A key decision in making US-led and China-led institutions complementary rests with the US Congress. Without the Congress ratifying the 2010 International Monetary Fund governance reforms to give greater voice to emerging markets, that will not happen. And as this is unlikely to happen any time soon, we perhaps need to start thinking of a "New Bretton Woods".

In the three-round match between the US and China to have influence in the Asian regional architecture, Round 2, which took place several months ago, went in China's favor. Countries like the United Kingdom, the Republic of Korea and Australia broke ranks with the US, and 57 countries from across the world, including Germany, France, Iran, the United Arab Emirates and Nepal, applied to be the founding members of the Asian Infrastructure Investment Bank. Japan has so far stuck to the US but it has indicated that it remains interested in joining the AIIB, which can be seen as the financing arm of China's Belt and Road Initiative.

Initially, the US attempted to dissuade potential applicants by citing poor governance and due diligence at the proposed AIIB. But it made a dramatic turnaround later.

Less well known is Round 1 after the Asian financial crisis of 1997-1998 when the US and the US-led IMF shot down proposals to establish the Asian Monetary Fund (AMF). At that time, IMF surveillance had failed to adequately identify the risks posed by the uneven pace of capital account liberalization in the region and the extent of the banking sector's weaknesses.

The IMF had, therefore, initially misdiagnosed the Asian financial crisis and prescribed inappropriate policies which exacerbated the impacts of the crisis and led to a free-fall of currencies, fanned the contagion, and pushed the region into sharp recession. This led countries in the region to initiate regional "self help" measures to take things under their control.

Although the AMF was stillborn, the region established a $240-billion crisis management fund called the Chiang Mai Initiative Multilateralization (CMIM) and the ASEAN+3 Macroeconomic Research Office, which is the "independent surveillance unit" for the CMIM. But the idea of the AMF has not been entirely forgotten and keeps coming up every now and then.

Round 3 of the China-US game is now being played in the field of international trade. We have the US-led Trans-Pacific Partnership that has kept China out, and the ASEAN-led (and China-led) Regional Comprehensive Economic Partnership that excludes the US.

Round 3, hangs in the balance. This is because unless the negotiators can conclude a deal soon, it will be impossible to get it ratified by the US Congress this year. By that stage the US presidential election is likely to overshadow trade talks and TPP approval may have to wait until the next presidential term. If TPP disappoints or, worse still, it is not concluded at all, it will be another major setback for the US in Asia as it is the economic arm of US President Barack Obama's "pivot" to Asia.

Although in a game of baseball, three strikes means "out", this is not the case in global and regional diplomacy. It only means that the US' clout in the region will weaken and the sparring between Beijing and Washington will continue in the future. China-led institutions in Asia will not pose a threat to the well-established IMF or the World Bank. They will, however, complicate global economic governance and make it more complex.

If US-led and China-led institutions cannot take joint decisions and work with each other in a complementary manner, 70 years after the original Bretton Woods agreement, we will need a "New Bretton Woods" agreement led by a select group from the truly "systemically important countries" of the world, not the motley group comprising the G20.

The author is associate professor and coordinator of the International Political Economy Programme in the Centre for Multilateralism Studies at the S. Rajaratnam School of International Studies, Nanyang Technological University, Singapore.