American foreign policy: Please don't go The World America Made. By Robert Kagan. Knopf; 149 pages; $21. Random House; £14.99. Strategic Vision: America and the Crisis of Global Power. By Zbigniew Brzezinski. Basic Books; 208 pages; $26 and £17.99. No One's World: The West, the Rising Rest, and the Coming Global Turn. By Charles Kupchan. Oxford University Press USA; 272 pages; $27.95. To be published in Britain in May; £16.99. Bending History: Barack Obama's Foreign Policy. By Martin Indyk, Kenneth Lieberthal and Michael O'Hanlon. Brookings Institution Press; 342 pages; $29.95 and £18.99. Obama and China's Rise: An Insider's Account of America's Asia Strategy. By Jeffrey Bader. Brookings Institution Press; 172 pages; $26.95. To be published in Britain in April; £18.99. AMERICA is irrepressible. Even authors fixated on its decline are optimists in disguise. Times may be hard and the world order is changing, but America has what it takes to bounce back, according to five new books on foreign policy. Indeed, it has to bounce back, because no successor stands ready to shoulder these responsibilities. In "The World America Made" Robert Kagan, a prominent neoconservative, argues that the liberal order America created after the second world war may not endure if America loses the power or will to defend it. As hegemons go, America has been exceptional. Democracy has spread under its watch, and its geographical isolation has made the world surprisingly accepting of its use of force. No combination of nations has felt the need to join together to counter America's power, leaving it free to perform vital tasks in the common good, such as keeping open trading routes. To those who believe that a multipolar world could be at least as peaceful as the one dominated by America, Mr Kagan says history proves otherwise. Rules rarely outlast the powers that created them. Nations go to war when they are "in doubt about which is stronger," he writes. The world is more stable when one nation dominates, especially when it is a nation like America. It is therefore fortunate, Mr Kagan concludes, that most talk about America's decline is overblown. The country has passed through such moods before, during the trauma of Vietnam in the 1970s, for example, and then again in the 1980s during Japan's breakneck ascent as an industrial power. And yet it bounced back. Although past success does not guarantee future triumph, the American system, with its relative freedom, is uniquely capable of recovering and adapting. The danger will come only if Americans believe they can put their global responsibilities on hold while they set their own house in order. Zbigniew Brzezinski, Jimmy Carter's national security adviser, is equally certain that a vigorous and powerful America is indispensable. But he shows more doubt in his new book, "Strategic Vision." He contends that America must wrestle down its own debt, steady its financial system, reduce inequality, rebuild its infrastructure and fix its gridlocked politics. Abroad, it must promote and guarantee an expanded West (embracing Russia and Turkey) and balance the great powers of Asia. Like Mr Kagan, Mr Brzezinski does not believe America's decline is foreordained. Its economy is still relatively vast, its population wealthy and young, its businesses and universities innovative. But if decline is not inevitable, nor is resurgence. He states that America is in danger of sliding into "systemic obsolescence," caused by political stalemate at home and misguided engagement abroad in "lonely and draining campaigns" against sometimes "self-generated" enemies, such as Iraq. If American leadership does collapse, what then? Like Mr Kagan, Mr Brzezinski argues that no single power is ready to supplant it. He foresees instead a protracted period of chaotic realignments. China may be ambitious and proud, but it is still in the throes of modernisation; it knows that its continued rise depends for now on the present order. A nationalist and militaristic China would swiftly isolate itself as anxious neighbours allied against it. For now it seems the alternative to a world dominated by America is "No One's World," the title of Charles Kupchan's book. A professor of international relations and a veteran of the Clinton White House, he is the gloomiest of these authors. For the first time in history, he says, the world will have no global guardian. Western policymakers are deluded to think that they can use their twilight of pre-eminence to lock rising powers into their own values and institutions. It is going to be much harder than that, Mr Kupchan says. The spread of liberal ideas has been driven less by their intrinsic appeal than by the material dominance of Western countries. Democracy might still advance, but not fast enough to match the great rebalancing of power now under way. And even if the rising powers do come to share the West's values, they will clash over status and prestige, because they feel that this is their turn for a place in the sun. The West "will have to give as much as it gets as it seeks to fashion a new international order that includes the rest." For example, the West will need to stop preaching that only liberal democracies are to be considered legitimate governments: "responsible governance" should be enough to put a state in good international standing. To his mind, America's "overzealous" promotion of democracy in Bosnia, Iraq and Afghanistan did more harm than good. The West must now show greater respect for the sovereignty of other nations and treat China with "a nuanced mix of engagement and containment." Grand theories of foreign policy are entertaining. The actual work of it is far messier, as shown in "Bending History," a close review of President Barack Obama's first term by three scholars at the Brookings Institution. They find that for all his inspiring speeches, the president's performance has at best been workmanlike. In fact the lofty speeches are a problem: they have often seemed detached from actual policy, raising expectations he cannot fulfil. The Brookings authors conclude that much of Mr Obama's agenda remains incomplete. Killing Osama bin Laden and decimating al-Qaeda were successes, but the outcome in Afghanistan and relations with Pakistan hang in the balance. Though "resetting" relations with Russia made possible the New Strategic Arms Reduction Treaty and paved the way for tighter sanctions on Iran, Russia's mercurial politics could always throw such progress into reverse. The "pivot" to Asia in November 2011 was "appropriate," but leaves future relations with a rising China unresolved. The abject failure of the first term was in Palestine. As these scholars see it, Mr Obama's determination to ignore Israeli public opinion while cultivating the Arab street doomed his diplomacy. In the Arab spring he balanced "prudent" support for the tide of democracy against a realistic regard for American interests. Even so, the net result is that the pillars of America's position in the region - its strategic alliances with Egypt and Saudi Arabia, and the virtuous triangle between Israel, Egypt and Turkey - are shaking. If America cannot bend the Middle East to its will, what of China? In "Obama and China's Rise" Jeffrey Bader, one of the architects of Mr Obama's China strategy until leaving the White House in 2011, explains in a brisk insider's narrative just how tricky it can be to concoct the "nuanced mix" of engagement and containment that Mr Kupchan advocates. But in the end Mr Bader is one of the optimists. America prevailed over Germany, Japan and the Soviet Union, which had imperial ambitions. China, he asserts, does not - not yet, at any rate. Maybe. But America's clashes with these powers came when its own economy was growing. How will it fare if it is truly in decline? Ultimately, these authors agree, America's power abroad stands on its health at home. If its economy cannot be restored, and America really is indispensable, then the whole world is in serious trouble.