# ML Wiki

## Cooperation Games

Unlike Pure Competition Games where players have opposite interests, here players have the same interests

• $\forall a \in A, \forall i, j: u_i(a) = u_j(a)$

## Coordination Game

Which side of the road you drive on?

• suppose two players meet at a passage
• they want to get through
• both need to choose either to go left or right
• win-win situation only when they both pick the same side
• otherwise both lose
Left Right
Left (1, 1) (0, 0)
Right (0, 0) (1, 1)

## Battle of the Sexes

This is not only a cooperation game, but also a Pure Competition Game

Description:

• 2 players - a husband and a wife
• 2 options - ballet and football
• they want to go together
• but Husband prefers to go to football, and wife wants to see the ballet
wife $\to$
husband $\downarrow$
$B$ $F$
$B$ (2, 1) (0, 0)
$F$ (0, 0) (1, 2)

There are two Nash Equilibria:

• $(B, B)$ and $(F, F)$
• in both these cases nobody wants to deviate as they would get worse payoff
• consider $(B, F)$ - in this case both want to deviate

## Sources

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