Our research suggests, however, that thinking of China as either a status quo or revisionist power is misleading. Rather, China’s approach to the global order has varied substantially. Beijing has played a constructive role that supports existing institutions in some issue areas, even as it challenges the U.S.-led order in others.

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Here are some key points to understand about China’s approach to multilateral cooperation:

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1. Multilateral institutions are often win-win

Many multilateral institutions — such as the World Trade Organization, the Nuclear Nonproliferation Treaty and the International Monetary Fund — produce benefits that are widely shared. People in all countries benefit from a freer flow of goods, a firebreak on the spread of nuclear weapons and a lender that can stave off financial crises. Everyone benefits as more countries like China join these shared efforts and contribute to maintaining the regimes that govern them.

Of course, not all issues allow for win-win solutions. Disputes over Taiwan and the South China Sea show that at times the United States and China have sharply divergent interests. Still, lumping agreements that manage zero-sum conflicts such as these together with multilateral agreements that advance shared interests is an oversimplification.

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2. China’s approach is strategic

In our new book, “China’s Strategic Multilateralism,” we show that China adopts different approaches to multilateral cooperation, depending on the strategic environment in any given context. Whether China actively helps sustain existing institutions, challenges them or simply free-rides on them depends not only on China’s interests as commonly understood, but also on its bargaining power and how it expects other countries to behave.

Here’s an example: China established the Shanghai Cooperation Organization as a mechanism to help promote stability in Central Asia. It did so because it values cooperation — but also expects that other countries are unlikely to sustain cooperation in the absence of Chinese leadership on this topic.

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But China is more likely to free-ride when it understands that other countries value cooperation and are willing to sustain it on their own. Beijing, for instance, has contributed little to U.S.-led efforts to build and maintain effective institutions to manage global nuclear proliferation.

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And China is most likely to use its clout to restructure existing arrangements when other states view Beijing as indispensable to cooperative efforts. This dynamic was evident in China’s recent efforts to renegotiate in its favor voting arrangements and the role of the renminbi at the International Monetary Fund.

3. China faces pushback when it makes a unilateral move

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China has been learning the hard way that the most effective way to advance shared interests is to work collaboratively and ensure that both Beijing and its partners have seats at the table.

For instance, China’s multilateral finance initiative, the Asian Infrastructure Investment Bank (AIIB), is governed by a board designed to reassure China’s partners that Beijing will not exert dominance. The AIIB also adopted the kinds of criteria the World Bank uses for evaluating projects. Yet China’s more unilateral efforts, such as the Belt and Road Initiative, have sometimes sparked a backlash, as seen in the resentment recently voiced by Malaysian Prime Minister Mahathir Mohamad.

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This sort of backlash is a concern for Beijing because it makes it harder for China to advance its interests regionally. Recent studies by Phillip Lipscy and Ayse Kaya complement ours by showing how China can limit this backlash by accepting the constraints that come through multilateralism, investing in international organizations where authority is shared, and binding itself to their governance rules.

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4. Leadership is not as easy as it looks

Some in China suggest that, although Trumpian unilateralism imposes costs on China — notably, the current trade war — it also presents China with opportunities to step into the global leadership void and serve its own interests by taking control of the agenda at multilateral institutions.

This view is shortsighted. Because many existing institutions advance shared interests and are not zero-sum contests, a U.S. retreat from global leadership reduces the effectiveness of multilateral governance, whether or not China tries to fill in the void. Moreover, leadership in complex multilateral negotiations requires skills that take a long time to build; Beijing’s difficulty shepherding post-Paris climate negotiations are an example of these ongoing challenges.

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But this very same logic also applies to Chinese leaders, who now find that exerting more leadership in international institutions does not always give them tools to advance their own national agenda. Indeed, given the country’s economic and political growing pains, China is likely to have difficulty stepping into America’s shoes, which means that a U.S. withdrawal from international leadership will be likely to hurt everyone, China included.

Scott L. Kastner is a professor in the Department of Government and Politics at the University of Maryland at College Park.

Margaret M. Pearson is a professor in the Department of Government and Politics at the University of Maryland at College Park.