U.S. Treasury Secretary Janet Yellen is headed to a China determined to avoid open conflict with the United States, yet the world's two largest economies still appear to be hashing out the rules on how to compete against each other.

There are tensions over Chinese government support for the manufacturing of electric vehicles and solar panels, just as the U.S. government ramps up its own aid for those tech sectors. There are differences in trade, ownership of TikTok, access to computer chips and national security — all of them a risk to what has become a carefully managed relationship.