Competitive Groups Create Unexpected Synchronicity
February 23, 2013

Competitive Social Thinking Leads To Synchronicity, Not Randomness

Jedidiah Becker for — Your Universe Online

A team of psychologists and brain researchers from Indiana University recently used a tweaked and slightly more complex version of rock-paper-scissors to help explore the kinds of competitive group dynamics that govern stock markets, political campaigns and fashion trends.

The aim of the study was to understand what group dynamics look like in situations where the positive or negative outcome of a person´s own decision hinges on the unknown decisions of others. In essence, they wanted to understand what happens to groups when each member is trying to figure out “what do you think I think you think I think.”

According to co-author of the study and doctoral candidate Seth Frey from the Department of Psychological and Brain Sciences at the IU College of Arts and Sciences, "people playing this kind of game subtly influence each other, converging on similar ways of reasoning over time. The natural analogy for the process is to a flock of birds veering in concert."

The authors suspect that the linchpin to this dynamic process is each person´s attempt to think ahead and predict what the others will do.

"Anticipation may be the motor that keeps fads running in circles. It could be a source of the violent swings that we see in financial markets. Anyone in a bidding war on eBay may have been caught in this dynamic,” Frey explained.

“If the bidders are tweaking their increasing bids based on the tweaks of others, then the whole group may converge in price and determine how those prices rise. The process isn't governed by the intrinsic value of that mint-condition Star Wars lunch box, but on the collective dynamics of people trying to reason through each other's thoughts."


In order to experimentally explore this kind of group dynamic, Frey teamed up with Professor Robert Goldstone to create a more complex version of rock-paper-scissors that they dubbed “the mod game.” Using small groups of five or six student volunteers, the researchers asked each participant to choose a number between 1 and 24. In each round, the students were able to earn money each time they chose a number that was exactly one greater than a number chosen by someone else in the group. The numbers choices made a closed loop such that 1 beat 24.

In order to be successful, the participants had to anticipate which numbers others were going to pick and then simply choose the next higher number. The trick, however, was keeping in mind the fact that everyone else was trying to do the exact same thing.

What the researchers found was that those individuals who performed best were not those who were able to think the highest number steps ahead of the others but rather those who thought just the right number of steps ahead. After numerous rounds, the researchers analyzed the results and realized that the ℠right´ number of steps to think ahead turned out to be around two, on average.

According to a popular economic theory, individuals in these types of situations become increasingly successful as they gain experience and increase the number of steps that they are able to think ahead. In the experimental mod game, the participants were allowed to study the results of each round before starting the next round in order to give them a chance to ℠learn´ how the others were behaving. However, instead of simply thinking more and more steps ahead, the researchers found that the participants´ predictions tended to form clusters around one part of the number loop. These clusters would then move around the loop in sync, creating a sort of periodic orbit around the number loop.

What´s more, the researchers also found that this ℠orbiting´ cluster of predictions gradually increased in speed the more the participants played, cycling faster and faster around the number loop with each additional round of the game. This acceleration, however, was relatively modest and far less dramatic than that predicted by dominant experimental economic theory. The students were allowed to play 200 rounds of the mod game, and during this time the average number of steps that they thought ahead only increased from 2 to 2.5.

Finally, the researchers also noticed that the tighter and tighter clustering of guesses tended to benefit all of the players. As the clusters grew denser, the opportunities to earn money increased dramatically compared to initial rounds of the game in which guesses were spread out across the entire number loop.


According to Professor Goldstone, the point of the mod game was to create "an elegant parable in a laboratory context" for the dynamics that take place in the real world when people are basing their decisions on predictions of what other people are thinking. The core question was essentially, “How does the group behave when each individual is trying to second guess everyone else.”

What they found was that people´s guesses tend to converge, an observation that Goldstone says is particularly significant since it flies in the face of a number of commonly accepted behavioral models. Whereas theories like Nash equilibrium predict that these guesses will end up randomly spread around the number loop, the results of Goldstone´s study clearly demonstrate an entirely different type of dynamic.

“We are getting this systematic behavior, which is not random,” he says. "Even though people are trying to beat each other out, they end up in synchronicity."

Frey and Goldstone say that social theories have historically tended to treat group behavior as though it were more or less random and mindless, producing results with no intelligible trends or patterns. But whether it occurs in the form of a billion-dollar Wall Street bidding war or the attempts of fashionistas to keep ahead of the next hot trend, this team believes that their study has given ample cause to suspect that the social dynamics of competitive anticipation are far more complex than many theorists previously suspected.

Their study, titled "Cyclic Game Dynamics Driven by Iterated Reasoning," is now available online at PLOS ONE.