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The classic rock-paper-scissors game encourages a strategy of second-guessing. In this particular showdown, "rock" (the closed fist) beats "scissors" (the forked fingers). "Paper" is represented by an open palm.

When people try to second-guess a rival, they don't eighth-guess or ninth-guess them: Using a glorified version of the classic rock-paper-scissors game, researchers have found that players tend to converge on a strategy of thinking around two steps ahead.

They say their findings could shed light on other pursuits where rivals have to engage in cycles of second-guessing — including fashion trends, political campaigns and the financial markets.

"Anticipation may be the motor that keeps fads running in cycles," Seth Frey, a doctoral candidate studying psychology and brain science at Indiana University, said in a news release. "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. 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."

Frey and Robert Goldstone, who directs the Percepts and Concepts Laboratory at Indiana University, designed a laboratory experiment designed to find out how strategies changed over repeated cycles. They decided against the relatively limited repertoire of rock-paper-scissors — the hand-flashing game in which scissors cuts paper, paper covers rock, and rock dulls scissors. Instead, they used a guessing game in which players guess a number between 1 and 24. A player wins a point when he or she guesses a number exactly one step higher than another competitor. There's one exception: 1 beats 24.

During 22 sessions at the university, 123 psychology students participated in the "Mod Game," in small groups. Each point that was won in the game earned a player 10 cents.

The results were published online by the journal PLOS ONE on Monday. Players could have simply guessed random numbers during each round, but that's not what happened. Over the course of repeated guessing games, the players tended to fall into the pattern of raising their guesses in a cluster that cycled through all the choices. The behavior suggested that players tried to guess what their rivals were guessing about their guess. In a video, Frey compared the pattern to a famous poisoning scene in the movie "The Princess Bride."

As the guessing games continued, the speed of the cycling accelerated. After 200 rounds, the rate of cycling gradually reached an average of 2.35 "thinking steps," Frey and Goldstone reported. They suggested that a synchronicity in the guessing was beneficial for the group as a whole, because the players earned no payoff if they thought too far ahead.

"At a core level, people's guesses do converge, and that's interesting because dominant models suggest otherwise," Goldstone said in the news release. "Even though people are trying to beat each other out, they end up in synchronicity."

More about the science of rock-paper-scissors:

• Rock-paper-scissors robot will beat you every time
• Science reveals how to win at rock-paper-scissors
• Judge orders rock-paper-scissors to decide dispute

Alan Boyle is NBCNews.com's science editor. Connect with the Cosmic Log community by "liking" the log's Facebook page, following @b0yle on Twitter and adding the Cosmic Log page to your Google+ presence. To keep up with Cosmic Log as well as NBCNews.com's other stories about science and space, sign up for the Tech & Science newsletter, delivered to your email in-box every weekday. You can also check out "The Case for Pluto," my book about the controversial dwarf planet and the search for new worlds.