Football at home or night out?

– Come on, let’s watch the game tonight and we’ll go out tomorrow. I promise.
– We never go out!! I think you don’t like me anymore!
– Please, do you know how painful it is to me to miss a game? From 0 to 10 I would say between 0 and 4.
– Yeah! And for me? Almost the same, 1 to 5. Not as bad as you because if I stay,I will be complaining all the time. That’s something I actually love as well.

Ever lived this situation? Game theory could help you making plans or strategies. Imagine the situation I told you: on a given night a couple has to decide whether they’ll stay in and watch the game or go out. Let’s build the pay-off matrix considering 10 is the best, 0 the worst for each of the “players”:

WIFE
In Out
HUSBAND In 10, 5 2, 4
Out 0, 1 4, 8

If the husband chooses first,he’ll choose to stay in. Therefore, the best move for the wife is to stay in (5 instead of 4, which means going out on her own).

WIFE
In Out
HUSBAND In 10, 5 2, 4
Out 0, 1 4, 8

On the contrary, if the wife chooses first, she’ll decide to go out. Then,the husband will accept and go out (4 instead of 2).

WIFE
In Out
HUSBAND In 10, 5 2, 4
Out 0, 1 4, 8

This ‘battle of the sexes‘ has two Nash equilibria: (in,in) and (out,out). A Nash equilibrium is a combination of strategies,one for each player, with the property that no player would unilaterally want to change her strategy given that the other players play their Nash equilibrium strategies. This example shows two Nash equilibria which prove that,only when both players choose the same strategy,it is in neither’s interest to switch strategies.

But, do you want to know how the story ends? They went out as women always choose first.

Antonio González

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