Is there anything the US could give North Korea that would make it end its nuclear and missile programmes?
Given the escalating war of words between the US and North Korea, and Donald Trump's warning of "fire and fury" if Kim Jong-un overtly threatens the United States or launches missiles against the US territory of Guam, it is unclear how useful diplomacy is as tool for moderating regional tensions.
Secretary of State Rex Tillerson and other senior Trump administration officials have stressed the importance of diplomacy, and even Mr Trump has in the past offered to talk to Mr Kim, but there are no signs that the North Koreans are open to dialogue.
Recent informal track two level talks with North Korean officials in Europe suggest that Pyongyang is single-mindedly focused on continuing with its missile and nuclear-weapons testing programmes.
Strikingly at the Asean Regional Forum meeting in Manila recently, there was no meeting between Mr Tillerson and Ri Yong-ho, the North Korean foreign minister, and a proposal for talks between Seoul and Pyongyang offered by Kang Kyung-wha, the South Korean foreign minister, was summarily rebuffed by the North Koreans.
In principle, there are incentives that the US could offer the North, including talks on a peace treaty ending the Korean War, preliminary steps towards diplomatic recognition (such as the establishment of a US liaison mission in Pyongyang), or an agreement on conventional arms reductions on the peninsula, but these are at best long-term objectives.
The North's repeated violations of past diplomatic agreements with the US has eroded any appetite for concessions in Washington where there is deep-seated distrust of the North on both sides of the political aisle and an assumption that pressure, via the latest round of tougher UN sanctions targeting the North's mineral and food exports, and restrictions on North Korean overseas labour, is the best way of bringing Pyongyang to heel.
Is North Korea's ultimate or unswayable goal the possession of a nuclear deterrent?
Since coming to power in late 2011, Kim Jong-un's priorities have been focused consistently on two simple objectives of military modernization and delivering economic prosperity for the North Korean public.
The North's nuclear aspirations date from the 1960s and are consistent with the regime's desire for political and military autonomy in the face of opposition not only from its traditional enemies such as the United States, Japan and South Korea, but also over the objections of its historical partners such as China and Russia.
Why?
Part of the North's motivation is a rational assessment of the country's strategic interests. The experience of Libya and Iraq is a reminder to Pyongyang that the only guarantee of national survival is the possession of a credible weapons of mass destruction capability.
While Washington has expressed no "hostile intent" to the North, Pyongyang maintains that the United States, as a conventionally superior and nuclear armed power, with 28,000 troops in South Korean, and a policy of maintaining a first-use nuclear option, represents a clear threat to the country.
Mr Kim's nuclear and missile testing ambitions are also an expression of identity politics. The legitimacy of the Kim dynasty's political leadership is rooted in a narrative of defence against an implacably hostile United States.
The 1950-53 Korean War, framed in North Korean propaganda as the result of direct US aggression, is used to depict the United States to the North Korean people as an adversary intent on destroying the country.
For the country's older generation that recall US actions during the war, when virtually every urban centre in the North was obliterated by American bombing, this narrative is a convincing one and is routinely reinforced for the wider population in the state's daily political messages.
Mr Trump's recent bellicose public statements are a propaganda gift to Kim Jong-un, allowing him to bolster his standing as the nation's commander in chief and protector of the country.
Could a nuclear-armed North Korea co-exist with the US?
The North's accelerated missile testing campaign and last year's two successful nuclear tests have materially enhanced the country's deterrent capabilities.
Recent intelligence reports from the US have suggested that the country may have as many as 60 nuclear bombs (a figure disputed by some analysts) and its long-range missile tests of 4 and 28 July indicate that the North may have the capacity to hit parts of the United States.
A recent report in the Bulletin of Atomic Scientists has questioned the extent to which this improved missile capability genuinely allows the North to deploy a nuclear warhead against the US, but there is little doubt that Pyongyang has made dramatic progress in the last year in securing full de-facto membership of the nuclear club.
Washington, however, has made it clear that it will not recognize or tolerate such a development. To do so would offer a propaganda victory to the North, critically undermine America's relations with its key regional allies - Japan and South Korea - prompt a destabilizing arms race in the region, and destabilize the global nuclear non-proliferation regime.
Is any of what North Korea wants realistic?
Pyongyang's priority is to push ahead aggressively with testing, both of its missiles and its nuclear weapons, in an effort to solidify its deterrent capabilities. For Mr Kim, this makes sense as means of boosting his political authority and legitimacy at home.
He can take comfort from China's apparent reluctance to impose, serious crippling economic restrictions on the North, despite its recent support for tougher UN sanctions.
He can also calculate rationally that ultimately the United States, as many experienced observers are arguing, will accept the need to negotiate some form of intermediate freeze in the North's military capabilities in the hope that this will stabilize the strategic situation while keeping the door open to future disarmament.
By then, Mr Kim may hope he will be able to secure a range of concessions from the US and South Korea, whether in the form of economic assistance, conventional arms reductions, or more importantly the political respect and status as an independent, sovereign state that the North has long craved.
The wild card in the current situation is how far President Trump's rhetorical brinkmanship will deter the North from pushing ahead with its missile testing programme. The North Korean military has threatened to test fire four intermediate range missiles in the vicinity of the US military facilities on Guam later this month.
No US President could tolerate a direct attack, but a test launch in the international waters close to the island would arguably represent a "grey zone" contingency that would require a more nuanced response, stopping short of full-blown military conflict.
Discussions of the current stand-off have focused on the parallels with the Cuban Missile Crisis of 1962 and the strategic judgment of the US president at the time, John F Kennedy. His caution in seeking to avoid nuclear war was shaped by his reading of Barbara Tuchman's book The Guns of August and its insights into the lessons of World War One.
It is ironic and telling that once again August is a time of acute strategic risk and uncertainty, when the rhetoric, assessments and actions of national leaders are likely to carry profound significance for regional and global security.
