Lord Alfred Tennyson described nature as “red in tooth and claw,” yet species from ants to humans consistently defy that depiction with acts of generosity and cooperation.

Now a new study by Alexander Stewart and Joshua Plotkin of Penn’s Department of Biology provides a mathematically based explanation of why generosity abounds.

The researchers made their insights by examining a construct known as the “Prisoner’s Dilemma,” a match-up frequently used by game theory economists to study whether individuals choose to cooperate or not. In the two-player version of the game, if both players cooperate, they earn a particular payoff. If one cooperates and one doesn’t, the cooperating player suffers while the defecting player receives the highest payoff. And if both players defect, both receive a payoff, but it is smaller than what they would have earned if both cooperated.

Putting a twist on the game, Stewart, a postdoctoral researcher, and Plotkin, an associate professor, set up the competition so that instead of there being only two players, an entire evolving population played the game repeatedly. Such a competition would mimic a natural society of humans or animals; successful players would have more opportunities to “reproduce,” or pass along their winning strategies to the next generation of players.

Reporting their findings in the journal PNAS, the scientists found that so-called “extortion” strategies, in which one player dominates another and forces his opponent to accept a lower payoff, did not fare well when played in a large population. On the other hand, generous strategies, in which players favor cooperation and even allow their opponents to maintain higher payoffs, found great success.

“You might think being generous would be a stupid thing to do, and it is if there are only two players in the game,” says Stewart. “But, if there are many players and they all play generously, they all benefit from each other’s generosity.”

Not only did generous strategies persist as the game was played over and over again, they were, in fact, the only strategies that succeeded in the long term. The result helps address the question of why generosity and cooperation have evolved.

“It’s a natural question that anyone with a conscious might wonder about,” says Plotkin. “There is a compelling explanation, even in this abstract scenario, for how generosity arises—and this should really resonate with people.”