Trump announced that he was going to pull the US out of TPP and was going to negotiate bilateral trade deals. To get better deals for the US: ‘to bring jobs and industry back’. The implication is that America has more of a bargaining power in bilateral rather than multilateral trade deals. Is that correct?
Usual power indices, I think, suggest otherwise. As trade deals are contracts, both sides, and in multilateral agreements all sides, need to agree. So, nominally, in bilateral deals, both parties have 50 per cent of the power to make the deal. In multilateral deals, nominally, all the parties have individually less than 50 per cent of power.
The power of coalition making
However, while in a bilateral negotiation there is only one coalition that can be made, which is the coalition of both parties, there are more possibilities for coalition-making in multilateral negotiations. The distribution of power then depends on what is the power of coalition-making. If in some relevant sense, the US is a heavy player (e.g. as a trading partner), its power to form coalitions will be higher than that of any of the others individually. In addition, the coalition of a light player with a heavy one will tend to be preferable to the light player, especially if there are more light players, because the chances of being in the winning coalition increases – even if, as it is the case in multilateral trade agreements, unanimity is needed, because selling the veto vote to the player with higher coalition power will fetch a higher value (the more so, the larger is the number of lighter or smaller players).
So, the US in coalition with one or two or a number of trading partners can have more than 50 per cent of power. Thus, the US bargaining power in a multilateral setting should be higher than in bilateral ones.
TPP and China
This applies in particular to negotiations with China. The US has more weight negotiating with China together with other TPP partners than bilaterally. And so do other TPP partners.
The last point explains why Obama opted for TPP before moving to negotiations with China. Because, if there are two weighty players in a multilateral negotiation, coalition formation and power sharing becomes tricky and, in some sense, the US and China have equal power overall and in terms of coalition formation. Then, the deal that the US on its own can make with China will be less favourable than the one that it could make as a partner to TPP.
Finally, if China comes up with its own TPP that excludes the US, then there indeed will be a power shift. The distribution of power will shift to China.
Trump’s mistake is the same that supporters of Brexit made and maybe still make that UK is better off negotiating trade deal on its own rather than as a member of EU. Also, that those who oppose TTIP make – each country has more power over foreign trade alone than as a coalition partner in a multilateral trade agreement. It is not an uncommon misperception, which is probably the better word than mistake. It is often implied in the demand for sovereignty too, which can mean preference not just for unilateral decisions but also for bilateral over multilateral agreements. Going it alone is seen as taking back the national power, which can in fact easily be diminished that way. In a way, however, both supporters of Brexit and Trump understand that EU is more powerful than would their individual members alone be acting on their own, so they have expressed their preference for the dissolution of EU.
Trump approaches trade with the assumption that everybody has more interest to trade with the US than the US has to trade with others. So, he assumes that the US has a lot of blackmailing or veto power: take it or leave is his approach to negotiating from strength. But, with the US current account basically balanced, the interest of the world to deal with the US is broadly equal to that of the US. So, that blackmailing power is exaggerated. Which is another misperception, I guess – in part due to the assumption that China is more interested to trade with the US than vice versa because it runs a significant trade surplus. So, it should be ready to give up more to hold on to the US market. If that is indeed the case, that strengthens the case for negotiating with China with the TPP already in place precisely because of the increased power that TPP provides.
Alternatively, and by the same logic, a China-led TPP will make it difficult for the US to use e.g. tariffs to extract concession from China.
Lessons from NATO
The same considerations about the distribution of power apply to the membership in the NATO. Now, it may seem as if the less powerful members of the alliance are free riding because they would be less powerful if they were out of the NATO alliance. Again, that is the same as in the case of trade agreements. Perhaps another misperception that is behind the claim that TPP ‘would be a disaster’. In the case of NATO, members clearly benefit from the alliance, in the sense that they gain power over the outsiders, as does the US. All of them contribute less than they would if they were outside of the alliance, so they all free ride to a certain extent. Clearly, in a global anarchy, costs to everybody would be higher.
So, beliefs that the US would have more power in dealing bilaterally with China in trade and with Russia in security are wrong.
 See for instance R. Aumann and R. Myerson, ‘Endogenous formation of links between players and of coalitions: an application of the Shapley value’, in: A. Roth (ed.), Shapley Value: Essays in Honour of Lloyd S. Shapley, Cambridge University Press, 1988, pp. 175-191.
 In a recent interview with the NY Times, when asked what would happen if other countries introduced tariffs on imports from the US if he were to pull out of the Paris Agreement, he just said something to the effect ‘They will not dare’.
 The classic paper is by M. Olson and R. Zeckhauser (1966), ‘An Economic Theory of Alliances’, The Review of Economics and Statistics 48, pp. 266-279.