How Hannibal defeated Game Theory—Summer


Today, I am going to examine with you, through the lens of game theory, the most famous war in my favorite era (Classical Antiquity!), the 2nd Punic war between Carthage and Roman Empire. In particular, Hannibal’s invasion into Roman territory through the Alps.

During 264-146BCE, Carthage and Rome engaged in three major battles over the control of the Mediterranean world called the Punic Wars. The most significant was the Second Punic war which began when Rome provoked Carthage to attack Saguntum and declared war against them. Hannibal, leader of Carthage, decided to attack Rome.

Here is where Game Theory comes into play. We can describe this situation in very simple terms: There are two ways into Rome, the easy way and the hard way through the Alps. The two players, Hannibal and Rome, each have the choice to attack/defend either but not both of the roads. Hannibal has two legions. If Hannibal decides to go through the Alps, he will lose 1 legion on the way. If Hannibal and the Romans encounter each other, he will also lose 1 legion. If Hannibal’s payoff depends on how many legions he gets to Rome and Romans’ payoff depends on how many legions were destroyed on the path, we get this simple payoff matrix:

Hannibal(left) / Roman Empire (top) Easy Hard
Easy 1, 1 2, 0
Hard 1, 1 0, 2

From this matrix, we can easily see that there is no strictly dominant strategy (a strategy that, no matter what others do, earns the player a better outcome than any other strategies) for either player. Yet, we can see that Hannibal has a weakly dominant strategy to choose the easy path over the hard path. (A weakly dominant is a strategy that, no matter what others do, earns the player as least as high and for at least one instance higher payoff than any other strategies.) Assuming both players are rational, the Roman Empire see that Hannibal will choose to attack from the easy route to obtain equal or higher payoff. Thus, the Roman Empire will then rationally choose to defend the easy route.

Yet, anyone who has studied Ancient Mediterranean History will be able to tell the problem with this prediction: Hannibal actually chose to attack through the Alps! He defied game theory and surprise attacked the Romans!

This is an excellent example of one of the limits of game theory which T. Susan asked me to consider in a comment to my last post. People are NOT always rational! Even though game theory is a great model for us to understand the world, it is NOT a literal representation of it. Given that, it becomes even more essential to understand and adjust to your opponent and the context of the game. If your opponent is not a rational person, DO NOT assume that s/he will play rationally! In fact, in the case of the Roman Empire, it was Scipio Africanus who violated all conventions in warfare that finally defeated Hannibal!

See you next week!

Work Cite: Mark, Joshua J. “Punic Wars.” Ancient History Encyclopedia, 20 Dec. 2011, Accessed 16 Sept. 2017.
Mark, Joshua J. “Scipio Africanus the Elder.” Ancient History Encyclopedia, 19 Dec. 2011, Accessed 16 Sept. 2017.
Image: Hannibal., Customwalks, 24 June 2013, Accessed 16 Sept. 2017.


3 thoughts on “How Hannibal defeated Game Theory—Summer

  1. Gwyneth Turner

    Up until now, the intimidating math behind Game Theory kept me from ever considering reading about it. But you succeeded in drawing me in with my weakness – history! This was a very well done post. It was interesting even to an avid math-hater like myself and you used the example of the Second Punic War to explain Game Theory in an easily digestible manner.Great work!

  2. Cotillion1161

    I think it is worth considering that game theory behind evolution, and consequently the evolution of how our psychological mechanisms(i.e. mind) work could have predicted this by taking into consideration the effects of ideology on decision making, and the consequent tendency to gamble. I am not too well versed on it, but just a thought.


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