The original answer assumed a much larger catastrophe than what appears to be the case based on previous eruptions and any projected events in the future. This edited answer proposes scenarios for a situation where complete, global, ecological collapse is not presumed to be imminent. However, depending on the magnitude and duration of such an eruption, the result could possibly imply dire consequences for global ecology. For example a month long eruption of the Yellow Stone caldera would almost completely coat the North American Continent in ash. This obviously implies complete shutdown of the economy of the continent, not to mention the devastation at ground zero from the explosion and greater than 1 meter of hot ash, however the global ecological impact is less clear. Does this mean a darkening of the skies for a period of one to several months over a significant portion of the planet? In the longer term, would the released gases significantly contribute to global warming, and how much of the sky darkening would offset such effects (via shading/reflecting the sun back into space) in the short term? These question are not addressed in this answer as they delve into longer term effects and the initial conditions which lead to those effects.
That said, here are some economic numbers which can help to narrow down the effects of the economic shut down of the North American Continent. For this purpose we will assume that the dominant econimic driver of North America is the United States and for simplicity we will exclude Mexico, which will be less affected by the eruption. The approximation is roughly as follows:
U.S. Imports (2015) $2.76 trillion
U.S. Exports (2015) $2.23 trillion
Canadian Imports (2015) $418.8 billion
Canadian Exports (2015) $407.1 billion
This means that Canadian imports and exports are ~15% and ~18% of the United States respectively.
Since about 75% of Canadian exports are to the United States and 50% of Canadian imports are from the United States, this means that we can subtract 75% of Canadian exports from the the U.S. imports total and 50% of Canadian imports from the U.S. exports total. This gives us the following amounts:
Estimated North American Import and Export Shutdown after Super Eruption
North American Imports $2.45 trillion
North American Exports $2.02 trillion
Now, to put this into perspective, global exports in 2014 in goods and services totalled $23.9 trillion, which means that North America represents about 10% of global exports.
In 2009 the World Trade Orgainzation, in a press release, projected a 9% decline in global exports as a result of the global economic collapse of 2007-8.
So this clearly links the removal of North America from the world economy to an economic down-turn, which at best would occur on the scale of the housing crisis and the effects of that. However, the issues with the economic collapse of the 2000's were financial in nature and there were no other natural or otherwise condemning circumstances to induce a deeper collapse of the world economy. In the case of catastrophic damage to North America, I would venture to speculate ( based on my virtually non-existent understanding of economics ) that a post-super-eruption world-economic collapse would be much deeper, more sustained and more vulnerable to ripples, which would be further propagated and perhaps amplified by North America's total collapse, and the combined effects of this would plunge the world into a total depression which would last several decades, perhaps half a century or more.
The best comparisson we have to such a scenario is the Great Depression which lead us into [incorrect]
World War I, and subsequent power shifts and struggles which re-emerged in [corrected] World War II. The Great Depression lasted about a decade from 1929 to 1941 when we entered WWII. From historical accounts, it seems that the US privately wanted a way into WWII as our leadership knew that it would help us recover from the depression and we got that opportunity when Japan bombed Pearl Harbor.
It is commonly opined, in high school history classes and backyard barbeques, that government spending in the run-up to World War II "got us out of the Depression."
And the politics are complicated. Up until the decision to enter. Roosevelt's public position was one of non-entry:
"I have said this before, but I shall say it again and again: your boys are not going to be sent into any foreign wars." - Roosevelt, 1940
The US was sucked further towards the conflict when its navy and air force began to ‘escort’ British convoys which transported Lend-Lease material across the Atlantic, protecting them from German submarines. Roosevelt’s announcement of a ‘shoot on sight’ policy in September 1941 following an attack on the USS Greer enraged isolationist senators; they alleged that Roosevelt was deliberately provoking skirmishes with the Germans. Meanwhile, Churchill repeatedly attempted to convince Roosevelt to enter the war.
However, the post eruption scenario is quite different. I would speculate that something like this would be worse than the Great Depression. My guess is that large scale conflict like what we saw in
the two world wars WWII would be less likely since the world would be so devasted, trade, and as a result production, would be so depressed that coordination on the scale of a world war would simply be impossible and for the remaining powers to sit at home, bicker at a distance and lob inter continental missles at each other would be pointless. However there may likely be a global devolvement into internal conflicts and power struggles for the better part of a century. Global economics would have to recover considerably before any kind of global conflict or outright war would help anyone to accomplish their goals.
So to answer the question of the global balance of power. The global economy would probably quickly collapse and render most governments largely ineffectual. Much of the world would devolve into something along the lines of tribal or clan based government and most conflicts for some time would be small and over local resources and control of local groups or clans.
You are describing a post apocalyptic world where politics will be reduced to might, endurance and wit to control enough resources to survive. Perhaps some groups already closely linked to the military will effectively defect, acquire strong holds, weapons, munitions and supplies and set out to build a new future, but among them will likely be back stabbing, morale will easily degrade and loyalties which once seemed meaningful will lose a great deal of perspective. Of course there will be some individuals who had little to live for to begin with, who drone on without much thought of the differences in the world and without much affect over the losses of others. We typically refer to such individuals as sociopaths, but in this case they would become your true survivors as this kind of thinking is necessary to prevent the above hinted kinds of moral and ethical dilemmas that most "normal" people would face.
If anyone survives the cataclysm, the detonation and the winds that will likely result from a huge movement of Earth mass through the atmosphere, a few hours later when the entire sky goes black and huge chunks of Earth rain down without warning, geo-politics will be immediately discarded from most everyone's minds, unlikely to return for perhaps centuries.
Suggestion, choose survivors from different classes and walks of life and explore why they survived, i.e. what makes them keep ticking, who loses how much and what parts of their humanity, and who holds on to how much of their humanity and which parts of ones humanity really seem to matter, if at all in that situation.