If you can stand a brief return to your college days, here is an idea based on international theory I developed—and a distinct way to deal with North Korea, by the U.S. and China, that follows.
The theory calls for conflict resolution based on salience differentials. Salience is defined as the relative importance or significance that an actor ascribes to a given issue. Salience-based bargains exploit the differences in salience that each party ascribes to the respective issues. For example, Country A and Country B may have disputes over issues x, y, and z. Country A considers issue x to be the most vital to its national interest, and although it contests issues y and z, it does not regard either as a core interest. Country B meanwhile considers issue z to be of paramount importance. A salience-based bargain then might involve Country B making concessions on issue x, Country A making concessions on issue z, and some sort of compromise over issue y.
How can the salience-based bargaining method be applied to Sino-U.S. relations? First, both sides would need to rank their interests, although not necessarily publicly. It is probable that stopping additional development of the North Korean missile and nuclear program—and preferably rolling it back—is very high on the U.S.' list for obvious reasons. The question then is what interest is salient enough for China to assume the high costs of pressuring North Korea to cap or cut back its program? And can the United States accommodate these interests at a low cost to itself?
The best approach is to ask China what it would take to ensure its cooperation. China might have a high interest in gaining assurances that if the North Korean regime collapses and the two Koreas are unified, the United States will not move its troops to the border with China. (It may prefer for the entire Korean Peninsula to become a neutral buffer zone). This is a no- or low-cost proposition for the United States, because once the North Korean nuclear program folds or the regime collapses, the United States would have little reason to move its troops north.
Second, China might ask for a U.S. commitment not to install the Terminal High-Altitude Area Defense (THAAD) missile defense system, which is currently due to be installed in 2017 in South Korea. China may well ask for more, and the U.S. may find that it can agree to stop the almost daily reconnaissance flights up and down China's coast lines, which China finds very troubling and which are of little value to the U.S. Most of the intelligence collected in this way is of value only if the U.S. plans to attack the mainland within weeks or months. It reveals which Chinese military units are in place, who their commanders are, how they communicate and so on. However, most of these details change over time, and thus are of limited value if one believes—as most military analysts agree—that China is at least a decade away from being ready to confront the U.S. China may also ask for U.S. planes to comply with the Air Defense Identification Zone (within which all planes are required to identify themselves), which China has declared it seeks to enforce over most of the South China Sea. China may have other items it considers salient that the United States does not. These are best revealed through bargaining.
Both sides may wish to add other items to the negotiations. For instance, the U.S. has a clear interest in ensuring that terrorists do not obtain nuclear weapons in Pakistan, which is a particularly pressing concern, as Pakistan's nuclear arms are not well secured. China has much more leverage over Pakistan than does the U.S. because China is a major supplier of arms to Pakistan; in fact, over half of Pakistan's weapons imports come from China. China also has much more substantial investments in Pakistan, possibly twenty times higher than those of the U.S. One can only guess what China will seek in return, although it may well include the U.S. ceasing to arm countries that border China.
This approach suggests that there is room for productive negotiations between the U.S. and China that do not entail either side yielding to the other or making unilateral concessions, as long as one takes into account the great differences of what truly matters to each nation.
