A lot of attention has been lavished on ideas "going viral," but this may not be the only way that ideas spread, according to an article published in PNAS last week. With some extensive theoretical work in game theory, two researchers have shown that trendy changes don't spread quickly just because they gain exposure to a high number of people. Instead, the spread of innovations may work more like a game where players are gauging whether to adopt something new based on what others immediately surrounding them do.

The popularity growth of things like websites or gadgets is often described as being similar to an epidemic: a network with a lot of connections between people increases exposure and then adoption, as do links stretching between dissimilar groups. When the trend in question spreads to a node with a lot of connections (like a celebrity), its popularity explodes. While this is fitting for some cases, in others it's an oversimplification—a person's exposure to a trend doesn't always guarantee they will adopt it and pass it on.

"It is not only the intrinsic value of a new technology (or other types of innovation) that makes it attractive. It is also the number of friends who have adopted it," Amin Saberi, one of the authors, told Ars. In instances where there is incentive to make the same decision as people around you, the authors of the paper argue, the spread of innovations may instead follow rules of game theory, which differ in big ways from the rules of viral or epidemic trends.

To demonstrate how this is possible, the two researchers set up a theoretical scenario with several people, or nodes, connected in a network, like friends in a social group. They then instituted a game where in each round, each node had to decide whether to adopt a new innovation based only on the current behavior of their neighbors.

For example, a node/person in the game would look around and see how many of his friends were participating in a trend, say, Farmville. If none were, the odds of the node starting to play Farmville were low; if all were, odds of playing Farmville were high. The game was weighted so that imitating neighbors' behavior had a higher payoff than going against the grain.

With only these rules, a social enclave where everyone has perfect information about what everyone else is doing would never adopt anything new. If people only made decisions based on that others were doing, none of the nodes would ever see changing as the best strategy.

To fix this, the researchers introduced some noise into the situation so many nodes had incomplete information. They weighted the decision so that a node with zero information about what his neighbors did would choose to adopt the innovation, whatever it was (this could be considered an analog to a reality where a person doesn't care what others think and evaluates new innovations based on other factors).

When they played around with the structure of the network operating on these rules, they found nodes with local connections, as opposed to the long-range ones that facilitate epidemics, spread innovations more quickly. Nodes that weren't as tightly integrated to the network and maintained fewer connections let change spread more quickly, while nodes with lots of connections actually slowed the spread down.

The highly connected nodes turned into roadblocks, because even without perfect information on its neighbors' outlook, the highly connected nodes get more external pressure from their unenlightened neighbors. A highly connected node must then be extremely ignorant of its neighbors to adopt a trend, or else must be surrounded by neighbors that have switched over first. This was one of the biggest differences between the game-theoretic spread and the epidemic spread.

The model seems to apply less to individual pieces of content, where simple exposure is enough to create huge growth. On the other hand, it could explain, for instance, loyalty to sites that distribute that content, like Digg and Reddit, or to particular genres of memes. The authors say it also crops up in choices that influence social connections, like the choice between voting Republican or Democratic, or to adoption of technology, like choosing between Verizon and AT&T.

Dr. Saberi gave the following example: "the reason I am using Facebook as opposed to another social network is not just its quality it is also because I have a lot of friends who are using it"; he notes this could also apply to operating systems. Likewise, while there are many reasons to choose one cell phone carrier or another, features like free calls or texts within a network can influence a group of friends to migrate to the same network as each other.

In the game theory model, networks trend to an equilibrium of everyone adopting the change—not terribly realistic. Still, the model shows that trends may spread quickly based on something other than the brute force of exposure. Even with a more complex, socially influenced process, the popularity of an innovation can grow rapidly.

PNAS, 2010. DOI: 10.1073/pnas.1004098107 (About DOIs).