In a commentary in PNAS, Thomas Dietz and Jinhua Zhao from Michigan State University, US, suggest using game theory and a scalable method of rewards and punishments (called linear compensation) to help develop strategies that encourage all nations to participate fully in greenhouse-gas mitigation programmes.

"If we assume that each nation will act rationally in its own self-interest, then the path to reducing climate-change risk is to design a set of rules for emissions that countries will agree to because they find the rules beneficial," says Dietz. "Punishments for not meeting the emissions targets are an important part of the design, but these punishments may discourage nations from joining. That's where the mechanism of linear compensation is useful."

Instead of imposing a fixed punishment, linear compensation calls for the punishment to be adjusted relative to how well other nations met the emissions goals.

"So if most other nations also failed to meet the emissions targets, the punishment for each nation would be less – nations would be punished most for being the farthest away from the results of the other nations," Dietz explains.

"A key feature of linear compensation is that if a nation fails to meet its treaty obligations, other nations punish it by reducing their own abatement," says Zhao. "So each nation has leverage: its own abatement helps make other nations abate more. This is the beauty of the linear compensation mechanism."