6. Two players play a thug game where the sender S of an insult is matched with a receiver R. There is a _ chance that S would be Surly and ; chance that she would be Weak. The R. player cannot observe types, but can only see what S had for breakfast: Beer or Quiche. After seeing what S had for breakfast, R could confront/ defy her (D) or flee (F). The game tree is shown below: N Weak Surly Beer Quiche Beer Quiche D F D D D F 20, 125 100, 75 120, 125 200, 75 120, 75 200, 125 20, 75 100, 125 (a) Write the payoff matrix. How many strategies does each player have? (b) What are the PBE in this game? (c) Use refinements to rule out some weird equilibria. (d) Suppose that the payoffs for S changed so that the 200 payoff now are 140 and the 120 are now 60. Draw the game tree and answer questions (a)-(c) above