Does it bother anyone besides me?

[Occhidiangela]

You seem to be reading my use of the word 'competition' as 'sport'.  (I was thinking in terms similar to evolutionary usage, or optimisation situations such as the Prisoners Dilemma where an increase along a particular independent axis may result in different levels of increase (or decrease) in two or more dependent axes)

As to the actual discussion, I'm not sure how you are using the term 'rival' either, unless you also consider your allies rivals as well?

In a hypothetical world, if Britain had the economic potentail of China, but the same political relations with the U.S. as it does in the real world, then would you vew it as a strategic rival?

Also, from your point of view, why is it neccessary for the U.S. to be the dominant force?

... I just realised I haven't put a smilie in this thread yet... perhaps therein lies my problem  ;)
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Some good questions, let me try to do them justice.

Japan is a trade rival in some respects, a trade partner in others, and a security partner in all respects to ensure stability that allows the trade in which we are rivals. Europe are economic rivals, yet we tend to be security partners and trade partners. China is a power rival, and we are NOT security partners as yet. If that changes, the security calculus in the Pacific Rim changes dramatically. US - USSR were power rivals. Shades of meaning, so easy for it to be vague. US and Russia need to be trade partners, security partners, and possibly trade rivals. That makes for peace.

Why is it necessary for the US to be dominant?

When other power blocks are dominant or co equal, we have World War. That is history. That fact makes our move into Iraq in 2003 all the more troubling, since if we weaken ourselves through that endeavour, the multi polar set up becomes LESS stable. Multi polar is how World War I started. Seven Years War. Thirty Years War. World War II. And so on.

Britain and the US operate under similar cultural assumptions, but not identical ones. US and China have few shared cultural assumptions in comparison. That analogy does not hold, since there are fewer areas of common interest to build on as paths to avoiding conflict where we diverge in approach.

Game theory approach is probably a valid lens through which to view the next couple of decades, particularly if the blocks line up as I expect they will. I tip my chapeau to you on that one. :) It also means to get the head out of the sand in re China, where it has been since WJ Clinton was in the White House.

Occhi