What is the rational course for US foreign policy regarding e.g. the Taiwan problem? What is China's? What is Taiwan's? Are the US, China, and Taiwan currently acting in rational ways in regards to this geopolitical issue? If not, why? If every actor was acting rationally, would this result in the possibility of cooperation to solve the problem peacefully? Or does at least one actor's rational course of action necessarily put them on a 'collision course' with the others? Or, worse, for this situation, is it possible that it is in every actors' most rational course of action to desire the same peaceful resolution/treaty, but some type of tragic coordination problem renders this impossible?
To avoid this being a culture war topic, let's avoid talking about what type of resolution would be best in the sense of most moral, just, etc. Let's only discuss what would be the most rational course of action for every party involved, whatever that may mean.
Of course there have been many attempts to solve geopolitics in the past (see: the various schools of international relations theory). Even still, I'd hope that this wouldn't prevent us from having a discussion of our own about this. Most schools of IR theory attempt to explain why nations do what they do, and some schools ascribe this to possibly non-rational reasons e.g. social constructivism which says that sometimes culture of a nation might explain that nation's actions, and of course often times cultures can hold irrational beliefs or encourage irrational actions. Other schools e.g. realism attempt to explain international relations by stating that nations are rational actors at least as wealth/power-maximizers, but this is obviously contentions, and even if true it could be said that nations that always act as wealth/power-maximizers are not acting rationally, etc.
I'll start the discussion by giving an example of what I consider to be an extreme version of an irrational geopolitical actor, and one for whose actual historical actions have well-understood explanations other than rational behavior: the Empire of Japan after the Meiji restoration. At a certain point it became clear to many Japanese elites that their country was on an undesirable path, one that put them on a collision course with the United States. This war was correctly predicted by many Japanese leaders to be an un-winnable war, if not at least a highly undesirable one. With this in mind, it would probably have been 'most rational' for Japan to abandon their colonial possessions in Manchuria and Korea in the interwar period in order to avoid war with the US, rather than starting a new and more ambitious war with China to try and expand their empire to acquire the natural resources required to prop up those colonies, instead. However, due to ideological sentiment, any Japanese leader against the expansion of empire was essentially selected against by a series of ultranationalist assassins, leaving only irrationally hawkish leaders to direct their country in terms of foreign policy. Thus, Japan irrationally went to war in China, which eventually brought them into war with the US which was disastrous for them.
And, I will provide examples of what I consider to be rational geopolitical actors, as well: both the US and the Soviet Union during the Cuban missile crisis. The Soviet Union initially began to emplace nukes in cuba for a variety of reasons, but for one because they correctly determined that they were at a disadvantage in terms of MAD and putting nukes in cuba could bring more core American territory into range, in order to better ensure their deterrence against a US first strike. Ensuring national security against that of e.g. nuclear destruction, for example, seems to me like a rational goal. The US felt rationally quite threatened by the development, and as well felt their global political situation was threatened unless the responded properly, and so there was a crisis. The US considered doing nothing, which is a rational thing to at least consider, but correctly concluded that a better outcome for their own self-interest could be reached by brinksmanship. The US (namely, Kennedy) also rationally decided against a full scale invasion of cuba despite the unanimous advice of the joint chiefs, probably correct in his assumption that an escalation such as that would have been beyond the pale, and would probably be matched by a soviet invasion of at least west berlin, etc, which would necessitate further escalation, and so reasoned again that a better resolution could be reached through diplomacy. Eventually, the crisis was resolved through a decently clever compromise, with the nuclear disarmament of cuba in exchange for the secret nuclear disarmament of turkey -- a resolution which involved both actors properly considering the others' positions and being willing to make concessions in order to accommodate for the other's circumstances, rather than being driven by ideology, pride, etc. at least in and of themselves. Khrushchev is considered to have lost face from this outcome, and it perhaps seriously contributed to his eventual ousting two years later, but considering the alternative was potentially nuclear armageddon, (i.e. a situation which would have greatly harmed the Soviet Union) it seems notably rational to have leaders at the helm of your nation willing to lose face/sacrifice their own personal career in order to achieve better outcomes for the nation as a whole such as not having it destroyed by nuclear bombs. If any actor can be said to be irrational in this situation, it might be the United States considering that there is an argument to be made that nukes in cuba wouldn't have seriously worsened the soviet nuclear threat and that Kennedy/US was more beheld to the irrational whims of the US public, and that they should have been the ones to rationally decide to take the PR hit by 'losing' the crisis in order to avert even the risk of extremely negative outcomes posed by engaging in brinksmanship. However, I think both the US and the USSR acted rationally enough on balance, at least to demonstrate enough individual examples of rational international relations behavior over the course of the historical anecdote, for the example of them as 'rational' to be sufficient.
With this in mind, how should we describe the geopolitical courses of China, the US, and Taiwan regarding the problem of Taiwanese sovereignty? Are any, or perhaps multiple of the involved actors making decisions meaningfully similar to imperial Japan on the leadup to war with the US i.e. irrationally? If so, why? Or are any or perhaps multiple of the involved actors acting more like the US/USSR during the cuban missile crisis, i.e. acting rationally -- but perhaps still on a collision course, even possibly on a collision course with other rational actors?