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Nash Equilibrium and Nuclear Standoff

In recent events, the Dow Jones Industrial Average climbed back above 22000 today according to the WSJ, and this is the first time the DJIA has hit that number in over a month due to the severity of Hurricane Harvey and Irma as well as because of the standoff with North Korea since investors have been fearing the effects of North Korea missile tests.

Comparing these thoughts to an article from the Londonist, they describe and compare the possible outcomes of North Korea nuking London. But regardless of who is involved in this conflict, there are many different scenarios and payoffs to discuss. This article continues to discuss the yield of these missiles, as well as the predicted causalities and injuries from such a “blast”. I found this article interesting because it shows the extreme injuries that would be caused from a nuclear war but inevitably describes how nuclear war is not a well-thought out or likely answer.

Here are some of the numbers the article provided. If North Korea’s missile that launched August 2017 was targeted at Westminster, there would be a predicted 334,290 casualties with 1,088,503 injuries. So, what if North Korea did launch a missile to hit London? Well, according to the article, London would have a few options. They could either choose to retaliate and launch a nuclear strike, choose not to retaliate and not launch a nuclear strike, allow the commander to use their own judgement, or offer their fleet to the United States. But what if the United states launched a missile at North Korea? If it detonated over Pyongyang, the device would cause 3,261,930 casualties and 2,900,200 injuries. So does the United States or North Korea really have any sort of incentive to launch an attack? After doing my own research and using the website given in the article to estimate casualties and injuries, I found that if North Korea’s missile that launched in 2017 was detonated in New York, New York, that there would be 728,220 casualties and 1,562,410 injuries. So, let me now compare this to a Nash Equilibrium scenario. I will say that “Player A” is the United States, and “Player B” is North Korea. For simplicity, both countries can either choose to fire a missile, or not fire a missile, and it is measured in casualties (doesn’t include injuries):

After looking at this table, there actually isn’t a Nash Equilibrium, but that is because I ignored the fact that other countries will take action. For an example, if North Korea launched a missile at the United States causing many casualties, there are high chances that another country will retaliate against North Korea, causing North Korea to have casualties. If this were to be the case, then both countries would always choose to not fire a missile that way they have no casualties at all, demonstrating a Nash Equilibrium.



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