International climate cooperation needs to be negotiated among sovereign countries. The key to cooperation, and to countervail free riding, is reciprocity. Using game theory and a human subject experiment, we show that reciprocity can be built into the negotiation design. Human players negotiating a reciprocal common commitment are substantially more successful in promoting cooperation than when negotiating individual commitments. Moreover, focusing on a uniform common commitment strongly facilitates agreement, as compared to negotiating a vector of commitments, one for each player. Because a carbon price is a natural candidate for a uniform common commitment, our findings suggest that international climate negotiations should focus on reciprocal carbon pricing. Economists advocate carbon pricing for its cost efficiency, yet the role of carbon pricing for promoting cooperation could be at least as important.