Hub attacks, as shown by Duncan Calloway of
Cornell, with Mark Newman, Strogatz, and Watts, can kill a scale-free
network in no time. However, it requires simultaneous removal (so that
links do not have time to reattach elsewhere). The problem then becomes
Cascades are not instant, Duncan Watts showed.
There is a tipping point there as well. The initial failure may result in a
catastrophe many times its size, a very long time later.
Steve Lawrence and Lee Giles of NEC Research
Institute showed that the Web is too big to know. Search engines can only
map a fraction, because from any given page, you can only reach 24% of the
Web via linking.
This is a feature of all scale-free networks
made of directed, non-reciprocal links, according to Sergey Dorogovstev,
Jose Mendes, and A. N. Samukhin.
Watts points out that friendships themselves are
not symmetric; usually there is a superior/subordinate relationship. An
acquaintance of lesser prominence is quicker to claim someone as a friend
than someone of high status.
In scale-free networks, there is no threshold
for virii to cross, according to Pastor-Satorras and Vespignani, in Aug
2000. This is because of the hubs.
You don’t need to know exactly who the hubs
are—Zoltán Dezsö showed that ANY preferential treatment restores the
threshold for infection. So if you’ve got something to sell, sell to those
likely to be hubs.
Networks remain balanced between chaos and order
as long as preferential attachment and growth are present. But remove
growth and what you get is a term from physics: Bose-Einstein condensation.
Also known as “monopolies.”
In other words, in some networks, it is possible
for the fittest nodes to grab ALL the links.
Pennock, Flake, Lawrence, Glover, and Giles at
NEC have a formula that predicts the attachment of new links to a
scale-free network accurately. The amount of rich-get-richer that occurs
varies per e-commerce category.
Assuming there PARITY of fitness, persistence,
and freedom of choice to create preferential attachments, Bose-Einstein
condensation will start to occur in all systems where there is no
possibility of competitive innovation.
If your game is zero-sum skill based, that will
cap audience size right there. Skill based games on the Internet will never
be huge, even with leagues.
You must find some way to overturn the rich get
richer scenario in all games with some form of accumulation. There must be
not just drains, but occasional catastrophic behaviors that topple the 20%
at the top of Pareto’s curve, so that others get a chance.
In other words, treadmills are not only good,
What’s more, the more different treadmills the
better. Get parity in one area even if you cannot have parity in all of
them. Provide “powergamer” style recognition to as many arenas of the game
Munger, Charlie. “The Psychology of Human
Misjudgement.” Speech at Harvard University, June 1995.
Pennock, David M., et al, “Winners don't take
all: Characterizing the competition for links on the web”, Proceedings of
the National Academy of Sciences USA, Vol. 99, Issue 8, 5207-5211, April
Powazek, Derek M. Design for Community. New
Rauch, Jonathan. “Seeing Around Corners.” The
Atlantic, April 2002.
Sellers, Mike. “Creating Effective Groups and
Group Roles in MMP Games.” Gamasutra, Sept. 2002.