The Grand Chessboard

One of the premiere international theorists of our time, Zbigniew Brizezinski, wrote a book about 12 years ago entitled The Grand Chessboard, where he set forth a description of and justification for American global primacy and dominance.  It is very possible that it is reasons like this that are behind Obama's decision to stay involved in Afghanistan.  Afterall, he was one of Obama's professors at Columbia University.

For America, THE chief geopolitical prize is Eurasia. For half a millennium, world affairs were dominated by Eurasian powers and peoples who fought with one another for regional domination and reached out for global power. Now a non-Eurasian power is preeminent in Eurasia—and America's global primacy is
directly dependent on how long and how effectively its preponderance
on the Eurasian continent is sustained.

Obviously, that condition is temporary. But its duration, and
what follows it, is of critical importance not only to America's wellbeing
but more generally to international peace. The sudden emergence
of the first and only global power has created a situation in
which an equally quick end to its supremacy—either because of
America's withdrawal from the world or because of the sudden
emergence of a successful rival—would produce massive international
instability. In effect, it would prompt global anarchy. The
Harvard political scientist Samuel P. Huntington is right in boldly
asserting:

A world without U.S. primacy will be a world with more violence
and disorder and less democracy and economic growth
than a world where the United States continues to have more
influence than any other country in shaping global affairs. The
sustained international primacy of the United States is central
to the welfare and security of Americans and to the future of
freedom, democracy, open economies, and international order
in the world. (P. 30)