Game Theory in the Civil War
September 13, 2012 marked the 150th anniversary of one of the bloodiest battles in American history: the Civil War Battle of Antietam. The Baltimore Sun in its article from September 13th summarizes the events of that fateful day and remembers some fatal mistakes made by the Confederate army by dividing the struggle into three parts. In each third, a historian can study the effects of game theory on the two players of this “game,” the Union and the Confederacy.
In the first phase of the battle, Union soldiers invaded a field of ready Confederate troops who forced regiments of the Union Army back into a wooded area, where the Rebels were well hidden and ready to pounce on the retreating Yanks. This, quite obviously, had extremely adverse effects on the Union Army, because of their decision to play offensively in the beginning of the phase. In the Union vs. Confederacy payoff matrix, this offensive move by the Union coupled with the defensive one by the Confederate Army had an extremely negative payoff for the North, and a “positive” one for the South.
The next phase had very different effects. While the Confederates waited defensively, Union soldiers shot at them from high ground. In this case, both players used defensive strategies (the Union army not invading to attack the Confederates, rather attacking them from a hidden position), which resulted in a positive payoff for the Northerners and a very negative one for the Rebels.
In the third and final portion of the battle, Union troops waded through a small creek to attack the superb defense of the Confederates, who held off the Yanks for a long period of time. Eventually, however, the Union Army broke through, and almost destroyed Confederate forces if it weren’t for a late arrival of 3,000 Southern troops. In this last phase of the Battle of Antietam, the payoff was exactly the opposite as it was in the first phase where the two armies used the same strategies. Although earlier the South’s defensive strategy against the North’s offensive one worked swimmingly, this time it resulted in a “positive” payoff for the Union and a negative one for the Confederates.
Overall, the battle displays the generic two player game in which both have to choose one of two strategies simultaneously, and without the aid of spies, ignorantly of the other’s decision. Idealistically, a mixed Nash equilibrium could be calculated by finding the equilibrium probabilities of each players’ strategies, however in a war-like situation where decisions need to be made quickly, it is an inconvenience. In future violent world struggles, will we see more use of game theory application? Or will conflicts resolve to be maintained on a peaceful level?
Biz