Part 2 1. Pass or shoot. In an ice hockey fast break, two forwards are involved. The first forward has the puck and can either pass or shoot on the goal. If he passes, the second forward can either shoot on the goal or pass back. In the latter case the first forward has to shoot. The first forward can be either experienced player or a new one. The second forward does not know the first forward's type but believes that the first forward is experienced with probability p. The payoff of the shooter is the scoring probability, and the payoff of the (last) passer is 70% of that. (This means that if the first forward decides to shoot without passing the payoff of the second forward is 0). The new forward will never shoot right away. If the experienced forward shoots right away, the probability of scoring is p1. If he shoots after passing and getting it back, he scores with probability p12. If the new first forward shoots after getting the puck back, he scores with probability q1. If the second forward shoots, he scores with probability p2. a) Suppose P12 = 0.7, pil = 0.5, p2 = 0.4, q1 = 0.3. Does a separating PBE exist under these conditions? b) Suppose p12 = 0.7, p11 = 0.5, p2 = 0.2, q1 = 0.3. Does a separating PBE exist? c) Suppose it is known that P12 > Pli > q1 > p2 > 0. Find the condition (an inequality or several inequalities) of existence of a separating PBE