Tariffs, Trade, and the Prisoner’s Dilemma
By Victor Odouard
An interesting game that’s making headlines these days is trade. The problem is often posed as a prisoner’s dilemma.
It goes like this: we are dealing with two countries (players). I won’t name names, so let’s call them Merica and Hina. They have two possible choices, tariff or free. 2 players and 2 strategies creates four possible outcomes:
- If they elect to have free trade between them, they both do pretty well—let’s say they get a payoff of four.
- However, if one Merica defects and imposes a tariff (equivalent to confessing in the prisoner’s dilemma), then they gets an even greater payoff, let’s say five, and the other country gets zero.
The logic here is that Merican goods will sell well both in Hina (since there are no tariffs on them), and they sell well domestically, since they will be competing with Hinese goods whose prices have been artificially inflated by tariffs. Thus, Merican goods will do better in both regions, increasing the payoff for Merica, and Hinese goods will do equally well in China but much worse in the US, decrease the payoff for Hina.
Of course, there are some nuances to this. Hinese goods may even end up doing worse in Hina, since the additional economies of scale gained by Merican firms may bring their costs down and make them even more competitive in Hina.
- Since we are formulating this as a symmetrical game, the case where Hina defects is a mirror image of Merica’s defection.
This symmetry, of course, may not be the case depending on the intricacies of the Merican and Hinese economies. We could imagine a scenario where the Hinese economy relies much more on exports to Merica than the Merican economy relies on its exports to Hina. In such a case, Hina would benefit more from free trade than Merica (though both countries would still benefit).
- If both impose a tariff (equivalent to both prisoners confessing), they both do just okay. Let’s give them a payoff of two.
Generally, trade makes countries better off, so if both are hampering trade by setting tariffs, it makes sense that their economies would perform only okay.
Here is the prisoner’s dilemma payoff matrix:
However, I object to this formulation of the game. In the prisoner’s dilemma version, both players’ dominant strategies are to impose tariffs, because no matter what the other player does, they are better off imposing tariffs.
This, I think, is wrong. I propose a new formulation of the game, changing payoffs (2) and (3) to (Merica: 3, Hina: 0) and (Merica: 0, Hina: 3). Here’s why. While it may seem compelling that the Merican economy does better (as compared with entirely free trade) when it imposes a tariff and the Hinese don’t, I would argue that this is in fact not true.
Yes, the Merican companies whose goods are selling well in both Hina and Merica are happy. But we need to think about all the Merican consumers, who are all paying more for their goods, and the Merican companies who purchase the raw materials being taxed, whose profits are getting curtailed. This is a much less rosy picture, and I would argue (as would the Economist) that it makes Merica as a whole worse off. Why are tariffs still popular? Probably because of Olson’s law of large groups—the benefits of tariffs are concentrated to a small group (steel workers, for example), while the costs of tariffs are spread among all American consumers. Steel workers are more likely to fight for their job than a consumer is to fight for a couple dollars here and there.
Here is the new payoff matrix that I propose:
We can see that this matrix actually has two Nash equilibria—both countries impose tariffs or both countries allow free trade. The optimal point is also one of the Nash equilibria, which is in some sense reassuring. However, the challenge is that:
- If Hina is imposing a tariff and Merica is not, and Hina shows no signs of budging, Merica does better by imposing a tariff
- Even if Hina does show signs of budging, and there is hope that both countries might move towards free trade, political pressure tends to push in the opposite direction (towards tariffs), because of Olson’s law of large groups.
The optimum is pretty clear, but the path there may be rocky (though not as rocky as the prisoner’s dilemma would indicate). Let’s see if we can get there.
Resource: https://www.tcd.ie/Economics/assets/pdf/SER/2017/9trump.pdf
Resource: https://www.economist.com/special-report/1998/10/01/why-trade-is-good-for-you