would have allowed more room for countries to adjust their path to the efficiency frontier while still ensuring that mutual benefits could be enjoyed along that path; by contrast, contemporary geopolitical tensions between the United States and China have arisen after countries have already arrived at or are at least near the international efficiency frontier, and such path adjustments are now not an option. And second, even beginning from a point on the international efficiency frontier, most shocks (such as changes in government objectives that might arise with shifts in political economy forces or, as we have shown, heightened national security concerns) could be expected to alter the internationally efficient sets of tariffs, thereby making the status quo tariffs inefficient and creating room for mutually beneficial tariff adjustments from the status quo as countries move toward the new efficiency frontier. But as we have demonstrated, the rise of great-power rivalry when interpreted as a quest for dominance does not itself alter the internationally efficient sets of tariffs, and so it does not share this feature.

Our analysis can be extended in at least three directions concerning the nature of policy instruments, the nature of trade and trade agreements, and the nature of geopolitical rivalry. First, we have assumed that with regard to policy instruments governments have only tariffs at their disposal. To the extent that governments have alternative means to make bilateral transfers as part of real-world trade negotiations, the use of such transfers might help them avoid the “uncomfortable choices” that we have highlighted here. Similarly, our analysis could be extended to consider the implications of geopolitics in a richer setting where governments have at their disposal both trade and domestic policy instruments (as in Bagwell and Staiger, 2001a, and Staiger and Sykes, 2011 and 2021) that they might use to pursue industrial policy goals more generally. Along these lines, extending the model to allow for the analysis of export restrictions would also be important given the recent prominence of these instruments as tools of geopolitical rivalry.<sup>32</sup> Second, while we have built on a standard framework used in economics to study trade cooperation and trade agreements, Antr`as and Staiger (2012a) and (2012b) have shown that important qualifications to the framework can arise in the presence of offshoring, if offshoring alters the nature of international price determination between buyers and sellers. Such qualifications could be particularly relevant in the China-US context that we have used to motivate our results. And there are other approaches to understanding the role of trade agreements that could also be adopted, and that might lead to different conclusions. For example, the commitment theory of trade agreements (Staiger and Tabellini, 1987; Maggi and Rodriguez-Clare, 1998 and 2007; Brou and Ruta, 2013), which holds that trade agreements can be useful to governments as a way to tie their hands against domestic actors, could yield distinct conclusions about the implications of geopolitical rivalry for trade cooperation. Finally, as we demonstrate in the Appendix, the analysis in this paper is valid for a

> 32For example, as reported in an October 7 2022 _New York Times_ article, “The Biden administration on Friday announced sweeping new limits on the sale of semiconductor technology to China, a step aimed at crippling Beijing’s access to critical technologies that are needed for everything from supercomputing to guiding weapons.”(New York Times, 2022). Our general equilibrium model does not allow a distinction between an import tariff and an export tax due to Lerner symmetry, but in a partial equilibrium extension of the model with many sectors (see also note 6) such export restrictions could be interpreted through the lens of the model as naturally arising in the context of geopolitical rivalry and the quest for dominance (in this case, over high-end microchips).

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