Dear Professor Dixit,
I am honored to be communicating with you over EconSpark. Your research in micro and game theory over the past decades have been an inspiration to me. You have been an eye opener to a lot of open research questions across the globe- including my own dissertation on the theory of competition in differentiated markets back in 2002.
If I may attempt to skeleton a preliminary response, we can consider a typical 2x2 game with US and rest of world as the two players ("US" and "Rest") with the following strategies. For the US: (1) US retaining WTO status (even if marginally), and (2) Trumpian effective departure from WTO. For "Rest": (1) Rule-based WTO system, and (2) Bilateral bargaining with possibility of a temporary trade war.
The simple 2x2 payoff matrix would be:
Rest of World
(1) vs. (2)
US Strategy (1) A, B C, D
US Strategy (2) E, F G, H
Some ideas on the outcomes:
(1), (1): A, B would be the base scenario (others are value-added benefits and costs relative to this scenario).
(1), (2): B would include retaining a rogue leader who undermines the rule of law, which maybe costly for the Rest of World, hence D > B is a possibility. For the sake of a strong Nash argument, assume this possibility is binding in the short term. If this is true, then on the other hand, for the US, G would be > C, i.e. the benefits of Trumpian departure from WTO would exceed US marginally retaining its WTO presence. This is the case of domestic political win for Trump, if bilateral bargaining provide protection of domestic jobs and local business interests in a relatively imperfect market scenario of extra positive profits relative to the more open world market (less imperfect market scenario) in the case of "C"- also in the short run.
(2), (1): Since the departure of a large player from WTO will be costly for BOTH players, then A>E and additionally B>F. The latter condition (B>F) would logically assume that the rest of world is better-off if US stays in the WTO, i.e. no follow ups on Brexit on the global level. If Rest of World domestic politics become geared towards protectionism, then B>F will cease to exist. It is ironic that such a constraint is invariant to the short run Nash equilibrium outcome of (2,2) as prescribed below.
(2), (2): Trumpian departure from WTO will trigger bilateral trade negotiations, albeit after the possibility of short run trade war announcements or calculated protectionist moves by Rest of World. In this case, H>F for Rest of World in this scenario, conditional on US strategy (2), if the rest of world value trade with the US more than trade without the US. This is a critical constraint because the difference between H and F, i.e. (H-F)> delta is itself the world trade with (relative to without) the US in it. Delta will be the importance of US inclusion in world trade from the benefits side of Rest of World. Assuming that delta is positive due to high opportunity costs of not trading with the US for Rest of World, then (2,2) will yield H>F. If, however, the Rest of World can operate in world trade without the US in such a system, with relative positive returns, then delta could be negative yielding F>H.
For the short term Nash solution: If delta is positive making H>F, along with G>C as discussed in scenario {(1),(2)} above, then the dominant Nash equilibrium will be scenario {(2),(2)} with no incentive to deviate. The US will effectively choose Trumpian departure from WTO, and the Rest of World will choose bilateral negotiations after short term trade war possibility. This short run Nash solution is an equilibrium solution with no incentive to deviate in the short term- albeit unless delta becomes zero or negative (i.e. value-added returns of world trade with US , becomes less than the returns of world trade without US). Notice also that this short run Nash equilibrium solution is invariant to B>F, since if F becomes >B, the short run Nash solution of {(2),(2)} persists.
The above can be extended on three fronts:
(1) inclusion of concrete costs for a trade war. In this case, G and H will be revised downwards by the respective negative trade war impacts on US and Rest of World, respectively. This makes the short run Nash solution of (G,H) relatively unstable in the longer term- the more is the severity of the costs of trade protection.
(2) inclusion of discounted future benefits due to a greater world trade pie from free trade (i.e. the extra benefits of mutual trade between US and Rest of World) in more concrete terms. This can be modeled either as additional benefits under free trade, or as additional opportunity costs without free trade. With inclusion of the dynamics of future opportunity loss due to non-free trade scenario, the short term Nash outcome of {(2),(2)} is likely to break down, since G and H will need to be revised downwards to accommodate such opportunity loss. However, (E,F) will also need to be revised, which makes the short run {(2),(2)} solution unstable.
(3) extension towards world trade simulation with impact on non-tradable services and structural job shifts affecting the political economy of the world trade system in the longer term.
It is important to note here that the (win,win) or (A,B) scenario will never converge to be the longer term Nash solution, even if G and H are revised downwards, since B must be >D for a win,win (A,B) Nash solution to persist towards the longer term. This essentially proves that stability of long term world trade system will hitherto be conditional on US domestic politics, as well as the valuation of Rest of World towards trading with the US. If such sentiment fuels the Rest of World to lower valuation of trade with the US, making F>H (delta negative), along with A>E as invariant to such an outcome, then the current trade system will never converge back to a (win,win) (A,B) as a long term Nash solution, and consequently a different fabric of world trade will be essential for the world economy moving forward.
The above are extremely preliminary thoughts on the open subject matter that Professor Dixit has introduced.
Respectfully,
Tarek H. Selim
Professor of Economics at the American University in Cairo,
and former Visiting Researcher at MIT Industrial Performance Center.
tselim@aucegypt.edu