Game theory in WWII
http://myslu.stlawu.edu/~nkomarov/450/AmberPaper.pdf
One can see the manifestation of Game Theory across many disciplines and domains, be it entertainment or analyzing sports strategies. One particularly interesting application of the game theory can be seen in military strategizing. In this post, I will explore how we can see game-theoretical decision making in the Battle of the Bismarck Sea, which was fought in February 1943, during the World War II in Southeast Asia, between the Japanese Navy and the U.S. Air Force. However, problem-solving methodology used in this post will differ from the way problems were thus far solved in class, and these differences will be highlighted. The Japanese Admiral ordered to deliver reinforcements to Japanese soldiers fighting in Papua New Guinea. The Japanese were forced to make a choice between two available routes —either the Northern route, through the Bismarck Sea, or the Southern route, through the Solomon sea. General Kenney knew all of the routes available to his enemy. If he predicted Japanese’s move correctly and sent his planes toward the route, then the U.S. Army would have more days to bomb the Japanese. The Japanese always would take 3 days to reach their destination, no matter which route they took. The “payoffs” in this game were the number of days the U.S. had to bomb. According to the United States military doctrine of decision, a military commander makes decision either based on enemy capabilities or on enemy intentions. In the Battle of the Bismarck Sea, the decision made by General Kenney was based on the enemy capabilities, that is, what Japanese Admiral was able to do to oppose him.
The bad weather was predicted to appear in the north, accompanied by the poor visibility. In addition, the poor visibility in the north would directly limit the number of bombing days for the U.S. to only two days, while for the south the good weather and visibility would ensure more days of bombing. For Japanese troop, no matter which route its commander choose, it would take three days to get to the final destination. In the first case, when both take the north route, there would be 2 bombing days (as mentioned before). In the second scenario, General Kenney would concentrate most of his aircraft along the Northern route again, but this time, Japanese Navy would take the Southern route. Since the reconnaissance was limited along the Southern route, the Japanese convoy could be missing during the first day, allowing only two days of bombing. Next, if the U.S. Navy takes the Northern route and the Japanese convoy takes the Southern route, the Japanese will be missed due to poor visibility and low levels of reconnaissance. In this case, there would only be one day for bombing. Lastly, if both take the Southern route, due to better visibility and the majority of the air fleet, General Kenney would have 3 days to bomb the Japanese convoy.
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Japanese Strategies |
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Northern Route |
Southern Route |
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Kenney’s Strategies |
Northern Route |
2, -2 |
2, -2 |
| Southern Route | 1, -1 |
3, -3 |
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For Kenney, he wanted to ensure his outcome to be greater than or equal to the minimum number in any row so he acquired as many days of bombing as possible. In this matrix, we can easily see that if Kenney stayed with the Northern route, he guaranteed two days of bombing. If Kenney stayed with the Southern route, he may face a situation that only allowed one day of bombing. Based on the doctrine that a commander makes his decision on the estimation of the enemy’s capability, Kenney would definitely select to search the Northern route, as it gave the greatest promise of success. Similarly, the Japanese Admiral would not choose the Southern Route because there is the worst possibility of letting the US Navy 3 days to bomb them, whereas in the Northern Route, there can only be a maximum of 2 bombing days. This is why even the Japanese choose to take the Northern route. Indeed, this is exactly what happened in real life! This variation of the two-person zero-game is worth further exploration as it not only has been used in previous battles but it may also benefits future military decision making process.