These countries – allies, strategic competitors, and potential foes alike – probably acted the way they did because they saw the downside of a world devoid of American power. For the allies, the calculus is simple: America guarantees their security.
For India, America provides a hedge against Chinese power. For China, an America-less Asia would bring to the surface latent but lethal rivalries among Japan, North Korea, South Korea, Taiwan, and China that could engulf Asia in war.
As for Russia, the demise of America would leave it alone facing a 1.3 billion-strong Chinese nation potentially eager to settle the empty former Chinese lands in the Russian Far East. America is uniquely valued as a market, a source of technology, and a place to educate elites.
Additionally, painful as it will be domestically, global recession ultimately will probably hurt other nations more than the United States. In China, Russia, Southeast Asia, and the poorer oil producers, economic downturns risk serious social and political upheavals. And in the developed world, neither the major European economies nor Japan are faring significantly better than the US. In relative terms, then, American power is not likely to decline as a result of the slump.
While these factors only mitigate the consequences of the financial and economic crises, they also suggest that the US could emerge stronger on a relative basis.