SMALL W RLDS:
Raph Koster
Creative Director
Sony Online Entertainment Austin
Competitive and Cooperative Structures in Online Worlds
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Understanding Scale-Free Networks and Their Impact on Online Worlds, Lecture notes of Game Theory
This document, presented at GDC 2003 by Raph Koster, explores the concepts of scale-free networks, six degrees of separation, clustering, and the power of hubs in the context of online worlds. It also discusses the implications of these concepts for game design, including the importance of weak ties and the role of hubs in network dynamics.
What you will learn
- How do hubs affect the dynamics of scale-free networks?
- How does the concept of six degrees of separation apply to scale-free networks?
- Why are weak ties important in scale-free networks?
- What is a scale-free network and how does it differ from other types of networks?
- What is the role of clustering in scale-free networks?
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2021/2022
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SMALL W RLDS:
Raph Koster Creative Director Sony Online Entertainment Austin
Competitive and Cooperative Structures in Online Worlds
SMALL W RLDS
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!
SMALL W RLDS
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
SMALL W RLDS
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
SMALL W RLDS
The Internet, 2001
SMALL W RLDS
The Internet, 2002
SMALL W RLDS
Random graph theory
- If you take a set of nodes, like say people, and link them randomly…
k= 1
SMALL W RLDS
Random graph theory
- …you end up with a complex graph where anyone can reach anyone.
k= 2
SMALL W RLDS
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).
SMALL W RLDS
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.
SMALL W RLDS
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
SMALL W RLDS Clustering
- 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...
SMALL W RLDS
Weak ties are more important
- Why Granovetter was right: weak ties bridge clusters. In the models proposed by Erdös, there are no clusters.
SMALL W RLDS
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.