The Application of Game Theory for Military Decisions
After learning in class how Game Theory essentially is about the best responses and payoffs to strategies, I thought of how military generals would think during World War II. This led me to find this article that covers two different battles from the war and how the military generals from opposite sides had to look at what they were facing and had to make decisions based on what the other general could do and how it could either benefit them or hurt them. For this blog post I chose to focus on the second scenario discussed in this article since it goes much more in-depth on mixed strategies, payoffs, and how their possible strategies could affect their choices.
In August 1944 in the European Theater, General Omar Bradley was in charge of destroying the German Ninth Army in the Avranches-Gap situation. The German commander, General Von Kluge and his army were exposed when the allies broke through the narrow gap by the sea of Avranches. Von Kluge had two options: attack or withdraw. On the other hand, Bradley had a possible gap that could be used for the attack because of the reserves he had. He had three options for his reserves: order them to defend the gap, send them to harass the Ninth Army’s retreat, or leave them where they were and move them into the gap only if necessary. Bradley chose the third option.
Game Theory kicks in when both generals weigh in what their payoffs are depending on their enemies opposing capabilities. While Bradley chose to hold his reserves, Von Kluge decided to withdraw. However, Hitler ordered him to attack the gap. The gap held, the ninth army was devastated by the British and US armies, and then finally Von Kluge committed suicide. The table above shows Von Kluge’s 2 strategies and Bradley’s 3 strategies forming 6 different battle results and the maximum and minimums of the rows and columns. In this scenario, Bradley is the maximizing player while Von Kluge is the minimizing player. Depending on what Bradley chooses, Von Kluge chooses the minimizing strategy that hurts the army the least, while Bradley goes for what puts the most amount of pressure on the Germans.
In the previous Avranches-Gap situation, the commanders were limited to “pure strategies”. For “mixed strategy”, a probability is assigned to each possible course of action. The figure above demonstrates the gap situation but instead of just the maximum of pure strategies, we get the maximum of mixed strategies. This is why a vertical line is drawn to show the most favorable course of action, and the dots represent the outcome. The probabilities 0, ½ and ½ were applied to strategies 1, 2, and 3. This is why in the article the author describes the decisions being taken on the “flip of a coin” and how Bradley’s expectation is the maximum of the mixed strategies. However, the problem with mixed strategies is that at times Bradley could receive an outcome that was less preferable than what could have been from a pure strategy. The article also mentioned how ‘mixed strategies’ are only applicable if the opposing commanders have no idea what their opponent will decide.
To conclude, this article is only meant to observe the military doctrines with game theory and how a commander establishes his order of preferences from what he visualizes. The current doctrine offers a strategy that has the greatest promise of success in the enemy’s capabilities. Game Theory provides a matrix for a decision to take place according to the data and then the methods for its solution. Although these matrices are simple, they provide what is able to be gained and the risk if the general deviates from the strategy. Mixed strategies is another part of Game Theory that provides intentions and capabilities for military situations that could work for smaller units.
https://pubsonline.informs.org/doi/abs/10.1287/opre.2.4.365