The Kyoto summit initiated an international game of cap and trade. Unlike a national cap‐and‐ trade policy, the essence of this game is the self‐selection of national emission targets. This is like the standard global public‐goods game except that targets are met in the context of a global carbon market. This changes the outcome of the notoriously uncooperative public‐goods game. The equilibrium of the new game may increase or decrease total abatement. If it increases abatement, the resulting carbon price will be no greater than the average public‐goods price. Typically, high abaters in the public goods game will target more abatement in the cap‐and‐trade game, while low abaters will target less. Given such a dismal outcome the Kyoto game should be changed to the global price‐target game. In the same setting where cap‐and‐trade reduces abatement, this game induces optimal abatement. But, realistically, it must include a Green Fund whose strength is linked to the price target. This will induce poor countries to favor as high a price target as rich countries, reversing the polarizing and anti‐cooperative tendencies of cap and trade.