To add to this comment, there’s more nuance when speaking less generally:
* In cases where there is competition between powerful nations, weaker nations can and do gain advantage by playing the interests of one country off of one another. For instance, during the Cold War the United States and Soviet Union would engage in trade, weapons, and security deals. States caught in the middle understood that both empires were competing with one another to either expand their network outward or prevent the other from doing so (America often included “and you may not trade with the Soviet Union” as an aspect of its bilateral negotiations) would try to internalize the security/strategic value that the empires sought - rather than the pure quid-pro-quo of markets.
* The United States effort with both NAFTA and the TPP were to contain Russia and China, respectively, by building a coalition of countries with trade that excludes each specific United States adversary. This strategically weaponizes the second point above: coalitions of nations together banded together against a more powerful economic force. Similarly, the Chinese RCEP agreement bands together trade centered around the Chinese economy, and excludes the United States. Indeed, the Soviet Union was, as a security/power concept, an idea that a trade network on the Eurasian Supercontinent would be able to outperform and outcompete other continental sized trade networks (the United States), which led the United States to disrupt the trade framework with proxy war, etc.
* Similar episodes are common throughout history: Nasser’s Egypt had tried, unsuccessfully, to create a Republic of Arab nations in the Middle East, so that they could collectively bargain and negotiate with external powers such as Europe and the United States. This was considered a security threat to these powers, because the West much preferred strong-on-weak bilateral agreements, protectorates and mandates.
From the security side of the coin, great nations including China, Russia (now the Eurasian Union), and the United States strategically try to build coalitions of small nations against their powerful adversaries in an attempt to disrupt their ability to successfully compete.
The Trump Administration decision to abandon this represents an idea that the United States will be able to “out-deal” regional competitors (primarily China but also Japan, South Korea) on a one-for-one basis. My guess is that the diplomacy will get very nasty - even if its all in the back room.
