Question 3 (40 points) Two people are involved in a dispute. P2 (Column player) does not know whether P1 (row player) is strong (Type S) or weak (Type W). P1 assigns a probability & to P2 being strong. P2 is fully informed about his own type. Each person can either Fight (F), Yield (Y) or Negotiate (N). The payoffs are de- scribed by the matrices below. P2 F YN FYN Type S F 3-1 3,0 2,1 Type W F 1,3 3,0 0,1 Y 0,3 0,0 0,1 Y 0,3 0,0 1,1 N1,3 1,0 2,1 N 1,3 1,0 1,1 P1 is Type S with prbx P1 is Type W with prb 1-a P2 a) (15 points) For what values of a, if any, is there a Pooling Bayesian Equilibrium in which Type W plays N and Type S both plays N (Negotiate)? If it exists, what does P2 do in this equilibrium? P2 F Y N FYN Type S F 3-1 3,0 2,1 Type W F 1,3 3,0 0,1 Y 0,3 0,0 0,1 Y 0,3 0,0 1,1 N 1,3 1,0 2,1 N 1,3 1,0 1,1 1 l Type S with prb Plis Type W with prb 1 P2 Question 3 (40 points) Two people are involved in a dispute. P2 (Column player) does not know whether P1 (row player) is strong (Type S) or weak (Type W). P1 assigns a probability & to P2 being strong. P2 is fully informed about his own type. Each person can either Fight (F), Yield (Y) or Negotiate (N). The payoffs are de- scribed by the matrices below. P2 F YN FYN Type S F 3-1 3,0 2,1 Type W F 1,3 3,0 0,1 Y 0,3 0,0 0,1 Y 0,3 0,0 1,1 N1,3 1,0 2,1 N 1,3 1,0 1,1 P1 is Type S with prbx P1 is Type W with prb 1-a P2 a) (15 points) For what values of a, if any, is there a Pooling Bayesian Equilibrium in which Type W plays N and Type S both plays N (Negotiate)? If it exists, what does P2 do in this equilibrium? P2 F Y N FYN Type S F 3-1 3,0 2,1 Type W F 1,3 3,0 0,1 Y 0,3 0,0 0,1 Y 0,3 0,0 1,1 N 1,3 1,0 2,1 N 1,3 1,0 1,1 1 l Type S with prb Plis Type W with prb 1 P2