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Isner and Mahut: A prisoner’s dilemma

John Isner and Nicholas Mahut are fighting an epic battle today in Wimbledon and The World’s longest ever game of tennis. It was halted last night at 59-59 in the final set.

In summary then, they have been trapped in game theory’s favourite metaphor: the Prisoner’s Dilemma. The Prisoner’s Dilemma is fundamental economic game theory which states at its simplest level that it is better to beat (defect against) your opponent than to draw (cooperate) with your opponent. However, without going into the details here because you already read them here, the Prisoner’s Dilemma also shows that for a certain number of turns in a multi turn game – such as tennis – it can appear to be ‘better’ to draw (cooperate) in the initial games of the tennis match.

In the match that Isner plays against Mahut, the 59-59 score at end of play last night is no coincidence or luck. Both players have fallen into an irrational version of Prisoner’s Dilemma where they are cooperating to ensure they both stay in the tournament even for a few more hours, probably motivated by the fear of not making it through to the next round.

In the 5th set, you have to be two games ahead to win. As each player focusses on winning their own serve, the other conserves energy while receiving serve by not fighting back. In this way both have agreed, tacitly or subconsciously, that they will not defect from the plan. In this way, both players extend their stay on the World’s premier tennis stage. Both players want to avoid the final game of the match, (game N in the Prisoner’s dilemma) where one of them will no longer be a competitor at Wimbledon 2010.

This extended cooperative play is irrational because the game of tennis is designed to have only one winner from two players. All they are doing is tiring each other out so that when the final game does come, instead of playing at their best, they will be sluggish and exhausted after all the previous play.

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