Two teenagers, Iain and Kay decide to play Chicken. They approach each other in sports cars from opposite directions at high speed. At the point where they are very close they must simultaneously choose between playing tough, T or Chicken, C. If they both play C they get a payoff of 50 each. If lain chooses C and Kay chooses T then lain loses self-esteem and gets a payoff of 30 while Kay feels like a hard woman and gets a payoff of 100. If Kay chooses C and Iain chooses T then Kay loses self- esteem and gets a payoff of 10 while lain feels like a hard man and gets a payoff of 70. (Note, the game is not symmetric). If they both play T however, they both die and get a payoff of zero. All these payoffs are common knowledge. Assume lain uses the mixed strategy (1,1 - 1) and Kay uses the mixed strategy (K,1 - K) where the first number is the probability of playing T. 

(a) What is lain's optimal response to K = 0? What is his optimal response to K = 1? Plot his optimal response to all values of K between 0 and 1. On the same diagram plot Kay's optimal response to all values of I between 0 and 1. 

(b) What are the equilibria of this game? 

(c) What prediction would you make about the outcome of this game?