3. You are one of n players sharing a house. At 3 am the house dog barks outside wanting to be let in. You can choose to get up or ignore the barking. Your payoffs are as follows:

Your strategy All others ignore At least one other player gets up

Get up 8 6

Ignore 4 11

(a) Is there a pure strategy equilibrium? If so, find it and show it is an equilibrium

(b) Is there a mixed strategy equilibrium with each player choosing get up and ignore with positive probabilities? Find it, if there is one.