March 19 (Bloomberg) -- Leaders who punish followers to promote cooperation and raise overall performance are doomed to failure, according to a U.S. government-funded study.

Punitive behavior in group settings is detrimental and self-destructive, said Martin Nowak, a Harvard University mathematics and biology professor. He and his colleagues based their conclusions on the results of a modified version of the game ``Prisoner's Dilemma'' played by 104 college students. The study will be published tomorrow in the journal Nature.

The five top-ranked players in the tournament never used costly punishments, which are acts that hurt both punisher and opponent. The players who relied most heavily on punishment earned the lowest payoffs in the game and didn't increase the average payoff of the group, Nowak said.

``Our finding has a very positive message: in an extremely competitive setting, the winners are those who resist the temptation to escalate conflicts, while the losers punish and perish,'' said Nowak in a statement.

Other research has suggested that punishment can elicit cooperation in one-time situations where participants aren't worried about damaged reputations or retaliation, the study said. That notion is unrealistic because reputations are ``always at stake,'' and most interactions are repeated, Nowak and his colleagues found.

``Punishment can lead to a downward spiral of retaliation, with destructive outcomes for everybody involved,'' said co- author David G. Rand of Harvard. ``The people with the highest total payoffs do not use costly punishment.''

In this computerized game, the players, who competed in pairs against unknown opponents, chose from three options in each round -- to cooperate, betray or punish. Players earn and cost opponents points based on their decisions.

The study was supported by the National Science Foundation, the National Institutes of Health, and several private foundations.

To contact the reporter on this story: Avram Goldstein in Washington at agoldstein1@bloomberg.net.

Last Updated: March 19, 2008 17:36 EDT