They visualize a U.S.-China bilateral deal to limit emissions (mainly of carbon dioxide from fossil-fuel burning) that would operate in parallel with the Kyoto Protocol (which neither country plans to ratify). In their plan, the United States buys emission rights from an arbitrary excess quota allotted to China. The authors call it headroom but I call it a subsidy. The United States pays, China gets, and the atmosphere does not benefit because emissions continue essentially unabated.
Fallacy: impossible expectations