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