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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