There are two options. One is to pursue the line of bravado. Deepen the engagement, and hope Mr Putin and Mr Xi Jinping both blink before Mr Obama does.
In the Baltic, match the deployment of short-range nuclear weapons that Russia has just deployed in Kaliningrad. In the Ukraine, provide more weapons, invite the Ukrainians to join Nato and deepen the sanctions against Russia. In Syria, create a no-fly zone by handing over air-to-surface weapons so the rebels in Aleppo can, from the ground up, turn Syria into a graveyard for Russians.
In the South China Sea, ignore the need for China to be treated with respect, intensify military speed runs past or over disputed areas and deepen the military relationships and exercises in the area.
The risk is that all of the allies of the superpowers have limits in military, ethical and political terms. The further the superpowers get engaged in distant wars, the more likely it is that things spin out of control. Accidents, mistakes and anger at a distance, in a world where nuclear triggers are set on 15 minutes timers, is the likely path to destruction.
Depending on how the superpowers react to such events, we all could be dead within a matter of hours.
The other option is to reach for a grand deal and lower the rising temperatures. A grand deal, made up of three parts, is necessary as all of the potential causes for conflict are interconnected.
First, in the Ukraine, accept that the Crimea is gone. Sanctions should be lifted if an internationally monitored referendum of the populations under occupation, are happy with the outcome.
If so, the Ukraine should promise it will not attempt to join Nato for at least a decade and the Russians should accept an internationally mandated investigation to examine what happened to MH17.
Second, Syria should be divided. As it was with the recent wars in Yugoslavia and Sudan, the hatred can be greater than the traditional boundaries of sovereignty and peace can only be achieved by divorcing the communities that once lived together.
An independent Kurdistan should be carved out of Syria. If Assad cannot be persuaded to leave power, the remaining land should be split between those who wish to live under an Assad-based dynasty, and those who wish to pursue a different path.
The different path must be secular, democratic and consistent with the values of the international community. Terror groups, such as Islamic State, must be fought through the United Nations, not the independent aims of the permanent members of the Security Council or their proxies.
It needs to rain peacekeepers, international aid, and a coordinated approach. Unfortunately, amnesties for atrocities may need to be given in exchange for truth commissions.
Finally, in the South China Sea, the entire area needs to be demilitarised. All of the countries that have claimeddisputed islands must not be able to plant them with weapons. The disputed areas should be dealt with through diplomacy and agreement. Cooperative and equitable arrangements for the sharing of resources should be pursued, or the disputed areas should be sold, or traded, to those who really want them.
Removing the nuclear potential of North Korea could be worth the price of a few disputed rocks in this area.
If neither of these options is possible, all claims to sovereignty in the area should be frozen for at least 50 years and a new international regime, which demilitarises the area should be sought.
The energy of the superpowers should then go into cooperative goals based around science and conservation, not competitive sabre rattling.
