12.8. Abu, Ben, and Cali can go to a bal (f) their decisions independently. If all three go, the bar is perceived to be overcrowded and they get 1 , if one silly alone and gets a payoff of 0 , while the other two get a payoff of 1 ; if all stay at home, they get a payoff of 1. (Note that this is a symmetric game.) (a) Find all pure strategy Nash equilibria in this game. (b) Find an asymmetric mixed strategy Nash equilibrium where one person always stays at home, and the other two randomize, choosing to go to the bar with probability p. (c) Is there an asymmetric mixed strategy Nash equilibrium where one person always goes, and the other two randomize, choosing to go to the bar with probability q ? Explain. (d) Is there a symmetric mixed strategy Nash equilibrium where each player goes to the bar with probability r ? Explain. e) Draw the extensive form game where Abu moves first, followed by Ben (who sees Abu's choice and then moves), and then Cali (who sees the choices of both Abu and Ben before moving). What is a pure strategy SPNE? Is it unique