous!

• The first appearance of ―six degrees‖ (except he said 5) is in Hungarian writer Frigyes Karinthy‘s story ―Láncszemek.‖
• The next was Stanley Milgram‘s experiment in 1967, which found that the distance was actually 5.5.
• The term came from John Guare‘s play from 1991 (and subsequent movie).

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Strong ties

• Mark Granovetter did the early research on weak ties. In ―The Strength of Weak Ties,‖ 1973, he found that strong ties tend to form triangles. Your two best friends likely know each other well.

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Weak ties vs. Strong ties

• In 1974 Granovetter‘s ―Getting a Job‖ found that you get most jobs from weak ties, not strong ones, because weak ties inhabit other clusters and therefore have different information. Applied directly

Formal means such as ads

Found job through a friend

A mere acquaintance A near stranger

A close friend

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• Watts and Strogatz introduced the ―clustering coefficient‖. It is the percentage of your cluster who are friends of each other. In a star network, the coefficient is low...

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Weak ties are more important

• Why Granovetter was right: weak ties bridge clusters. In the models proposed by Erdös, there are no clusters.

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The power of hubs

• In a small world network, six degrees of separation exists because of hubs.
• Hubs are relatively rare, but they bridge multiple clusters.