Hezbollah and the Prisoner’s Dilemma

Can game theory solve the Israel-Lebanon war?

By Tim Harford

http://www.slate.com/id/2146867/

This article discusses how game theory relates to the Israel-Lebanon war.  If Hezbollah were to attack Israel, Israel will respond with a far greater counter attack.  Unfortunately, Israel’s strategy has not deterred Hezbollah’s attacks.

This article addresses how economic theories such as the prisoner’s dilemma can be overly simplistic.  The article describes a solution to the prisoner’s dilemma, differently than the Nash Equilibrium where both prisoners will confess:

“The champion was “tit for tat,” which begins by cooperating with its

fellow prisoner (staying silent) but punishes a squealer by confessing

on the next turn. Axelrod argued that “tit for tat” was successful

because it was easy to interpret, hard to exploit, began

cooperatively, and quickly forgave transgressions by returning to

cooperation. It has proved a magical myth: that you should speak

softly and carry a big stick, that “an eye for an eye” can produce

cooperation in unpromising situations. Axelrod’s idea was repeated in

a horde of popular science books.”

Here the article contradicts our homework solutions, where we found that:

“in the second play of the game, the players are essentially playing a

one-shot prisoner’s dilemma. In this game, C is a dominant strategy

for each player. So (C,C) will be played and they should both realize

that this is how the game will be played the second time round. This

happens regardless of how the first game was played. As a result, in the first game the players should realize that nothing they do can affect the outcome of the second play of the game. This means that the first play of the game is also essentially a one-shot prisoner’s dilemma and again we would expect to observe (C,C). This logic suggests that we would expect to see (C,C) played repeatedly.”

Overall I am not convinced that the prisoner’s dilemma is a useful analogy to the Israel-Lebanon war.  There are far more issues, options, and players in the situation.