Using stochastic games to analyze evolution of cooperation, leads to a surprising discovery. The tragedy of the commons is resolved if the environment deteriorates in response to defection. The new approach offers invaluable insight into how cooperation plays a role in social issues ranging from sustainability to curbing climate change. It can also help policy makers to design systems which empower cooperation among the public.

At the start, the players begin with the higher-value game. As long as both players cooperate, they continue to play that game, but a defection from either player results in them moving to the lower-value game. Once both players again cooperate, they might return to the higher-value game.

“Amazingly even if both games are set up so that cooperation does not evolve, when we put them together, we get cooperation,” Nowak said. “It’s almost like a paradox.”

The key to making the system work, Nowak said, is the difference in value between the two games.

“If we defect, we are destroying something, but if we cooperate we are building something,” he said. “So when we cooperate, we play subsequently for something that is more valuable, and if we defect, we play subsequently for something that is less valuable.

“That’s what makes the new approach exciting,” Nowak added. “The idea is so simple and yet it changes everything. If you defect in the first game, you lose out twice, because your opponent will retaliate and you have to play a less valuable game.”

The stochastic framework can also be applied to multi-player games, including public goods games and there resolve what is known as the “Tragedy of the commons”.

“Humans are exploiting the environment in a public goods game,” Nowak said. “In the old framework, we decide to cooperate or defect, but the next day we play the same game again, and the state of the environment is always the same. But in our new theory, if we exploit the environment badly, in the next round it may be deteriorated, and then we face a less valuable public good,” he added.

Source: Game changing game changes