Game Theory in World War 2
Game Theory is used around us from financial markets to board game strategy. It provides us with the means of quantifying decisions and their outcomes as well as justifying those decisions. Although the game theory that we have looked at so far in class have revolved around harmless hypothetical situations, game theory has been heavily involved in decision making for battle plans during World War 2. In the academic paper Historical Uses of Game Theory in Battles the World War II by Nanjiang Liu, the decisions and outcomes of the Battle of the Bismarck Sea are analyzed and discussed.
In the Battle of the Bismarck Sea, the Japanese Admiral was forced to make the decision of either taking the Northern route or the Southern route around New Britain. The American general, General Kenney, knew that these were the Japanese’s only two options so he attempted to predict which route they would take in order to coordinate an attack. In this game, each route has an associated number of days the Americans would be able to bomb the Japanese Navy depending on if the Japanese Navy picked the North or South route and if General Kenney predicted the North or South route. The resulting matrix is as follows:
Both routes would take 3 days to complete by the Japanese, but due to bad weather on the Northern route, poor visibility reduces the number of days by one.
With this we have 4 possibilities:
- (North, North) – Poor visibility reduces number of days of attack to 2
- (North, South) – 1 wasted day of reconaissance
- (South, North) – 1 wasted day of reconaissance and 1 lost due to poor visibility
- (South, South) – 3 fulls days of attack
Analyzing this game matrix we see that taking the Northern route is a safer bet for both forces as it allows the American’s 2 days of bombing minimum and saves the Japanese from the possibility of 3 days of bombing. As history shows, this is exactly what happened.
As discussed in class, this analysis assumes that this is a two-person zero-sum game. Looking for the Nash Equilibrium, we can clearly see that it is (Northern route, Northern route). Both commanders would act in their troops’ best interest whether it be maximizing attack or minimizing losses as what happened in real life. This goes to show that game theory is a very powerful tool that helps us make predictions and work out the best decisions for us even if we don’t know what the other person is going to do. The benefits of game theory stretch far beyond the examples in class and this battle making it a very useful tool in statistical decision analysis in a variety of fields from engineering to medicine.
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http://myslu.stlawu.edu/~nkomarov/450/AmberPaper.pdf