In 2009, the Obama administration tried to patch up America’s relations with the world. In 2010, it may have to make hard choices about who it really trusts. The United States has gone out of its way to accommodate rising powers like India, Brazil and – above all – China, giving them a place at the top table in negotiations on the financial crisis. This has alienated some traditional allies, mostly in Europe, who fear they are being downgraded. Nicolas Sarkozy is said to believe Obama is putting the very idea of “the West” at risk.

Yet while the rising powers believe they deserve their new-found recognition, Obama’s strategy presents them with a novel dilemma. Should they reciprocate by aligning more with the United States – or challenge American policies to reaffirm their own autonomy? There was a broad welcome for Barack Obama’s leadership during the financial crisis, not least his decision to prioritise economic talks through the Group of 20 (G20) – which includes not only China, Brazil and India but also Saudi Arabia and other emerging economies like Mexico and Indonesia – rather than the Eurocentric G8. When the G20 met in London last spring, the Indian premier Manmohan Singh asked for Obama’s autograph. Things have grown a little bit chillier since then.

In recent months, there have been frictions between the United States and China over the Copenhagen climate change conference and Iran’s nuclear programme. Indian leaders have also vocally opposed American policy on climate change. President Luis Ignacio Lula da Silva of Brazil irritated Washington by inviting his Iranian counterpart, Mahmoud Ahmadinejad, to Brasilia to discuss the Middle East peace process last November – although Brazil and the United States have since co-operated closely in Haiti.

Those who believed a new American administration could guarantee an era of harmony (a group that probably did not include the highly realistic Obama) have been disappointed. At the same time, many hawkish commentators in the United States have jumped on what they perceive as anti-American slights from lesser powers, arguing that they invalidate Obama’s approach. Rather fewer have tried to understand the foreign policy choices the emerging powers face: as they gain influence, they are experimenting with it, starting to test its limits and frequently stumbling over unexpected consequences.

Perhaps as a result, alarmist predictions of what the coming multipolar world will look like abound: the United States, having given international engagement a chance, will retreat into unilateralism; the G20, UN and international financial institutions will wither; the rising powers will grow ever more competitive in the hunt for resources, perhaps even resorting to force.

This is all possible but unlikely. There are at least two reasons to be optimistic that the United States and the rising powers can successfully work together. The first is that, while the rising powers may want a greater authority, they know that undercutting the current international order is not in their interests. China and India are adept at getting their way in the United Nations, where they enjoy the support of developing countries. They have used their economic clout firmly in the G20 – in contrast to the constantly-bickering Europeans. Why should they wreck a system that, more often than not, works for them?

Second, foreign policy experts in rising and established powers alike are aware that they face a range of transnational threats that can only be addressed through international co-operation. These range from piracy to pandemic diseases and climate change. India and China have sent warships to operate alongside US and European vessels chasing pirates in the Gulf of Aden. And while they may have clashed with the US over terms at Copenhagen, they aren’t in denial about climate change: China in particular boasts of its innovations in clean technology. If the emerging powers do well enough in international institutions now, they know that they will need stronger institutions soon.

So there is still an opportunity for the United States and rising powers to develop pragmatic and hard-headed forms of multilateral co-operation – and largely on the basis of existing international institutions. This won’t look like the US-led multilateralism of the early post-Cold War period, when Washington was able to set (and break) the rules in international institutions. In that era, European governments provided essential financial and political support to institutions like the UN, partly because they hoped it would win them friends in Washington (Europeans still pay 40 per cent of the UN peacekeeping budget, for example).

This generosity didn’t persuade George W Bush to heed European warnings about the importance of the UN before invading Iraq. And they haven’t swayed the Obama administration, which is not anti-European but has concluded that international institutions need to reflect the real-world balance of power – even if bargaining with the rising powers is not always as congenial as parlays with the EU in scenic historic cities. The next generation of multilateralism will involve making complex deals to address shared threats – like nuclear proliferation – that established and rising powers alike can more or less accept.

This is most likely to emerge through the G20, which has an economic focus at present but could evolve at speed. The G20 – or variations such as the Major Economies Forum, which discusses climate change – has the potential to become a clearing-house for international discussions that would get bogged down in other forums. Rather than tackle nuclear proliferation or international trade negotiations through unwieldy international conferences, the US and other big powers could cut initial deals through the G20.

This sort of deal-making may not be especially pretty. Western human rights activists are already very worried that the Obama administration has been too ready to play down talk of rights and democracy for the sake of diplomacy. Leaders from poor countries argue that the G20 lacks democratic legitimacy, cutting them out of economic decision-making.

There is certainly a risk that the G20 could become a club where major powers stitch up unsavory agreements on issues from counter-terrorism to market access for lower income countries. But the majority of G20 members are full democracies, and their choices will be scrutinised at home. A network of NGOs has grown up to track the G8’s performance on issues like development aid, and similar corps of do-gooders will grow around the G20.

And there are few real alternatives to the G20. The G8 may be a tighter discussion group, but half its members are European, and that just won’t work any more. The UN General Assembly gives a voice to every state on earth – the result is a cacophony. The fabled “league of democracies”, often mentioned in the Bush era, has entered the realm of grand ideas that never quite made it, like Esperanto.

These aren’t reasons to be sanguine about the G20’s future. It could still falter – some financial experts are already arguing that it is losing relevance as the economic crisis fades. Politically, it will only keep momentum if the rising powers fully engage with it. To date, western members (primarily the United States and United Kingdom) have driven most of its agenda. The longer this remains the case, the less credible it will seem. Emerging powers should lead the way in expanding the G20 agenda – after its peacekeepers bore the brunt of the Haiti earthquake, for example, Brazil could launch a G20 initiative on humanitarian aid.

While the new powers should take the lead on specific issues, they will also have to accept that the United States still enjoys a privileged position in the G20 (as it does at the UN). It is still, after all, the only power that is relevant to almost every issue globally – even if China is also increasingly indispensable. And it is the only power with a sufficient depth of diplomatic contacts to handle the technicalities of an expanding G20 in the near future.

For now, the United States is well-paced to co-ordinate the G20, though not to dominate its decisions. That’s a bargain the rising powers should take seriously. America’s omnipresence may sometimes be irksome – American isolationism would be far worse.