Question: Mike Caruso, the three-time national wrestling champion from Lehigh University, had two great take-down moves: a quick single leg and his legendary barrel roll. (By the way, Mike wrestled in 1967 when Michigan State won the NCAA team championship.) His opponent could better defend the barrel roll with a more upright stance. The better option against the single leg was a more crouched stance. Of course, in wrestling everything happens so fast that you can think of it as a simultaneous game. The probability of a take-down for Mike is given in the table

                                           Defender

Mike Caruso            Stand upright              Crouch

Single leg                      0.8                        0.4

Barrel roll                       0.2                        0.6

a. Is there a Nash equilibrium in pure strategies? Explain briefly.

b. Determine the optimal mixing probability for Mike. Please show your calculation equation.

c. If Mike mixes as you suggest in part b., what is the probability that he makes the take-down?