Sunday, November 12, 2006

Battle of the Sexes, Where do they go?

The Battle of the Sexes is a two player game used in game theory. Imagine a couple, Kelly and Chris. Kelly would most of all like to go to the football game. Chris would like to go to the opera. Both would prefer to go to the same place rather than different ones. If they cannot communicate where should they go?

The the payoff matrix labeled "Battle of the sexes (1)" is an example of Battle of the Sexes, where Chris chooses a row and Kelly chooses a column.

This representation does not account for the additional harm that might come from going to different locations and going to the wrong one. In order to account for this, the game is sometimes represented as in "Battle of the sexes (2)".

How do we find the Nash Equilibrium in this case? Is there more than one?

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